2011/05/18 by Tobias Lindstrøm Jensen, Jensen, Tobias Lindstrøm, Jørgensen, Jakob Heide +4
Engineering · Mathematics · #Sparse and Compressive Sensing Techniques #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging
paper · pdf · doi:10.48550/arxiv.1105.3723
We present a practical implementation of an optimal first-order method, due\nto Nesterov, for large-scale total variation regularization in tomographic\nreconstruction, image deblurring, etc. The algorithm applies to \μ-strongly\nconvex objective functions with L-Lipschitz continuous gradient. In the\nframework of Nesterov both \μ and L are assumed known -- an assumption\nthat is seldom satisfied in practice. We propose to incorporate mechanisms to\nestimate locally sufficient \μ and L during the iterations. The mechanisms\nalso allow for the application to non-strongly convex functions. We discuss the\niteration complexity of several first-order methods, including the proposed\nalgorithm, and we use a 3D tomography problem to compare the performance of\nthese methods. The results show that for ill-conditioned problems solved to\nhigh accuracy, the proposed method significantly outperforms state-of-the-art\nfirst-order methods, as also suggested by theoretical results.\n