Filtered Back Projection

The Filtered Back Projection (FBP) algorithm has been the standard algorithm for image reconstruction
in computed tomography (CT) for many years, but it creates possible streak artifacts
and a notable increase in image noise when radiation dose is reduced exceedingly. With
technological advancement and increased computational capacities in workstations, iterative
reconstruction (IR) algorithms have re-emerged as a potential alternative. The purpose of this
review is to establish if there is a general consensus that IR algorithms faithfully reduce radiation
dose and improve image quality in CT in comparison with the FBP algorithm. A systematic
review of the literature from 2012 to 2015 was conducted using Ovid MEDLINE and PubMed
databases, as well as various well-known journals such as the American Journal of Roentgenology,
European Journal of Radiology, Physica Medica and the Korean Journal of Radiology.
A total of 57 articles were categorized as either synopsis articles or performance evaluation
clinical studies, where the latter was further divided into 6 sub-categories according to the type
of IR algorithm examined. The results show that the use of IR algorithms reduces objective
image noise, and at least preserves spatial resolution and low contrast detectability, even when
dose is reduced. The findings are also applicable to specific patient groups, such as pediatrics
and obese patients. In conclusion, there is a general consensus that IR algorithms can faithfully
reduce radiation dose and improve image quality in CT in comparison with the FBP algorithm.

A new, low cost, device based on a first generation CT-scanner has been developed. The instrument exploits the high performance of radiographic films in terms of spatial resolution and image definition and is able to produce tomographic images of small objects (10 Â 10 cm). It can be used at different energies and it is a useful instrument for examining a large amount of different samples. The entire system is composed of an X-ray tube, a rotating table, a scanner, a simple system for radiographic film translation and software based on a Filtered Back Projection algorithm for the image reconstruction.

We analyzed breast percent density (PD) estimated from 35 women with existing or recently detected abnormalities. Analyzed were digital mammograms (DM) and the central digital breast tomosynthesis (DBT) reconstructed slices. PD was estimated from the breast contralateral to cancer. We have examined the effect of modifying the DBT reconstruction filter on the accuracy of dense tissue segmentation; we selected the filter that effectively reduced image intensity overshoot near the breast edge, which interfered with segmentation. The Pearson correlation coefficient between PD estimates from DM and the central reconstructed DBT slices was r = 0.90. The corresponding quadratic-weighted kappa coefficient was κ = 0.78, indicating substantial agreement. The observed results are comparable with the agreement between PD estimates from DM and the central DBT projection images (r = 0.89 and κ = 0.74). This suggests that PD is robust to variations in acquisition conditions.

Various fitness functions have been evaluated for image reconstruction using Binary Genetic Algorithm (BGA) based parallel ray transmission tomography. The population initialization is carried out using the Filtered Back-Projection (FBP) technique. Various fitness functions used for image reconstruction include: Root Mean Squared error (RMSE), Mean Squared error (MSE), Mean Absolute error (MAE), Relative Squared error (RSE), Root Relative Squared error (RRSE) and Relative Absolute error (RAE). RMSE and MAE outperformed for small as well as large size images with different shape complexities. Mixed selection scheme with two variations of crossover operators, namely Image-Row and Block crossover operators have been used for crossover. Binary mutation operator has been used for creating diversity in local search scope. For 64 × 64 head and lung phantoms, BGA has resulted in PSNR values with RMSE 19.26 and 16.49 respectively and 27.20 and 29.65 dB with MAE.

IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 44, NO. 3, JUNE 1997 ... Evaluation of 3D Reconstruction Algorithms for a Small Animal PET Camera ... CA Johnson', Member, IEEE, J. Seide12, RE Carson3, Member, IEEE, WR Gandler', Senior Member, IEEE, A. ...

Despite major advances in x-ray sources, detector arrays, gantry mechanical design and especially computer performance, one component of computed tomography (CT) scanners has remained virtually constant for the past 25 years-the reconstruction algorithm. Fundamental advances have been made in the solution of inverse problems, especially tomographic reconstruction, but these works have not been translated into clinical and related practice. The reasons are not obvious and seldom discussed. This review seeks to examine the reasons for this discrepancy and provides recommendations on how it can be resolved. We take the example of field of compressive sensing (CS), summarizing this new area of research from the eyes of practical medical physicists and explaining the disconnection between theoretical and application-oriented research. Using a few issues specific to CT, which engineers have addressed in very specific ways, we try to distill the mathematical problem underlying each of these issues with the hope of demonstrating that there are interesting mathematical problems of general importance that can result from in depth analysis of specific issues. We then sketch some unconventional CT-imaging designs that have the potential to impact on CT applications, if the link between applied mathematicians and engineers/ physicists were stronger. Finally, we close with some observations on how the link could be strengthened. There is, we believe, an important opportunity to rapidly improve the performance of CT and related tomographic imaging techniques by addressing these issues.

Positron Emission Tomography (PET), Computed Tomography (CT), PET/CT and Single Photon Emission Tomography (SPECT) are non-invasive imaging tools used for creating two dimensional (2D) cross section images of three dimensional (3D) objects. PET and SPECT have the potential of providing functional or biochemical information by measuring distribution and kinetics of radiolabelled molecules, whereas CT visualizes X-ray density in tissues in the body. PET/CT provides fused images representing both functional and anatomical information with better precision in localization than PET alone. Images generated by these types of techniques are generally noisy, thereby impairing the imaging potential and affecting the precision in quantitative values derived from the images. It is crucial to explore and understand the properties of noise in these imaging techniques. Here we used autocorrelation function (ACF) specifically to describe noise correlation and its non-isotropic behaviour in experime...

