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
Hauptverfasser: Selesnick, Ivan, Lanza, Alessandro, Morigi, Serena, Sgallari, Fiorella
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.07.2020
Springer Nature B.V
Schlagworte:
Algorithms
Applications of Mathematics
Computer Science
Convexity
Cost function
Image Processing and Computer Vision
Mathematical Methods in Physics
Noise reduction
Parameters
Random noise
Regularization
Signal,Image and Speech Processing
Forward-backward splitting algorithm
Signal denoising
Total variation regularization
Convex non-convex regularization
ISSN:0924-9907, 1573-7683
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Zusammenfassung: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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ISSN:0924-9907
1573-7683
DOI:10.1007/s10851-019-00937-5