Journal
INVERSE PROBLEMS AND IMAGING
Volume 6, Issue 3, Pages 547-563Publisher
AMER INST MATHEMATICAL SCIENCES
DOI: 10.3934/ipi.2012.6.547
Keywords
Image reconstruction; random projection; total variation; quadratic penalty; alternating direction method
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Funding
- NSF of China [NSFC-11001075, NSFC-11001123, NSFC-91130007]
- Hong Kong General Research Fund [202610]
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Total variation (TV) regularization is popular in image reconstruction due to its edge-preserving 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 matrix-vector 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.
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