Background: Low peak kilovoltage (kV p) computed tomography (CT) may be used to reduce contrast medium doses in patients at risk of contrast medium-induced acute kidney injury if image noise can be controlled by increasing X-ray tube loading (mAs). Purpose: To evaluate objective and subjective image quality in 80-kV p CT with reduced contrast medium dose and compensated mAs for unchanged image noise in patients with estimated glomerular filtration rate <45 mL/min compared with the standard 120-kV p protocol. Material and Methods: 80-kV p CTwith 300 mg I/kg in 40 patients (body mass index 18-32 kg/m 2 , glomerular filtration rate <45 mL/min) and 120-kV p CT with 500 mg I/kg in 40 patients (body mass index ¼ 17-30 kg/m 2 , glomerular filtration rate !45 mL/min) was compared on mean hepatic attenuation, image noise, contrast medium enhancement, signalto-noise ratio, contrast-to-noise ratio, effective radiation dose, and subjective image quality. Results: There were no significant differences regarding median hepatic post-contrast attenuation, image noise, contrast medium enhancement, signal-to-noise ratio, contrast-to-noise ratio, or effective dose between the 80-kV p and 120-kV p cohorts: 114/110 HU; 14/14 HU; 57/53 HU; 8.0/7.4; 3.8/3.5; and 5.3/5.9 mSv, respectively. However, subjective image visual grading showed statistically significantly inferior scores for 80 kV p for six of eight items. After exclusion of seven inferior examinations not caused by the chosen kV p technique, only three items showed inferior scores for 80 kV p. Only 5% of gradings regarding overall image quality were <3 of 5 points. Conclusion: Despite lower subjective image quality, objective data indicate that 80-kV p CT with reduced contrast medium doses and compensated mAs may have the potential to provide satisfactory diagnostic quality in patients with body mass index <30 kg/m 2 , which could benefit patients at risk of contrast medium-induced acute kidney injury.

In this paper the use of the Filtered Back Projection (FBP) Algorithm, in order to reconstruct tomographic images using the high energy (200-250 MeV) proton beams, is investigated. The algorithm has been studied in detail with a Monte Carlo approach and image quality has been analysed and compared with the total absorbed dose. A proton Computed Tomography (pCT) apparatus, developed by our group, has been fully simulated to exploit the power of the Geant4 Monte Carlo toolkit. From the simulation of the apparatus, a set of tomographic images of a test phantom has been reconstructed using the FBP at different absorbed dose values. The images have been evaluated in terms of homogeneity, noise, contrast, spatial and density resolution.

Computed tomography (CT) has been extensively studied and widely used for a variety of medical applications. The reconstruction of 3D images from a projection series is an important aspect of the modality. Reconstruction by filtered backprojection (FBP) is used by most manufacturers because of speed, ease of implementation, and relatively few parameters. Iterative reconstruction methods have a significant potential to provide superior performance with incomplete or noisy data, or with less than ideal geometries, such as cone-beam systems. However, iterative methods have a high computational cost, and regularization is usually required to reduce the effects of noise. The simultaneous algebraic reconstruction technique (SART) is studied in this paper, where the Feldkamp method (FDK) for filtered back projection is used as an initialization for iterative SART. Additionally, graphics hardware is utilized to increase the speed of SART implementation. Nvidia processors and compute unified device architecture (CUDA) form the platform for GPU computation. Total variation (TV) minimization is applied for the regularization of SART results. Preliminary results of SART on 3-D Shepp-Logan phantom using using TV regularization and GPU computation are presented in this paper. Potential improvements of the proposed framework are also discussed.

OBJECTIVE. The objective of our study was to compare the performance of three hybrid iterative reconstruction techniques (IRTs) (ASiR, iDose4, SAFIRE) and their respective strengths for image noise reduction on low-dose CT examinations using filtered back projection (FBP) as the standard reference. Also, we compared the performance of these three hybrid IRTs with two model-based IRTs (Veo and IMR) for image noise reduction on low-dose examinations. MATERIALS AND METHODS. An anthropomorphic abdomen phantom was scanned at 100 and 120 kVp and different tube current-exposure time products (25-100 mAs) on three CT systems (for ASiR and Veo, Discovery CT750 HD; for iDose4 and IMR, Brilliance iCT; and for SAFIRE, Somatom Definition Flash). Images were reconstructed using FBP and using IRTs at various strengths. Nine noise measurements (mean ROI size, 423 mm(2)) on extracolonic fat for the different strengths of IRTs were recorded and compared with FBP using ANOVA. Radiation dose, which was...

Thermoacoustic signals are generated over a large field of view by 900 ns TE 10 pulses with 108 MHz carrier frequency. Test specimens selectively absorb the TE 10 pulse energy producing rapid thermal expansions that generate ultrasonic pulses. 108 MHz irradiation provides excellent depth penetration in soft tissue, allowing blood and physiologic saline to generate strong signals. Thermoacoustic signal generation from a depth of several cm is well above our system's noise floor. Rotating the test specimen provides single-slice tomographic signal encoding. Filtered backprojection reconstruction yields images over a 6.4 cm field of view. Reconstructions of tissue mimicking prostate phantoms and fresh porcine kidney tissue are presented.

