Non-convex Total Variation Regularization for Convex Denoising of Signals
Total variation (TV) signal denoising is a popular nonlinear filtering method to estimate piecewise constant signals corrupted by additive white Gaussian noise. Following a ‘convex non-convex’ strategy, recent papers have introduced non-convex regularizers for signal denoising that preserve the conv...
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| Veröffentlicht in: | Journal of mathematical imaging and vision Jg. 62; H. 6-7; S. 825 - 841 |
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| Abstract | Total variation (TV) signal denoising is a popular nonlinear filtering method to estimate piecewise constant signals corrupted by additive white Gaussian noise. Following a ‘convex non-convex’ strategy, recent papers have introduced non-convex regularizers for signal denoising that preserve the convexity of the cost function to be minimized. In this paper, we propose a non-convex TV regularizer, defined using concepts from convex analysis, that unifies, generalizes, and improves upon these regularizers. In particular, we use the generalized Moreau envelope which, unlike the usual Moreau envelope, incorporates a matrix parameter. We describe a novel approach to set the matrix parameter which is essential for realizing the improvement we demonstrate. Additionally, we describe a new set of algorithms for non-convex TV denoising that elucidate the relationship among them and which build upon fast exact algorithms for classical TV denoising. |
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| AbstractList | Total variation (TV) signal denoising is a popular nonlinear filtering method to estimate piecewise constant signals corrupted by additive white Gaussian noise. Following a ‘convex non-convex’ strategy, recent papers have introduced non-convex regularizers for signal denoising that preserve the convexity of the cost function to be minimized. In this paper, we propose a non-convex TV regularizer, defined using concepts from convex analysis, that unifies, generalizes, and improves upon these regularizers. In particular, we use the generalized Moreau envelope which, unlike the usual Moreau envelope, incorporates a matrix parameter. We describe a novel approach to set the matrix parameter which is essential for realizing the improvement we demonstrate. Additionally, we describe a new set of algorithms for non-convex TV denoising that elucidate the relationship among them and which build upon fast exact algorithms for classical TV denoising. |
| Author | Morigi, Serena Sgallari, Fiorella Selesnick, Ivan Lanza, Alessandro |
| Author_xml | – sequence: 1 givenname: Ivan orcidid: 0000-0002-4939-3971 surname: Selesnick fullname: Selesnick, Ivan organization: Department of Electrical and Computer Engineering, New York University – sequence: 2 givenname: Alessandro orcidid: 0000-0002-4904-0682 surname: Lanza fullname: Lanza, Alessandro organization: Department of Mathematics, University of Bologna – sequence: 3 givenname: Serena orcidid: 0000-0001-8334-8798 surname: Morigi fullname: Morigi, Serena organization: Department of Mathematics, University of Bologna – sequence: 4 givenname: Fiorella orcidid: 0000-0002-9166-8879 surname: Sgallari fullname: Sgallari, Fiorella email: fiorella.sgallari@unibo.it organization: Department of Mathematics, University of Bologna |
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| Keywords | Forward-backward splitting algorithm Signal denoising Total variation regularization Convex non-convex regularization |
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