Regularization theory

We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of regularization, MOR) approach to reconstruct the estimator of the quantity for the non-linear ill-posed inverse problem. The estimator is defined as the minimizer of a Tikhonov functional, which is the sum of a data misfit term and a quadratic penalty term. We develop a theoretical analysis for the minimizer of the Tikhonov regularization scheme using the ansatz of reproducing kernel Hilbert spaces. We discuss optimal rates of convergence for the proposed scheme, uniformly over classes of admissible solutions, defined through appropriate source conditions.

—This study uses remote sensing technology that can provide information about the condition of the earth's surface area, fast, and spatially. The study area was in Karawang District, lying in the Northern part of West Java-Indonesia. We address a paddy growth stages classification using LANDSAT 8 image data obtained from multi-sensor remote sensing image taken in October 2015 to August 2016. This study pursues a fast and accurate classification of paddy growth stages by employing multiple regularizations learning on some deep learning methods such as DNN (Deep Neural Networks) and 1-D CNN (1-D Convolutional Neural Networks). The used regularizations are Fast Dropout, Dropout, and Batch Normalization. To evaluate the effectiveness, we also compared our method with other machine learning methods such as (Logistic Regression, SVM, Random Forest, and XGBoost). The data used are seven bands of LANDSAT-8 spectral data samples that correspond to paddy growth stages data obtained from i-Sky (eye in the sky) Innovation system. The growth stages are determined based on paddy crop phenology profile from time series of LANDSAT-8 images. The classification results show that MLP using multiple regularization Dropout and Batch Normalization achieves the highest accuracy for this dataset.