Purpose Reconstruction of DaTSCAN brain studies using OS-EM iterative reconstruction offers better image quality and more accurate quantification than filtered back-projection. However, reconstruction must proceed for a sufficient number of iterations to achieve stable and accurate data. This study assessed the impact of the number of iterations on the image quantification, comparing the results of the iterative reconstruction with filtered back-projection data. Methods A striatal phantom filled with 123 I using striatal to background ratios between 2:1 and 10:1 was imaged on five different gamma camera systems. Data from each system were reconstructed using OS-EM (which included depth-independent resolution recovery) with various combinations of iterations and subsets to achieve up to 200 EMequivalent iterations and with filtered back-projection. Using volume of interest analysis, the relationships between image reconstruction strategy and quantification of striatal uptake were assessed. Results For phantom filling ratios of 5:1 or less, significant convergence of measured ratios occurred close to 100 EMequivalent iterations, whereas for higher filling ratios, measured uptake ratios did not display a convergence pattern. Assessment of the count concentrations used to derive the measured uptake ratio showed that nonconvergence of low background count concentrations caused peaking in higher measured uptake ratios. Compared to filtered back-projection, OS-EM displayed larger uptake ratios because of the resolution recovery applied in the iterative algorithm. Conclusion The number of EM-equivalent iterations used in OS-EM reconstruction influences the quantification of DaTS-CAN studies because of incomplete convergence and possible bias in areas of low activity due to the nonnegativity constraint in OS-EM reconstruction. Nevertheless, OS-EM using 100 EM-equivalent iterations provides the best linear discriminatory measure to quantify the uptake in DaTSCAN studies.

In low-dose X-ray computed tomography (CT), it is necessary to reduce the excessive X-ray quantum noise of the acquired data. This is the case especially when the filtered back-projection method is used for image reconstruction from sinogram data. In this study, we compare the conventional radial filtering direction of the sinogram to the recently introduced angular stackgram filtering technique. Our experimental tests were performed on simulated lowdose CT data. We modelled the X-ray quantum noise using a Gaussian distribution with a signal dependent variance for numerical phantoms simulating stop-and-shoot CT acquisitions. The noise model has been reported elsewhere. This experimentally verified model describes calibrated projection data, i.e. the acquired data after CT system calibration (including logarithmic transform, beam hardening, etc.). For our quantitative tests, we employed both linear Gaussian low-pass filters and non-linear L-filters with Gaussian weights. The stackgram technique provides the best resolution-noise trade-off in comparison with the radial sinogram filtering method, and thus a potential filtering approach to low-dose CT sinograms.

Various types of cancer remain the second leading cause of death in the world. As a consequence, the detection of these tumors has a vital importance. Optoacoustic imaging (OA), a novel imaging technique, offers high contrast and resolution to detect them by ...

By means of a home made X-ray dual-energy computer tomography (CT) provided with a double set of X-ray detector arrays separated by a copper foil and by using a proper variant of filtered back projections reconstruction algorithm together with a set of well calibrated standard samples we have been able to determine with a precision varying between 3.5 % and 2 % the density as well as the effective atomic number distribution in any section of a great diversity of samples. In this way it was possible to discriminate different domestic materials that on a normal radiography generate the same signature such as soap, paper, leather, tooth past, the content of spray tubes, etc. The same CT has been use to investigate different geologic samples consisting of sediment cores collected at depth up to 600 m from the continental platform of the Black Sea and fragments of metamorphic rocks collected from the Sibischel shear zone from the Central Carpathian mountains. In the case of deep sea cores we have evidenced about 225 distinct laminae, 2 to 4 mm thick that by means of time series analysis revealed a periodicity of about 7 years, while in the case of metamorphic rocks we have observed diverse features such as garnet size and distribution, shear zones, mica laminations, etc. Numerical values of both density and especially effective atomic numbers allowed distinguishing between natural silicates and calcium carbonates, irrespective of the host rock.

The use of paired, opposing position-sensitive phototube scintillation cameras (SCs) operating in coincidence for small animal imaging with positron emitters is currently under study. Because of the low sensitivity of the system even in 3D mode and the need to produce images with high resolution, it was postulated that a 3D expectation maximization (EM) reconstruction algorithm might be well suited for this application. We investigated six reconstruction algorithms for the 3D SC PET camera: 2D filtered back-projection (FBP), 3D reprojection (3DRP), 2D EM, 3D EM, 2D ordered subset EM (OSEM), and 3D OSEM. Noise was assessed for all slices by the coefficient of variation in a simulated uniform cylinder. Resolution was assessed from a simulation of 15 point sources in the warm background of the uniform cylinder. At comparable noise levels, the resolution achieved with EM and OSEM (0.9-mm to 1.2-mm) is significantly better than that obtained with FBP or 3DRP (1.5-mm to 2.0-mm.) Images of a rat skull labeled with 18 F-fluoride suggest that 3D EM and 3D OSEM can improve image quality of a small animal PET camera.

