Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Alternating algorithms for total variation image reconstruction from random projections

Language

English

Abstract

Total variation (TV) regularization is popular in image reconstruction due to its edgepreserving property. In this paper, we extend the alternating minimization algorithm recently proposed in [37] to the case of recovering images from random projections. Specifically, we propose to solve the TV regularized least squares problem by alternating minimization algorithms based on the classical quadratic penalty technique and alternating minimization of the augmented Lagrangian function. The per-iteration cost of the proposed algorithms is dominated by two matrixvector multiplications and two fast Fourier transforms. Convergence results, including finite convergence of certain variables and q-linear convergence rate, are established for the quadratic penalty method. Furthermore, we compare numerically the new algorithms with some state-of-the-art algorithms. Our experimental results indicate that the new algorithms are stable, efficient and competitive with the compared ones. © 2012 American Institute of Mathematical Sciences.

Keywords

Alternating direction method, Image reconstruction, Quadratic penalty, Random projection, Total variation

Publication Date

2012

Source Publication Title

Inverse Problems and Imaging

Volume

6

Issue

3

Start Page

547

End Page

563

Publisher

American Institute of Mathematical Sciences

DOI

10.3934/ipi.2012.6.547

Link to Publisher's Edition

http://dx.doi.org/10.3934/ipi.2012.6.547

ISSN (print)

19308337

ISSN (electronic)

19308345

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