Noise reduction for T2 derived magnetic resonance images

C o m p ure rize d Me dic al Imaging Printed in the USA. a nd G ra p hic r. Vo l. 14. No . 3, p p . 185- 190. 1990 Copyright All rights reserved. 0895-61 II190 $3.00 + .oO 0 1990 Pergamon Press plc NOISE REDUCTION FOR T, DERIVED MAGNETIC RESONANCE IMAGES E. Loren Buhle, Jr. ‘,* , Peter Bloch’ and Robert E. Lenkinski2 ‘Department of Radiation Oncology and *Department of Radiology, University of Pennsylvania School of Medicine, 3400 Spruce Street, Philadelphia, PA 19104 (Received 15 Augusr 1989; Revised 8 December 1989) Abstract-Calculation of magnetic resonance images composed of signals arising from T, and proton densities can be performed using a least squares fitting procedure from three or four multiple spin-echo images. This procedure works well in regions of high signal-to-noise (S/N) in the multiple spin-echoes. Erroneous T, values predominate in regions of low S/N, precluding the routine use of T, images in diagnostic and quantitative analysis. This study demonstrates that only three spin-echoes signals (TE = 20, 40, and 60 msec) and a simple preprocessing selection criteria are necessary to significantly reduce erroneous T, values. This simple selection criteria obviates the need to apply a median filter to the T, image and thus preserve both the high inherent contrast and spatial resolution of the T, derived image. Key Words: MRI imaging, T, imaging, Tumor quantitation, Image processing, MRI diagnostics T,. The time required to acquire the necessary imaging data is similar to a T, weighted image. Both the derived T, and proton density images have the potential to contain the spatial resolution of the spin-echo images, typically 0.6 mm X 0.6 mm size pixels. The T, image often contains high tissue contrast in comparison to the proton density image. However, the noise in the T, derived image can often lead to difficulty in both diagnostic interpretation and quantification. This paper discusses the noise in the T, derived image and how this noise can be significantly reduced to make the derived images of diagnostic quality and permit quantification of T, and proton density distributions in the image. INTRODUCTION Proton MR images are dependent on three parameters: proton density and the longitudinal (T,) and transverse (T2) relaxation times. Selective pulse sequences have heen developed to weight one of these parameters over the other in the image. Some of the pulse sequences permit rapid acquisition of the data with high tissue contrast and good spatial resolution. However, the quantification of the magnetic environment within the imaged tissue has proven difficult. Thus despite advances in MR imaging, characterization of tissue histology or pathology in terms of intrinsic MR parameters has not been routinely performed, even in the cases where intrinsic tissue-specific relaxation parameters have provided adequate contrast detail. In an attempt to better understand the tissue hetereogenity within a tumor bed, we are performing a quantitative analysis of the proton density and T, distribution of the voxels in the tumor volume for patients with head and neck disease (1). The MR parameters are obtained within each pixel of the image from an analysis of the amplitudes of multiple spin-echo signals. The T, signal within each pixel is obtained from the slope of the log of the amplitude of multiple spin-echo signals as a function of spin-echo time (TE). The mobile proton density is the intercept at zero time (2). The pulse sequence uses a 90” pulse followed by multiple 180” refocussing pulses within a single pulse repetition cycle, METHODS MR imaging was performed on patients using a 1.5 Tesla GE-Signa whole body scanner. The pulse sequence consisted of a 90” pulse followed by four 180” refocusing pulses with spin-echo times corresponding to 20, 40, 60, and 80 msec. The pulse repetition rate, T,, was 2500 msec. The uniformity in the derived T, values throughout a 20 cc CuSO, phantom of cubic geometry was within 7%, and the long term reproducibility over a two week period was 3%. A least squares regression analysis of the logarithm of the amplitudes of the multiple spin-echo signals was used to compute a 256 X 256 map of a relative T, and proton density distribution (2). Each three dimensional pixel, or voxel, was typically 0.6 x 0.6 x 6.0-10.0 mm thick. The regression analysis yields T, values as the slope and the proton density values as the intercept. A poor fit of the spin-echoes results in large deviations in the T, values *Correspondingauthor. Supported in part by M.L. Smith Charitable Lead Trust #04269-06-J. 18.5 Computerized Medical Imaging and Graphics 186 Fig. 1. Axial section through a tumor in the neck. (a) T, calculated