Permuted Coordinate-Wise Optimizations Applied to Lp-Regularized Image Deconvolution

Jaeduk Han, Ki Sun Song, Jonghyun Kim, Moon Gi Kang

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Image deconvolution is an ill-posed problem that usually requires prior knowledge for regularizing the feasible solutions. In the literature, iterative methods estimate an intrinsic image, minimizing a cost function regularized by specific prior information. However, it is difficult to directly minimize the constrained cost function, if a nondifferentiable regularization (e.g., the sparsity constraint) is employed. In this paper, we propose a nonderivative image deconvolution algorithm that solves the under-constrained problem (i.e., a non-blind image deconvolution) by successively solving the permuted subproblems. The subproblems, arranged in permuted sequences, directly minimize the nondifferentiable cost functions. Various Lp-regularized (0<p ≤1, p=2) objective functions are utilized to demonstrate the pixel-wise optimization, in which the projection operator generates simplified, low-dimensional subproblems for estimating each pixel. The subproblems, after projection, are dealt within the corresponding hyperplanes containing the adjacent pixels of each image coordinate. Furthermore, successively solving the subproblems can accelerate the deconvolution process with a linear speedup, by parallelizing the subproblem sequences. The image deconvolution results with various regularization functionals are presented and the linear speedup is also demonstrated with a parallelized version of the proposed algorithm. Experimental results demonstrate that the proposed method outperforms the conventional methods in terms of the improved signal-to-noise ratio and structural similarity index measure.

Original languageEnglish
Pages (from-to)3556-3570
Number of pages15
JournalIEEE Transactions on Image Processing
Issue number7
Publication statusPublished - 2018 Jul

Bibliographical note

Funding Information:
Manuscript received April 3, 2017; revised October 12, 2017, December 18, 2017, and March 23, 2018; accepted April 2, 2018. Date of publication April 9, 2018; date of current version April 20, 2018. This work was supported by the Basic Science Research Program through the National Research Foundation of Korea, Ministry of Science, ICT and Future Planning, under Grant 2015R1A2A1A14000912. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Jean-Francois Aujol. (Corresponding author: Moon Gi Kang.) The authors are with the School of Electrical and Electronic Engineering, Yonsei University, Seoul 03722 , South Korea (e-mail:

Publisher Copyright:
© 1992-2012 IEEE.

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Graphics and Computer-Aided Design


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