Multi-Parseval frame-based nonconvex sparse image deconvolution

Wen-Ze Shao; Hai-Song Deng; Zhi-Hui Wei

doi:10.1117/1.OE.51.6.067008

6 June 2012 Multi-Parseval frame-based nonconvex sparse image deconvolution

Wen-Ze Shao, Hai-Song Deng, Zhi-Hui Wei

Author Affiliations +

Optical Engineering, Vol. 51, Issue 6, 067008 (June 2012). https://doi.org/10.1117/1.OE.51.6.067008

Abstract

Image deconvolution is an ill-posed, low-level vision task, restoring a clear image from the blurred and noisy observation. From the perspective of statistics, previous work on image deconvolution has been formulated as a maximum a posteriori or a general Bayesian inference problem, with Gaussian or heavy-tailed non-Gaussian prior image models (e.g., a student's t distribution). We propose a Parseval frame-based nonconvex image deconvolution strategy via penalizing the l₀-norm of the coefficients of multiple different Parseval frames. With these frames, flexible filtering operators are provided to adaptively capture the point singularities, the curvilinear edges and the oscillating textures in natural images. The proposed optimization problem is implemented by borrowing the idea of recent penalty decomposition method, resulting in a simple and efficient iteration algorithm. Experimental results show that the proposed deconvolution scheme is highly competitive among state-of-the-art methods, in both the improvement of signal-to-noise ratio and visual perception.

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Wen-Ze Shao, Hai-Song Deng, and Zhi-Hui Wei "Multi-Parseval frame-based nonconvex sparse image deconvolution," Optical Engineering 51(6), 067008 (6 June 2012). https://doi.org/10.1117/1.OE.51.6.067008

Published: 6 June 2012

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