using the first three spin-echoes (TE = 20, 40, and 60 msec). (b) T, calculated using four spin-echoes (T,=20, 40, 60, and 80 msec). Note the increased quantity of artifactual T, values outside the patient volume. (c) T, calculated using the first three echoes, the selection criteria and median filter. (d) Proton density. variations in the proton density values. To minimize the number of pixels with erroneously assigned T, values, the signal from each pixel arising from the different spin-echo images was examined to satisfy the following selection criteria before performing the least squares regression: (a) T, values were calculated only where a significant proton density was present. A suitable proton density threshold was determined in the following manner: The mean, Sp(Air), and standard deviation of the proton signal from the area outside the patient volume was determined. The threshold was set to Sp(Air) plus two standard deviations; (b) the magnitude of the signal arising from each pixel in the successive spin-echo images must be equal or less than the magnitude of the signal from the previous spin-echo. The pixels from the multiple spin-echo images satisfying these criteria were used to compute the pixels composing the T, image. This was called the sorting criteria. with only slight Violation of either of these two criteria resulted in the T, value being set to zero. The signal-to-noise (S/N) ratio was calculated by assuming the noise in the image corresponds to the mean proton density signal, Sp(Air), measured in air outside the patient volume. The mean of the spin-echo signal (S,) from within the subject corresponds to signal plus noise within the image. Since all values of the spin-echo images were positive (range of O-2048), the following relationship was thenused: S/N = (S, - S,(Air)/Sp (Air). This algorithm was written in FORTRAN-77 and implemented in a VAX/VMS environment. T, images were optionally smoothed with a 3 x 3 median filter. Image display and quantitation were performed using the general image processing package, MDPP (3). Images were photographed with a 35 mm camera from the screen of a Gould-Deanza 8500 display or Raster Technology Model One/25 display. Noise reduction Table 1. Signal-to-noise msec 0 E. L. BUHLE, Jr., P. BL~CH and R. E. LENKINSKI ratios. Subject 1 Subject Z(total) Subject 2(tumor) Subject 3 20 40 60 80 30.504 23.225 17.374 12.982 9.845 6.595 5.640 3.228 13.575 11.605 10.216 8.441 11.028 7.190 5.393 4.213 proton 25.765 9.659 10.876 10.936 S/N is computed by obtaining the mean of the spin-echo pixels within the subject in question (S,) and of the air cavities surrounding or within S,(Air) from the proton density images. The following relationship was then used: S/N = (S, - S,(Air))/S,(Air). RESULTS A high signal-to-noise (S/N) ratio is critically important for reliable calculation of T, images. Least squares 187 regression of spin-echo signals from regions containing areas of low MRI signal generated erroneous T, values. While these erroneous T, values are seen in regions of low S/N, they are most clearly seen in regions void of tissue, such as outside the patient (Fig. la and lb) or within air cavities of the patient. Less than 0.1% of the erroneous pixels originated from areas of soft tissue. Multiple spin-echo signals are often modelled with an exponentially decaying amplitude (4, 5). Analysis of the S/N of the individual spin-echoes (Table 1) demonstrates the decrease in S/N ratio with longer spin-echo times. Subject 2 shows the S/N from within the tumor bed tends to be higher than in normal tissue. This occurs because of the longer T, values found in tumors. Figure la shows a T, calculation using only the first three spin-echoes. The number of pixels in the entire 256 X 256 image with erroneously assigned T, values increased from 50 to 65% when the number of spin-echo Fig. 2. Axial section through the head and neck region. (a) T, calculated using the Fist three echoes (TE = 20, 40, and 60 msec), T, selection criteria and 3 x 3 median filter. (b) T, calculated using four echoes (T,=20, 40, 60, and 80 msec). T, selection criteria and 3 x 3 median filter. The arrow points to a large missing region. (c) Difference of three echoes (Fig. 2a) minus four echoes (Fig. 2b). (d) Proton density. 