Filtered Back-Projection (FBP) has become an outdated image reconstruction technique in new-generation positron emission tomography (PET)/computed tomography (CT) scanners� Iterative reconstruction used in all new-generation PET scanners is a much improved reconstruction technique� Though a well-calibrated PET system can only be used for clinical imaging in few situations like ours, when compromised PET scanner with one PET module bypassed was used for PET acquisition, FBP with sinogram correction proved to be a better reconstruction technique to minimize streak artifact present in the image reconstructed by the iterative technique�

Segmentation of the body edge in tomographic images with low count, noisy edges is needed for both PET and SPECT respiratory motion correction and brain SPECT attenuation correction. To reduce noise we re-projected tomographic images and searched for edges in the projection count profiles or their spatial derivatives. Edge location versus projection angle was fitted with cosine basis functions after rejecting outliers and including information about edges of previous sections. We processed 10 s duration FDG PET of the thorax, HMPAO brain, DAT brain and lung perfusion SPECT. Stable edges for all four types of scan were achieved but with different profiles. Edges were validated against edges of coregistered CT or MRI. The best root mean square (rms) accuracy was 8.2 mm (PET) and 5.2 mm (brain SPECT). Inter-scan variability (standard deviation) in the estimated-to-control edge distance for 17 PET scans was 0.4 mm, for 25 ordered subset expectation maximisation (OSEM) reconstructed brain SPECT 1.0 mm and for 18 filtered back-projection (FBP) reconstructed brain SPECT 1.4 mm.

The ultrasonic computed tomography (UCT) as a coupling of the ultrasonic transmission method and the image reconstruction technique based on the iterative ÿltered back-projection was applied to investigate the cross-sectional distributions of gas and particle holdups in a slurry bubble column. The dispersion system of air-water-TiO 2 was used in this study. The loading of the titanium dioxide particle has a ected on the increase of the gas holdup. The UCT was used to analyze the macroscopic ow scheme of the system under various operating conditions. Based on the experimental results and the observation during the experiments, the macroscopic bubble ow scheme may be considered to be a helical rising ow.

A very high resolution small animal positron emission tomograph (PET) which can achieve submillimeter spatial resolution is being developed using silicon pad detectors. The prototype PET for a single slice instrument consists of two 1 mm thick silicon pad detectors, each containing a 32 × 16 array of 1.4 mm × 1.4 mm pads read out with four VATAGP3 chips which have 128 channels lownoise self triggering ASIC in each chip, coincidence units, a source turntable and tungsten slice collimator. The silicon detectors were located edgewise on opposite sides of a 4 cm field-of-view to maximize efficiency. Energy resolution is dominated by electronic noise, which is 0.98% (1.38 keV) FWHM at 140.5 keV. Coincidence timing resolution is 82.1 ns FWHM and coincidence efficiency was measured to be 1.04 × 10-3 % from two silicon detectors with annihilation photons of 18 F source Image data were acquired and reconstructed using conventional 2-D filtered-back projection (FBP) and a maximum likelihood expectation maximization (ML-EM) method. Image resolution of approximately 1.45 mm FWHM is obtained from 1-D profile of 1.1 mm diameter 18 F line source image. Even better resolution can be obtained with smaller detector element sizes. While many challenges remain in scaling up the instrument to useful efficiency including densely packed detectors and significantly improved timing resolution, performance of the test setup in terms of easily achieving submillimeter resolution is compelling.

Purpose: To compare the image quality and radiation dose between iterative reconstruction (IR) and standard filtered back projection (FBP) in CT of the chest and abdomen. Materials and Methods: Thoracic CT was performed in 50 patients (38 male, 12 female; mean age, 51 ± 23 yrs; range, 7-85 yrs) and abdominal CT was performed in 50 patients (36 male, 14 female; mean age, 62 ± 13 yrs; range, 20-85 yrs), using IR as well as FBP for image reconstruction. Image noise was quantitatively assessed measuring standard deviation of Hounsfield Units (HU) in defined regions of interest in subcutaneous tissue. Scan length and Computed Tomography Dose Index (CTDI) were documented. Scan length, image noise, and CTDI of both reconstruction techniques were compared by using paired tests according to the nature of variables (McNemar test or Student t test). Overall subjective image quality and subjective image noise were compared. Results: There was no significant difference between the protocols in terms of mean scan length (p>0.05). Image noise was statistically significantly higher with IR,

When excessive quantum noise is present in extremely low dose X-ray CT imaging, statistical properties of the data has to be considered to achieve a satisfactory image reconstruction. Statistical iterative reconstruction with accurate modeling of the noise, rather than a filtered back-projection (FBP) with low-pass filtering, is one way to deal with the problem. Estimating a noise-free sinogram to satisfy the FBP reconstruction for the Radon transform is another way. The benefits of the latter include a higher computation efficiency, more uniform spatial resolution in the reconstructed image, and less modification of the current machine configurations. In a clinic X-ray CT system, the acquired raw data must be calibrated, in addition to the logarithmic transform, to achieve the high diagnostic image quality. The calibrated projection data or sinogram no longer follow a compound Poisson distribution in general, but are close to a Gaussian distribution with signal-dependent variance. In this paper, we first investigated a relatively accurate statistical model for the sinogram data, based on several phantom experiments. Then we developed a penalized likelihood method to smooth the sinogram, which led to a set of nonlinear equations that can be solved by iterated conditional mode (ICM) algorithm within a reasonable computing time. The method was applied to several experimental datasets acquired at 120 kVp, 10 mA/20 mA/50 mA protocols with a GE HiSpeed multi-slice detector CT scanner and demonstrated a significant noise suppression without noticeable sacrifice of the spatial resolution. Index Terms-Iterated conditional mode, low dose, penalized weighted least square, sinogram smoothing, X-ray computed tomography (CT). I. INTRODUCTION T HE X-RAY exposure to patients has been a major concern since the introduction of computed tomography (CT) in the 1970s. It now represents the largest single source of radiation exposure because of its rapidly increasing use. Minimizing Manuscript

