Image restoration using a stochastic variant of the alternating direction method of multipliers

Ono, Shunsuke; Yamagishi, Masao; Miyata, Takamichi; Kumazawa, Itsuo

doi:10.1109/icassp.2016.7472533

Cited by 7 publications

(4 citation statements)

References 31 publications

(39 reference statements)

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“…Incorporating variational image decomposition models, e.g., [50]- [53], into the proposed method is an interesting direction of future work. Also, a stochastic image restoration methodology [54] would be able to further accelerate our method.…”

Section: Resultsmentioning

confidence: 99%

Image Restoration with Multiple Hard Constraints on Data-Fidelity to Blurred/Noisy Image Pair

Takeyama¹,

Ono

Kumazawa

2017

IEICE Trans. Inf. & Syst.

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SUMMARYExisting image deblurring methods with a blurred/noisy image pair take a two-step approach: blur kernel estimation and image restoration. They can achieve better and much more stable blur kernel estimation than single image deblurring methods. On the other hand, in the image restoration step, they do not exploit the information on the noisy image, or they require ad hoc tuning of interdependent parameters. This paper focuses on the image restoration step and proposes a new restoration method of using a blurred/noisy image pair. In our method, the image restoration problem is formulated as a constrained convex optimization problem, where data-fidelity to a blurred image and that to a noisy image is properly taken into account as multiple hard constraints. This offers (i) high quality restoration when the blurred image also contains noise; (ii) robustness to the estimation error of the blur kernel; and (iii) easy parameter setting. We also provide an efficient algorithm for solving our optimization problem based on the so-called alternating direction method of multipliers (ADMM). Experimental results support our claims.

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Section: Resultsmentioning

confidence: 99%

Image Restoration with Multiple Hard Constraints on Data-Fidelity to Blurred/Noisy Image Pair

Takeyama¹,

Ono

Kumazawa

2017

IEICE Trans. Inf. & Syst.

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“…If Φ is a sparse matrix, we offer to use a preconditioned conjugate gradient method [42] for approximately solving the inversion or to apply primal-dual splitting methods [43][44][45] instead of ADMM (Primal-dual splitting methods require no matrix inversion but in general their convergence speed is slower than ADMM. Otherwise, randomized image restoration methods using stochastic proximal splitting algorithms [46][47][48][49] might be useful for reducing the computational cost.…”

Section: Hs Image Restoration By Hsstvmentioning

confidence: 99%

A Constrained Convex Optimization Approach to Hyperspectral Image Restoration with Hybrid Spatio-Spectral Regularization

2020

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We propose a new constrained optimization approach to hyperspectral (HS) image restoration. Most existing methods restore a desirable HS image by solving some optimization problems, consisting of a regularization term(s) and a data-fidelity term(s). The methods have to handle a regularization term(s) and a data-fidelity term(s) simultaneously in one objective function; therefore, we need to carefully control the hyperparameter(s) that balances these terms. However, the setting of such hyperparameters is often a troublesome task because their suitable values depend strongly on the regularization terms adopted and the noise intensities on a given observation. Our proposed method is formulated as a convex optimization problem, utilizing a novel hybrid regularization technique named Hybrid Spatio-Spectral Total Variation (HSSTV) and incorporating data-fidelity as hard constraints. HSSTV has a strong noise and artifact removal ability while avoiding oversmoothing and spectral distortion, without combining other regularizations such as low-rank modeling-based ones. In addition, the constraint-type data-fidelity enables us to translate the hyperparameters that balance between regularization and data-fidelity to the upper bounds of the degree of data-fidelity that can be set in a much easier manner. We also develop an efficient algorithm based on the alternating direction method of multipliers (ADMM) to efficiently solve the optimization problem. We illustrate the advantages of the proposed method over various HS image restoration methods through comprehensive experiments, including state-of-the-art ones.

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“…Finally, applying Cardano formula to (15) yields (13). 3 Algorithm 1: Proposed algorithm for solving (5) input :…”

Section: Remark 2 (Projection Computations In Algorithm 1)mentioning

confidence: 99%

“…Roughly speaking, at each iteration, the algorithms activate only the operations associated with randomly chosen variables, so that the said costs are significantly reduced. Actually, several studies show the utility of such block-coodinatewise randomization in image restoration [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection

Ono

2019

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper proposes a randomized optimization framework for constrained signal reconstruction, where the word "constrained" implies that data-fidelity is imposed as a hard constraint instead of adding a data-fidelity term to an objective function to be minimized. Such formulation facilitates the selection of regularization terms and hyperparameters, but due to the non-separability of the data-fidelity constraint, it does not suit block-coordinate-wise randomization as is. To resolve this, we give another expression of the data-fidelity constraint via epigraphs, which enables to design a randomized solver based on a stochastic proximal algorithm with randomized epigraphical projection. Our method is very efficient especially when the problem involves non-structured large matrices. We apply our method to CT image reconstruction, where the advantage of our method over the deterministic counterpart is demonstrated.

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Image restoration using a stochastic variant of the alternating direction method of multipliers

Cited by 7 publications

References 31 publications

Image Restoration with Multiple Hard Constraints on Data-Fidelity to Blurred/Noisy Image Pair

Image Restoration with Multiple Hard Constraints on Data-Fidelity to Blurred/Noisy Image Pair

A Constrained Convex Optimization Approach to Hyperspectral Image Restoration with Hybrid Spatio-Spectral Regularization

Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection

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