2017
DOI: 10.1137/16m1101684
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Infimal Convolution of Data Discrepancies for Mixed Noise Removal

Abstract: We consider the problem of image denoising in the presence of noise whose statistical properties are a combination of two different distributions. We focus on noise distributions that are frequently considered in applications, in particular mixtures of salt & pepper and Gaussian noise, and Gaussian and Poisson noise. We derive a variational image denoising model that features a total variation regularisation term and a data discrepancy that features the mixed noise as an infimal convolution of discrepancy term… Show more

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Cited by 51 publications
(102 citation statements)
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References 53 publications
(113 reference statements)
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“…We notice that the auxiliary variable t is introduced to transfer the discrete gradient operator out of the possibly non-convex non-smooth regulariser whereas the variable r is aimed to adjust the regularisation parameter µ along the ADMM iterations such that the computed solution u * satisfies the discrepancy principle [54], i.e. belongs to the discrepancy set D in (10). In order to solve problem (42)-(43) via ADMM, we start defining the augmented Lagrangian functional as follows:…”
Section: Numerical Solution By Admmmentioning
confidence: 99%
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“…We notice that the auxiliary variable t is introduced to transfer the discrete gradient operator out of the possibly non-convex non-smooth regulariser whereas the variable r is aimed to adjust the regularisation parameter µ along the ADMM iterations such that the computed solution u * satisfies the discrepancy principle [54], i.e. belongs to the discrepancy set D in (10). In order to solve problem (42)-(43) via ADMM, we start defining the augmented Lagrangian functional as follows:…”
Section: Numerical Solution By Admmmentioning
confidence: 99%
“…Furthermore, its convexity makes it appealing for several efficient optimisation methods -see [12] for a review -and it is often used as a reference model for the study of either higher-order regularisations (e.g. the Total Generalised Variation [8]) or of non-Gaussian [3,35,15,44] and possibly combined [10,33] noise distributions. However, in addition to the well-known reconstruction drawbacks such as the staircasing effect, the TV regulariser in (3) suffers from additional limitations.…”
Section: Introductionmentioning
confidence: 99%
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“…Recently in [14], a non-standard variational model for noise removal of mixtures of Salt & Pepper and Gaussian, and Gaussian and Poisson noise has been studied. The model, which will be referred to as TV-IC model, is based on the minimisation of an energy functional which is the sum of |Du|(Ω) and an infimal convolution of single noise data discrepancy terms.…”
Section: Infimal Convolution Modelling Of Data Discrepanciesmentioning
confidence: 99%
“…
We analyse a variational regularisation problem for mixed noise removal that was recently proposed in [14]. The data discrepancy term of the model combines L 1 and L 2 terms in an infimal convolution fashion and it is appropriate for the joint removal of Gaussian and Salt & Pepper noise.
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mentioning
confidence: 99%