The Radon transform (RT) on straight lines deals as mathematical foundation for many tomographic modalities (e.g. Xray scanner, Positron Emission Tomography), using only primary radiation. In this paper, we consider a new RT defined on a pair of half-lines forming a letter V, arising from the modeling a two-dimensional emission imaging process by Compton scattered gamma rays. We establish its

In this paper, a filtered adjoint inversion scheme for turntable inverse synthetic aperture radar (ISAR) data is derived for three spatial dimensions from a scalar wave equation model. The proposed data inversion scheme motivates the use of filtered back projection (FBP) and convolution back projection (CBP) imaging algorithms. This paper also provides a derivation of a general imaging filter needed for accurate near-field FBP and CBP imaging algorithms, which will be shown to reduce to familiar results found in SWISAR (Spherical-Wave ISAR) imaging.

In this study, our goal is to employ a novel 3-D alignment method for dynamic positron emission tomography (PET) scans. Because the acquired data (i.e. sinograms) often contain noise considerably, filtering of the data prior to the alignment presumably improves the final results. In this study, we utilized a novel 3-D stackgram domain approach. In the stackgram domain, the signals along the sinusoidal trajectory signals of the sinogram can be processed separately. In this work, we performed angular stackgram domain filtering by employing well known 1-D filters: the Gaussian low-pass filter and the median filter. In addition, we employed two wavelet de-noising techniques. After filtering we performed alignment of objects in the stackgram domain. The local alignment technique we used is based on similarity comparisons between locus vectors (i.e. the signals along the sinusoidal trajectories of the sinogram) in a 3-D neighborhood of sequences of the stackgrams. Aligned stackgrams can be transformed back to sinograms (Method 1), or alternatively directly to filtered back-projected images (Method 2). In order to evaluate the alignment process, simulated data with different kinds of additive noises were used. The results indicated that the filtering prior to the alignment can be important concerning the accuracy.

Sejak diperkenalkannya tomografi pada tahun 1917, tomografi menjadi lingkup studi penting yang menggabungkan matematika murni dengan terapan. Dengan tomografi kita dapat melihat irisan penampang melintang suatu objek tanpa harus merusak objek tersebut. Terdapat beberapa metode untuk rekonstruksi citra tomografi saat ini, salah satunya adalah metode FBP (filtered back-projection). FBP dianggap sebagai metode rekonstruksi yang cepat dan akurat dalam beberapa dekade belakangan ini. Tugas akhir ini membahas simulasi metode FBP untuk merekontruksi suatu citra irisan dari benda uji dan menganalisis filter-filter yang digunakan dalam metode FBP agar dapat menghasilkan citra rekonstruksi yang baik. Filter yang digunakan dalam simulasi metode FBP pada tugas akhir ini adalah filter Ram-Lak, filter Shepp-Logan, filter Cosine, filter Hamming, filter Hann, dan filter Blackman. Penggunaan filter ini sangat mempengaruhi kualitas dari citra hasil rekonstruksi yang dihasilkan. Dengan menggunakan filter, citra yang dihasilkan menjadi tidak blur karena filter-filter yang digunakan merupakan high-pass filter atau modifikasi dari high-pass filter. Dilakukan beberapa analisis terhadap citra hasil yang dihasilkan oleh masing-masing filter. Analisis yang dilakukan antara lain analisis dengan menggunakan SNR (Signal to noise ratio), persebaran frekuensi, dan perbandingan sinyal sebelum dan setelah dilakukan filtering. Berdasarkan analisis-analisis tersebut dapat disimpulkan bahwa filter Blackman menghasilkan citra rekonstruksi yang paling baik dengan SNR 75,4768 dB.

A novel time-domain spectroscopic EPR imaging approach, that is a unique combination of already known techniques, is described. The first one is multi-gradient Single Point Imaging involving pure phase-encoding where the oximetry is based on T Ã 2. Line width derived from T Ã 2 is subject to susceptibility effects and therefore needs system-dependent line width calibrations. The second approach utilizes the conventional 90°-s-180°Spin-Echo pulse sequence where the images are obtained by the filtered backprojection after FT of the echoes collected under frequency-encoding gradients. The spatially resolved oximetry information is derived from a set of T 2-weighted images. The back-projection images suffer susceptibility artifacts with resolution determined by T Ã 2 , but the oximetry based on T 2 is quite reliable. The current approach combines Single Point Imaging and the Spin-Echo procedure to take advantage the enhanced spatial resolution associated with the former and the T 2 dependent contrast of the latter. Pairs of images are derived choosing two time points located at identical time intervals on either side of the 180°pulse. The refocusing pulse being exactly in the middle of the two points ensures that artifacts associated with susceptibility and field inhomogeneities are eliminated. In addition, the net phase accumulated by the two time points being identical results in identical field of views, thus avoiding the zoomin effect as a function delay in regular SPI and the associated interpolation requirements employed in T Ã 2-weighted oximetry. The end result is superior image resolution and reliable oximetry. In spite of the fact that projection-reconstruction methods require less number of measurements compared to SPI, the enormous advantage in SNR of the SPI procedure makes the echo-based SPI equally efficient in terms of measurement time. The Fourier reconstruction, line width independent resolution and the true T 2-weighting make this novel procedure very attractive for in vivo EPR imaging of tissue oxygen quantitatively.

