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2009
IEEE

Monotone Operator Splitting For Optimization Problems In Sparse Recovery

10 years 4 months ago
Monotone Operator Splitting For Optimization Problems In Sparse Recovery
This work focuses on several optimization problems involved in recovery of sparse solutions of linear inverse problems. Such problems appear in many fields including image and signal processing, and have attracted even more interest since the emergence of the compressed sensing (CS) theory. In this paper, we formalize many of these optimization problems within a unified framework of convex optimization theory, and invoke tools from convex analysis and maximal monotone operator splitting. We characterize all these optimization problems, and to solve them, we propose fast iterative convergent algorithms using forward-backward and/or Peaceman/Douglas-Rachford splitting iterations. With nondifferentiable sparsity-promoting penalties, the proposed algorithms are essentially based on iterative shrinkage. This makes them very competitive for large-scale problems. We also report some experiments on image reconstruction in CS to demonstrate the applicability of the proposed framework.
Added 10 Nov 2009
Updated 26 Dec 2009
Type Conference
Year 2009
Where ICIP
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