188 Computerized Medical Imaging and Graphics May-June/l990, Volume 14, Number 3 Fig. 3. Axial section through the head and neck region. (a) T, calculated using the first three spin-echoes with no proton density cutoff or median filter. (b) T, calculated using the Fist three echoes (TE = 20, 40, and 60 msec) in areas where the proton density > = 25. A 3 x 3 median filter was then applied. Note the loss of bone marrow at arrow. (c) T, calculated as in (b), but no median filter was applied. (d) Proton density. images used to derive the T, image increased from three (Fig. la) to four (Fig. lb). Pixels were deemed erroneous when high intensity or long T, values were computed in what appeared on the proton density image to be air cavities. Application of selection criteria based on the presence of proton density signal (Fig. Id) and ordering of the spin-echo signals is shown using three spin-echoes in Fig. lc, Figure lc has also been further processed with a 3 x 3 median filter, thereby degrading the spatial resolution of the T, image as compared with Fig. la. Application of the selection criteria and median filter on the three spin-echo T, calculation and the four spin-echo T, calculation is shown in Fig. 2a and 2b, respectively. The low S/N ratio introduced by the fourth spin-echo image (Tn= 80 msec) sometimes results in spin-echo signals that are not monotonically decreasing in amplitude with increasing Tn. This failure of the spin-echo signals to monotonically decrease resulted in failure of the second selection criteria and thus no T, calculations were performed in these regions. The high degree of noise in the fourth spin-echo introduces greater error into the regression fit of the T, pixels. This poor fit then triggers the selection criteria and sometimes results in false zeroing of T, information (see arrow, Fig. 2b). Figure 2b, computed with four spin-echoes should be compared with the T, image computed from three spin-echoes (Fig. 2a) and the proton-density image (Fig 2d). Thirty-one percent of the pixels in the three spinecho T, image were zeroed in accord with the selection criteria whereas 44% were zeroed in the four spin-echo T, image. A subtraction of Fig. 2a (three spin-echoes) and Fig. 2b (four spin-echoes) is shown in Fig. 2c. White areas in this difference image portray T, values present in the three spin-echo T, calculation that are diminished or absent from the four spin-echo T, calculation. The average value of this difference image was Noise reduction 0 E. L. BUHLE,Jr., P. BLCCHand R. E. LENKINSKI 0.97 msec, with a standard deviation of 8.7 msec. A comparison of the T, values in regions of high proton density signal (usually high S/N) in three and four spin-echo T, images, with and without selection criteria showed the derived T, values to vary less than 3%. In areas of high S/N, the T, values are essentially identical between the three and four spin-echo calculations. In areas of low S/N, using only the first three spin-echoes images results in more T, pixels with a good linear regression fit. In calculations arising from four spinechoes, the regression fit is effected by the noise of fourth echo and results in a poor regression fit. This T, pixel is then masked according to the selection criteria. With three spin-echo images, the T, pixel would not have been zeroed. Selection of the appropriate proton density threshold obviates the need for post-processing of the T, image by a median filter. The threshold value of proton signal for T, calculation was empirically set to the mean of the proton signal plus two standard deviations, as measured outside the patient volume. Figure 3c shows the effective application of both the proton threshold and enforcement of the decreasing signal amplitude on a T, image computed from three spin-echo images. Figure 3c should be compared with Fig. 3a, where only the sorting criteria was performed. Figure 3b was computed with the same proton threshold and sorting criteria as Fig. 3c and further processed with a 3 X 3 median filter. Comparison of the proton density (Fig. 3d) and the T, image without the median filter (Fig. 3c) clearly reveals a loss of features upon application of the median filter (Fig. 3b, see arrows). The bone marrow of the skull in Fig. 3b is clearly missing when compared with Fig. 3a, 3c, and 3d. 189 fit of the spin-echoes. We have imposed two novel selection criteria for computing T, values from multiple spin-echoes. T, values were only computed from spin-echo pixels containing a proton signal above a user-defined threshold. Secondly, the magnitude of the spin-echo signals from each pixel was expected to be less than or equal to the magnitude of the corresponding pixel from the previous spin-echo. Deviations from this expectation usually indicated the dominance of noise over the signal and thus the T, value was not computed. Commercial software, supplied with the GE-Signa, removes some of the erroneous T, pixels by application of a median filter. The 3 x 3 median filter is a simple filter that extracts the median pixel from the nine pixels composing a 3 x 3 box and replaces the center pixel of the 3 x 3 box with this median value. While the median filter is