We analyzed breast percent density (PD) estimated from 35 women with existing or recently detected abnormalities. Analyzed were digital mammograms (DM) and the central digital breast tomosynthesis (DBT) reconstructed slices. PD was estimated from the breast contralateral to cancer. We have examined the effect of modifying the DBT reconstruction filter on the accuracy of dense tissue segmentation; we selected the filter that effectively reduced image intensity overshoot near the breast edge, which interfered with segmentation. The Pearson correlation coefficient between PD estimates from DM and the central reconstructed DBT slices was r = 0.90. The corresponding quadratic-weighted kappa coefficient was κ = 0.78, indicating substantial agreement. The observed results are comparable with the agreement between PD estimates from DM and the central DBT projection images (r = 0.89 and κ = 0.74). This suggests that PD is robust to variations in acquisition conditions.

Abstract Filtered back projection is a popular algorithm for the reconstruction of n -dimensional signals from their ( n -1)-dimensional projections (in the sense of line integrals). Here we specifically treat the problem of the three-dimensional (3D) reconstruction of an object from its two-dimensional (2D) projection images. In this work we analyze the implementation of the filtered back projection method in shared-memory multiprocessor systems. The resulting parallel algorithm turns out to be scalable as the result of the use of large/medium granularity and an adequate allocation ofdata on the processors. A number of experimental results (such as run time, speed-up and efficiency) on a BBN Butterfly are also reported.

Positron Emission Tomography (PET) has gained a tremendous momentum recently for clinical applications notably with the availability of 18 F-fluorodeoxyglucose for staging and evaluation of therapy efficacy in various types of cancers. Nonconventional positron emitting nuclides are now being investigated for the development of novel imaging and therapeutic strategies. However, these nuclides have less than ideal imaging properties. This article compares the performance for imaging of nonconventional nuclides such as 61 Cu, 68 Ga, 86 Y and 94m Tc with the standard imaging nuclide 18 F for high-resolution small animal PET imaging. Quantitative imaging performance was evaluated in terms of spatial resolution and hot spheres recovery coefficients from image resolution and image quality phantoms representing the mouse. The data were reconstructed using algorithms of 2D filtered-back-projection, 2D ordered-subsets expectation maximization and maximum-aposteriori. It is shown that the spatial resolution point spread function can be well explained by a double-gaussian function due to the generally long range of the positron. We show that, with the knowledge of the measured point spread functions, the accurate activity concentration in small lesions can be recovered when imaging with long-range positron emitters.

A novel time-domain spectroscopic EPR imaging approach, that is a unique combination of already known techniques, is described. The first one is multi-gradient Single Point Imaging involving pure phase-encoding where the oximetry is based on T Ã 2. Line width derived from T Ã 2 is subject to susceptibility effects and therefore needs system-dependent line width calibrations. The second approach utilizes the conventional 90°-s-180°Spin-Echo pulse sequence where the images are obtained by the filtered backprojection after FT of the echoes collected under frequency-encoding gradients. The spatially resolved oximetry information is derived from a set of T 2-weighted images. The back-projection images suffer susceptibility artifacts with resolution determined by T Ã 2 , but the oximetry based on T 2 is quite reliable. The current approach combines Single Point Imaging and the Spin-Echo procedure to take advantage the enhanced spatial resolution associated with the former and the T 2 dependent contrast of the latter. Pairs of images are derived choosing two time points located at identical time intervals on either side of the 180°pulse. The refocusing pulse being exactly in the middle of the two points ensures that artifacts associated with susceptibility and field inhomogeneities are eliminated. In addition, the net phase accumulated by the two time points being identical results in identical field of views, thus avoiding the zoomin effect as a function delay in regular SPI and the associated interpolation requirements employed in T Ã 2-weighted oximetry. The end result is superior image resolution and reliable oximetry. In spite of the fact that projection-reconstruction methods require less number of measurements compared to SPI, the enormous advantage in SNR of the SPI procedure makes the echo-based SPI equally efficient in terms of measurement time. The Fourier reconstruction, line width independent resolution and the true T 2-weighting make this novel procedure very attractive for in vivo EPR imaging of tissue oxygen quantitatively.

The aim of this study was to evaluate the effect of ordered-subset expectation maximization reconstruction algorithm with scatter correction and attenuation correction based on computed tomography maps and to find out the optimum number of subsets and iterations upon image quality for 123I-DaTSCAN neuroimaging. We retrospectively studied SPECT/CT scans of 44 consecutive patients with clinical indications of Parkinson&amp;amp;amp;amp;amp;#39;s disease. Images

A dedicated breast PET/CT system has been constructed at our institution, with the goal of having increased spatial resolution and sensitivity compared to whole-body systems. The purpose of this work is to describe the design and the performance characteristics of the PET component of this device. Average spatial resolution of a line source in warm background using maximum a posteriori (MAP) reconstruction was 2.5 mm, while average spatial resolution of a phantom containing point sources using filtered back projection (FBP) was 3.27 mm. A sensitivity profile was computed with a point source translated across the axial field of view (FOV) and the peak sensitivity of 1.64% was measured at the center of FOV. Average energy resolution determined on a per-crystal basis was 25%. Characteristic dead time for the front-end electronics and data acquisition (DAQ) was determined to be 145 ns and 3.6 µs, respectively. With no activity outside the FOV, a peak noiseequivalent count rate of 18.6 kcps was achieved at 318 µCi (11.766 MBq) in a cylindrical phantom of diameter 75 mm. After the effects of exposing PET detectors to x-ray flux were evaluated and ameliorated, the combined PET/CT scan was performed. The percentage standard deviations of uniformity along axial and transaixal directions were 3.7% and 2.8%, respectively. The impact of the increased reconstructed spatial resolution compared to typical whole-body PET scanners is currently being assessed in a clinical trial.

