Advanced Sparsity Techniques In Medical Imaging And Image Processing

Abstract

In the past decades, sparsity techniques has been widely applied in the fields of medical imaging, computer vision, image processing, compressive sensing, machine learning etc., and gained great success. In this work, we propose new models of sparsity techniques, which is an extension to the standard sparsity used in the existing works and in the vein of structure sparsity families. First, we introduce the wavelet tree sparsity in natural images. It shows that the tree sparsity regularization often outperforms the existing standard sparsity based techniques in magnetic resonance imaging. Second, we extend the tree sparsity to forest sparsity on multi-channel data. A new theory is developed for forest sparsity, which is compared with the standard sparsity, tree sparsity and joint sparsity both empirically and theoretically. Motivated by the special datasets in remote sensing, we propose a new sparsity model called dynamic gradient sparsity to improve the fusion results. Moreover, a novel model called deep sparse representation is investigated and successfully used in image registration. Finally, we propose a set of fast reweighted least squares algorithms for different optimization problems based on sparsity regularization.