Paper Info
Title
Analysis of the Block Coordinate Descent Method for Linear Ill-Posed Problems
Abstract
Block coordinate descent (BCD) methods approach optimization problems by performing gradient steps along alternating subgroups of coordinates. This is in contrast to full gradient descent, where a gradient step updates all coordinates simultaneously. BCD has been demonstrated to accelerate the gradient method in many practical large-scale applications. Despite its success no convergence analysis for inverse problems is known so far. In this paper, we investigate the BCD method for solving linear inverse problems. As the main theoretical result, we show that for operators having a particular tensor product form, the BCD method combined with an appropriate stopping criterion yields a convergent regularization method. To illustrate the theory, we perform numerical experiments comparing the BCD and the full gradient descent method for a system of integral equations. We also present numerical tests for a nonlinear inverse problem not covered by our theory, namely one-step inversion in multispectral X-ray tomography.
Year
DOI
Venue
2019
10.1137/19M1243956
SIAM JOURNAL ON IMAGING SCIENCES
Keywords
DocType
Volume
ill-posed problems,convergence analysis,regularization theory,coordinate descent,multi-spectral CT
Journal
12
Issue
ISSN
Citations 
4
1936-4954
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Simon Rabanser111.04
Lukas Neumann255518.65
Markus Haltmeier37414.16