Use of a normal database in quantitative regional analysis of brain single-photon emission tomography (SPET) facilitates the detection of functional defects in individual or group studies by accounting for intersubject variability. Different reconstruction methods and suboptimal attenuation and scatter correction methods can introduce additional variance that will adversely affect such analysis. Similarly, processing differences across different instruments and/or institutions may invalidate the use of external normal databases. The object of this study was to minimise additional variance by comparing reconstructions of a physical phantom with its numerical template so as to optimise processing parameters. Age-and gender-matched normal scans acquired on two different systems were compared using SPM99 after processing with both standard and optimised parameters. For three SPET systems we have optimised parameters for attenuation correction, lower window scatter subtraction, reconstructed pixel size and fanbeam focal length for both filtered back-projection (FBP) and iterative (OSEM) reconstruction. Both attenuation and scatter correction improved accuracy for all systems. For single-iteration Chang attenuation correction the optimum attenuation coefficient (mu) was 0.45-0.85 of the narrow beam value (Nmu) before, and 0.75-0.85 Nmu after, scatter subtraction. For accurately modelled OSEM attenuation correction, optimum mu was 0.6-0.9 Nmu before and 0.9-1.1 Nmu after scatter subtraction. FBP appeared to change in-plane voxel dimensions by about 2% and this was confirmed by line phantom measurements. Improvement in accuracy with scatter subtraction was most marked for the highest spatial resolution system. Optimised processing reduced but did not remove highly significant regional differences between normal databases acquired on two different SPET systems.

A multiresolution approach to 3D reconstruction from an electron microscope (EM) tilt series is presented. It is designed for reconstruction from a tilt series with a limited number of projections where the tilt angles are assumed to be known. Its main feature is that it solves the alignment problem very accurately from the image data without additional gold particles, including

... Volta&amp;amp;amp;amp;quot;, Universita degli Studi di Pavia, via A. Bassi 6, I-27100 Pavia, Italy (Received 9 March 1994) We propose an alternative method for ... (2) In the number representation the change of ... The Gaussian curve with variance equal to the ex-perimental rms error is superimposed. ...

The qualitative equivalence between the Fourier reconstruction (FR) algorithm and the filtered back projection (FBP) algorithm is demonstrated when all the different phase errors that can occur in FR are eliminated. The causes of phase errors are underlined and methods to eliminate them are presented. The practical comparison between FR and FBP has been evaluated on a numerical test image and the results are reported, demonstrating the qualitative equivalence. FR has the advantage of being very computationally efficient. In fact, the time spent to obtain the FR image was 1/20 of that used to obtain the FBP image. Because of the computational efficiency of FR and the good quality of the results obtained, an iterative version of FR has been used to implement the spectral-spatial imaging (SSI) algorithm in the field of electron paramagnetic resonance imaging (EPRI). An experimental example, demonstrating its good performance, is reported.

The impact of iterative reconstruction (IR) on myocardial perfusion imaging (MPI) interpretation and functional results is under investigated. We evaluated the effect of IR on the interpretation and functional results of MPI compared with filtered back-projection (FBP). Material and Methods: Sixty patients with previously acquired MPI were randomly selected. Studies were processed using FBP and 2D ordered-subsets expectation-maximization (OSEM). Two physicians interpreted the images after IR and FBP processing. Results were confirmed by coronary angiography and/or clinical course. Left ventricular ejection fraction (LVEF), end-diastolic volume (EDV) and end-systolic volume (ESV) were calculated with IR and FBP. Results: The sensitivity, specificity, positive and negative predictive values and accuracy of physician 1 were 95%, 87%, 80%, 97%, and 90% with FBP and 100%, 80%, 72%, 100%, and 87% with IR. For physician 2, they were 95%, 95%, 91%, 97%, and 95% with FBP and 81%, 95%, 90%, 90%, and 90% with IR. There were no statistically significant differences between physicians' interpretations (P=0.71 for FBP and 0.09 for IR). There was good correlation between IR and FBP calculated LVEF (r=0.98), EDV (r=0.99), and ESV (r=0.99) but significant difference per patient (P=0.02, 0.03 and 0.02, respectively). Conclusion: There is no statistically significant difference in interpretation of MPI with IR versus FBP but there were statistically significant differences in functional results.