effective in reducing the effect of discrete impulse noise, the noise suppression is also coupled with signal suppression and loss of spatial resolution. This loss of spatial resolution in the median filtered T, image may or may not be critical, depending on the resolution of the detail present in the original spin-echo images. A comparison of Fig. 3b and Fig. 3c clearly shows the loss of signal arising from the bone marrow of the skull upon application of the median filter. Use of the selection criteria outlined in this paper make the application of the median filter superfluous. Selective thresholding of the commercially computed T, image is often performed to suppress the erroneous T, values. While this may yield a aesthetically pleasing image, this image may mask high T, values computed in an area of very good S/N. Setting arbitrary criteria for the threshold on the basis of appearance makes quantitation of the T, images much more subjective. DISCUSSION We have generated T, images relatively free of erroneous values. These erroneous T, values arise from attempting a least squares fit of multiple spin-echo pixels containing a low S/N ratio. The amount of noise introduced by using the fourth spin-echo (Tn= 80 msec) increased the number of erroneous T, values. A comparison of the T, images computed from three spinechoes and four spin-echo images showed this difference to predominantly occur in regions of low proton density signal. The fourth spin-echo appears at best to be inconsequential or at worst, deleterious, to the least squares regression fit for T, calculation. The overall magnitude of the signal of spin-echo images decreases much more rapidly than the noise component of these images. By the fourth spin-echo the S/N ratio is quite low and appears to degrade the least squares regression SUMMARY The use of a least squares regression analysis for T, calculation works well in regions of good S/N. Regions of low S/N results in erroneous T, values. Three spinechoes (Tn= 20, 40, and 60 msec; T,= 2500 msec) appear to be sufficient for an accurate T, measurement. The fourth spin-echo (Tn = 80 msec) can be dominated by noise and degrade the resulting T, image. Use of two selection criteria: (a) computation of T, values only in regions of proton density signal and (b) imposing the constraint of monotonically decreasing spin-echo signals with longer T, times. Application of these criteria can result in routine computation of T, images containing high contrast and high resolution for both diagnostic and quantitative purposes. 190 Computerized Medical Imaging and Graphics May-June/l990, Volume 14, Number 3 REFERENCES About the Author-E. LOREN BUHLE, Jr., received a Ph.D. in Structural Biology from The Johns Hopkins School of Medicine in 1984. He did his postdoctoral training at the Pennsylvania Muscle Institute. at the University of Pennsylvania. He is presently an Assistant Professor in the Department of Radiation Oncology at the University of Pennsylvania. His primary research interest includes biomedical visualization and medical information theory. 1. McKenna, W.G.; Lenkinski, R.E.; Hendrix, R.A.; Vogele, K.E.; Bloch, P. The use of magnetic resonance imaging and spectroscopy in the assessment of patients with head and neck and other superficial human malignancies. Cancer 64:93-99; 1989. 2. Breger, R.K.; Wehrli, F. W.; Charles, H.C. ; MacFall, J.R.; Haughton, V.M. Reproducibility of relaxation and spin-density parameters in phantoms and human brain measured by MR imaging at 1ST. Magn. Reson. Imaging 3649-662; 1986. 3. Smith, P.R. An integrated set of computer programs for processing electron micrographs of biological structures. Ultramicroscopy 3:153-160; 1978. 4. Dixon, R.L.; Ekstrand, K.E. In: Thomas, S.R.; Dixon, R.L., eds. 5. NM R in medicine: The instrumentation and clinical applications. New York: Am. Inst. of Physics; 1986:1-31. Wehrli, F.W. In Thomas, S.R.; Dixon, R.L., eds. NM R in medicine: The instrumentation and clinical applications. New York: Am. Inst. of Physics; 1986: 216-228. About the Author-F’mm BLOCH received a Ph.D. in Radiological Physics from the University of Pennsylvania in 1968. He is presently a Professor at the University of Pennsylvania in the Department of Radiation Oncology. His primary research interest includes dosimetry, Magnetic Resonance Imaging, and spectroscopy. About the Author-ROBERTE. LENK~NSKI received a Ph.D. in chemistry from the University of Houston in 1973 and did postdoctoral training at the Weizman Institute of Science, Israel. He is presently an Associate Professor of Radiological Sciences at the University of Pennsylvania in the Department of Radiology. His primary research interest is in Magnetic Resonance Imaging and spectroscopy.