Iterative Censoring and Highly Efficient Machine Learning with Condition Number in LSMR Method

The least squares minimal residual method, which is an iterative solution method, is adopted for an ill-conditioned linear equation with a large-dimensional sparse matrix as a coefficient. In this study, we address a blurred-image-sharpening problem, which contains noise. Thus, the iterative computation should be stopped after an appropriate number of iterations to reduce the effect of noise. The condition number in the bidiagonal matrix can be used as an iterative stopping rule. The optimal condition number is machine-learned from the condition number generated at each iteration. For machine learning, we propose the application of singular value computation as a preprocessing method for the training data.