Epidepride labelled with iodine-123 is a suitable probe for the in vivo imaging of striatal and extrastriatal dopamine D2 receptors using single-photon emission tomography (SPET). Recently, this molecule has also been labelled with carbon-11. The goal of this work was to develop a method allowing the in vivo quantification of radioactivity uptake in baboon brain using SPET and to validate it using positron emission tomography (PET). SPET studies were performed in Papio anubis baboons using 123I-epidepride. Emission and transmission measurements were acquired on a dual-headed system with variable head angulation and low-energy ultra-high resolution (LEUHR) collimation. The imaging protocol consisted of one transmission measurement (24 min, heads at 90 degrees), obtained with two sliding line sources of gadolinium-153 prior to injection of 0.21-0.46 GBq of 123I-epidepride, and 12 emission measurements starting 5 min post injection. For scatter correction (SC) we used a dual-window method adapted to 123I. Collimator blurring correction (CBC) was done by deconvolution in Fourier space and attenuation correction (AT) was applied on a preliminary (CBC) filtered back-projection reconstruction using 12 iterations of a preconditioned, regularized minimal residual algorithm. For each reconstruction, a calibration factor was derived from a uniform cylinder filled with a 123I solution of a known radioactivity concentration. Calibration and baboon images were systematically built with the same reconstruction parameters. Uncorrected (UNC) and (AT), (SC + AT) and (SC + CBC + AT) corrected images were compared. PET acquisitions using 0.11-0.44 GBq of 11C-epidepride were performed on the same baboons and used as a reference. The radioactive concentrations expressed in percent of the injected dose per 100 ml (% ID/100 ml) obtained after (SC + CBC + AT) in SPET are in good agreement with those obtained with PET and 11C-epidepride. A method for the in vivo absolute quantitation of 123I-epidepride uptake using SPET has been developed which can be directly applied to other 123I-labelled molecules used in the study of the dopamine system. Further work will consist in using PET to model the radioligand-receptor interactions and to derive a simplified model applicable in SPET.

Recent studies in the field of molecular imaging have demonstrated the need for PET probes capable of imaging very weak activity distributions. Over this range of applications the sensitivity and the energy resolution of a PET system can be critical, as it can possibly affect the minimum amount of activity which can be reliably detected. Clinical PET systems, as opposed to small animal systems, are less sensitive and, therefore, imaging of very low activity sources could be challenging. Moreover the presence of LSO crystal detectors can further raise the minimum detection threshold due to the intrinsic radioactivity of the 176 Lu contained in the LSO compound. Our aim is to examine the feasibility of using an LSO-based clinical PET scanner for imaging activity distributions of 4nCi/mm 3 or less. In this study the parameter of minimum detectable activity (MDA) has been used for the quantification of the detection threshold of a system. A series of acquisitions was simulated using the Monte Carlo simulation software package of GATE. Existing validated GATE models of the clinical Siemens Biograph 6 PET/CT and pre-clinical microPET Focus 220 scanners have been applied to quantify and compare the effect of the LSO background and the energy window on the MDA performance of the systems. Four square regions, each with a unique signal-to-background activity concentration ratio (SBR), were scanned simultaneously. The intrinsic LSO background spectrum and the total energy spectrum, as well as their relative positions and intensities were estimated. The simulated data were histogrammed on various time frames, which were later reconstructed using a filtered back-projection algorithm. Detectability in every image was quantified using a modified Currie equation to associate an MDA value with a specific region and frame length. In the case of Biograph an MDA of 4nCi/mm 3 can be reliably detected for frame lengths longer than 5min and in regions where the SBR was higher than 4. When higher contrast regions are imaged, detection can be achieved even for frame lengths down to 1min. The previous analysis was repeated by using a GATE model of a hypothetical BGO-based clinical PET scanner. The results between the two scanner models were compared with each other as well as with those of a previous MDA study on a preclinical microPET Focus 220 scanner.

A three-dimensional (3D) electron paramagnetic resonance imaging (EPRI) method was developed to probe the structure and size of pores in ceramic materials. The imaging device that was added to the EPR instrument consisted of a computer-controlled current source and magnetic field gradient. This add-on facility was tested using a well-defined diphenylpicrylhydrazyl phantom sample. Pumice was then used to demonstrate the potential of the technique. This stone was immersed in a 0.5 mM "N-substituted perdeutereted tempone water solution to fill the pores with spin labels. Images were reconstructed using a filtered backprojection technique. A two-dimensional (2D) imaging plane was constructed by collecting 33 projection planes over 180". A 3D image was derived from 22 planes each constructed by 22 projections. At present, the facility allows a resolution of 69 and 46 pm for 2D and 3D imaging, respectively. Advancements of the imaging apparatus, software, and line width of the spin labels will be needed to enhance the resolution of this technique. [

Reconstruction of two-dimensional images by filtered back-projection (FBP) and by the maximum entropy method (MEM) was compared for spectral-spatial EPR images with differing signal-to-noise ratios. Experimental projections were recorded using direct-detected rapid scans in the presence of a series of magnetic field gradients. The slow-scan absorption lineshapes were calculated by Fourier deconvolution. A Hamming filter was used in conjunction with FBP, but not for MEM. Imperfections in real experimental data, as well as random noise, contribute to discrepancies between the reconstructed image and experimental projections, which may make it impossible to achieve the customary MEM criterion for convergence. The Cambridge MEM algorithm, with allowance for imperfections in experimental data, produced images with more linear intensity scales and more accurate linewidths for weak signals than was obtained with other MEM methods. The more effective elimination of noise in baseline regions by MEM made it possible to detect weak trityl 13 C trityl hyperfine lines that could not be distinguished from noise in images reconstructed by FBP. Another advantage of MEM is that projections do not need to be equally spaced. FBP has the advantages that computational time is less, the amplitude scale is linear, and there is less noise superimposed on peaks in images. It is useful to reconstruct images by both methods and compare results. Our observations indicate that FBP works well when the number of projections is large enough that the star effect is negligible. When there is a smaller number of projections, projections are unequally spaced, and/or signal-to-noise is lower MEM is advantageous.