Journal
IEEE TRANSACTIONS ON IMAGE PROCESSING
Volume 22, Issue 8, Pages 3074-3086Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2013.2258354
Keywords
Image deconvolution; alternating direction method of multipliers (ADMM); boundary conditions; nonperiodic deconvolution; inpainting; total variation; frames
Funding
- Fundacao para a Ciencia e Tecnologia [PTDC/EEA-TEL/104515/2008, PEst-OE/EEI/LA0008/2011, PTDC/EEI-PRO/1470/2012, SFRH/BPD/69344/2010]
- Fundação para a Ciência e a Tecnologia [PTDC/EEA-TEL/104515/2008, SFRH/BPD/69344/2010, PTDC/EEI-PRO/1470/2012] Funding Source: FCT
Ask authors/readers for more resources
The alternating direction method of multipliers (ADMM) has recently sparked interest as a flexible and efficient optimization tool for inverse problems, namely, image deconvolution and reconstruction under non-smooth convex regularization. ADMM achieves state-of-the-art speed by adopting a divide and conquer strategy, wherein a hard problem is split into simpler, efficiently solvable sub-problems (e. g., using fast Fourier or wavelet transforms, or simple proximity operators). In deconvolution, one of these sub-problems involves a matrix inversion (i.e., solving a linear system), which can be done efficiently (in the discrete Fourier domain) if the observation operator is circulant, i.e., under periodic boundary conditions. This paper extends ADMM-based image deconvolution to the more realistic scenario of unknown boundary, where the observation operator is modeled as the composition of a convolution (with arbitrary boundary conditions) with a spatial mask that keeps only pixels that do not depend on the unknown boundary. The proposed approach also handles, at no extra cost, problems that combine the recovery of missing pixels (i.e., inpainting) with deconvolution. We show that the resulting algorithms inherit the convergence guarantees of ADMM and illustrate its performance on non-periodic deblurring (with and without inpainting of interior pixels) under total-variation and frame-based regularization.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available