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A Fast Algorithm for Total Variation Image Reconstruction from Random Projections

Yunhai Xiao(yhxiaomath***at***gmail.com)
Junfeng Yang(jfyang***at***nju.edu.cn)

Abstract: Total variation (TV) regularization is popular in image restoration and reconstruction due to its ability to preserve image edges. To date, most research activities on TV models concentrate on image restoration from blurry and noisy observations, while discussions on image reconstruction from random projections are relatively fewer. In this paper, we propose, analyze, and test a fast alternating minimization algorithm for image reconstruction from random projections via solving a TV regularized least-squares problem. The per-iteration cost of the proposed algorithm involves a linear time shrinkage operation, two matrix-vector multiplications and two fast Fourier transforms. Convergence, certain finite convergence and $q$-linear convergence results are established, which indicate that the asymptotic convergence speed of the proposed algorithm depends on the spectral radii of certain submatrix. Moreover, to speed up convergence and enhance robustness, we suggest an accelerated scheme based on an inexact alternating direction method. We present experimental results to compare with an existing algorithm, which indicate that the proposed algorithm is stable, efficient and competitive with TwIST \cite{TWIST} --- a state-of-the art algorithm for solving TV regularization problems.

Keywords: Total variation, image restoration, image reconstruction, compressive sensing, alternating direction method

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: TR10-01, Nanjing University

Download: [PDF]

Entry Submitted: 01/11/2010
Entry Accepted: 01/11/2010
Entry Last Modified: 01/11/2010

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