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Image denoising by generalized total variation regularization and least squares fidelity

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Abstract

Inspired by the ability of \(\ell _p\)-regularized algorithms and the close connection of total variation (TV) to the \(\ell _1\) norm, a \(p\)th-power type TV denoted as TV\(_p\) is proposed for \(0\le p \le 1\). The TV\(_p\)-regularized problem for image denoising is nonconvex thus difficult to tackle directly. Instead, we deal with the problem by proposing a weighted TV (WTV) minimization where the weights are updated iteratively to locally approximate the TV\(_p\)-regularized problem. The difficulty of WTV minimization is dealt with in a modified split Bregman framework. Numerical results are presented to demonstrate improved denoising performance of the new algorithm with \(p<1\) relative to that obtained by the standard TV minimization and several recent denoising methods from the literature on a variety of images.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Victoria, 3800 Finnerty Rd., Victoria, BC , V8P 5C2, Canada

    Jie Yan & Wu-Sheng Lu

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  1. Jie Yan
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  2. Wu-Sheng Lu
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Correspondence to Jie Yan.

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Yan, J., Lu, WS. Image denoising by generalized total variation regularization and least squares fidelity. Multidim Syst Sign Process 26, 243–266 (2015). https://doi.org/10.1007/s11045-013-0255-2

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  • DOI: https://doi.org/10.1007/s11045-013-0255-2

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