Spatially adapted regularization parameter selection based on the local discrepancy function for Poissonian image deblurring

Chen, Dai-Qiang; Cheng, Lizhi

doi:10.1088/0266-5611/28/1/015004

Cited by 36 publications

(22 citation statements)

References 39 publications

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“…• The modification of our approach to spatially adapted regularization parameter selection, see [22,29,44], will be interesting. For this task, further estimates of appropriate parameters τ will be useful.…”

Section: Discussionmentioning

confidence: 99%

“…Considering (P 1,τ ) in the form (22) and solving the inner I-divergence constrained least square problems based on the discrepancy principle by a Newton method, we obtain the following algorithm which was recently also suggested in [17,18].…”

Section: Admm Involving Least Squares Problems With I-divergence Consmentioning

confidence: 99%

“…For f 2 as in our setting (22) and q (k) := p (k) /t these two steps are exactly those of the ADMM algorithm for updating y = (y…”

Section: Other Primal-dual Algorithmsmentioning

confidence: 99%

“…The method in [38] uses a predictor-corrector scheme [23] in the alternating direction iterations for the dual variable. This algorithm can be adapted to our setting (22) as follows:…”

Section: Algorithm II (Pdhgmp With Inner Newton Iterations)mentioning

confidence: 99%

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Minimization and parameter estimation for seminorm regularization models with I -divergence constraints

2013

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In this papers we analyze the minimization of seminorms L · on R n under the constraint of a bounded I-divergence D(b, H·) for rather general linear operators H and L. The I-divergence is also known as Kullback-Leibler divergence and appears in many models in imaging science, in particular when dealing with Poisson data. Often H represents, e.g., a linear blur operator and L is some discrete derivative or frame analysis operator. We prove relations between the the parameters of I-divergence constrained and penalized problems without assuming the uniqueness of their minimizers. To solve the I-divergence constrained problem we apply first-order primal-dual algorithms which reduce the problem to the solution of certain proximal minimization problems in each iteration step. One of these proximation problems is an I-divergence constrained least squares problem which can be solved based on Morosov's discrepancy principle by a Newton method. Interestingly, the algorithm produces not only a sequence of vectors which converges to a minimizer of the constrained problem but also a sequence of parameters which convergences to a regularization parameter so that the corresponding penalized problem has the same solution as our constrained one. We demonstrate the performance of various algorithms for different image restoration tasks both for images corrupted by Poisson noise and multiplicative Gamma noise.

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Section: Discussionmentioning

confidence: 99%

Section: Admm Involving Least Squares Problems With I-divergence Consmentioning

confidence: 99%

“…For f 2 as in our setting (22) and q (k) := p (k) /t these two steps are exactly those of the ADMM algorithm for updating y = (y…”

Section: Other Primal-dual Algorithmsmentioning

confidence: 99%

“…The method in [38] uses a predictor-corrector scheme [23] in the alternating direction iterations for the dual variable. This algorithm can be adapted to our setting (22) as follows:…”

Section: Algorithm II (Pdhgmp With Inner Newton Iterations)mentioning

confidence: 99%

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Minimization and parameter estimation for seminorm regularization models with I -divergence constraints

2013

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“…For 'sparsity' models the reader may again consider [61,40]. Further modifications for spatially adapted regularization parameter selection as in [15,22] are also of interest. However, one of the main topics is still the estimation of the noise statistics.…”

Section: Discussionmentioning

confidence: 99%

Homogeneous Penalizers and Constraints in Convex Image Restoration

2012

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Recently convex optimization models were successfully applied for solving various problems in image analysis and restoration. In this paper, we are interested in relations between convex constrained optimization problems of the form argmin{Φ(x) subject to Ψ(x) ≤ τ } and their penalized counterparts argmin{Φ(x) + λΨ(x)}. We recall general results on the topic by the help of an epigraphical projection. Then we deal with the special setting Ψ := L · with L ∈ R m,n and Φ := ϕ(H·), where H ∈ R n,n and ϕ : R n → R ∪ {+∞} meet certain requirements which are often fulfilled in image processing models. In this case we prove by incorporating the dual problems that there exists a bijective function such that the solutions of the constrained problem coincide with those of the penalized problem if and only if τ and λ are in the graph of this function. We illustrate the relation between τ and λ for various problems arising in image processing. In particular, we point out the relation to the Pareto frontier for joint sparsity problems. We demonstrate the performance of the constrained model in restoration tasks of images corrupted by Poisson noise with the I-divergence as data fitting term ϕ and in inpainting models with the constrained nuclear norm. Such models can be useful if we have a priori knowledge on the image rather than on the noise level.

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A Dual Adaptive Regularization Method to Remove Mixed Gaussian-Poisson Noise

Gao

et al. 2017

Computer Vision – ACCV 2016 Workshops

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Spatially adapted regularization parameter selection based on the local discrepancy function for Poissonian image deblurring

Cited by 36 publications

References 39 publications

Minimization and parameter estimation for seminorm regularization models with I -divergence constraints

Minimization and parameter estimation for seminorm regularization models with I -divergence constraints

Homogeneous Penalizers and Constraints in Convex Image Restoration

A Dual Adaptive Regularization Method to Remove Mixed Gaussian-Poisson Noise

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