Blind Deconvolution Methods: A Review

Chaudhuri, Subhasis; Velmurugan, Rajbabu; Rameshan, Renu

doi:10.1007/978-3-319-10485-0_3

Cited by 26 publications

(20 citation statements)

References 93 publications

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“…for q ≥ 1, where R(x) is a regularization (or penalty) function such as l 1 , total variation (TV), etc (Chaudhuri et al, 2014;Sarder & Nehorai, 2006;McNally et al, 1999). In some inverse problems, the measurement operator H is not well defined so that both the unknown operator H and the image x should be estimated.…”

Section: Introductionmentioning

confidence: 99%

Optimal Transport Structure of CycleGAN for Unsupervised Learning for Inverse Problems

Sim

2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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The penalized least squares (PLS) is a classic approach to inverse problems, where a regularization term is added to stabilize the solution. Optimal transport (OT) is another mathematical framework for computer vision tasks by providing means to transport one measure to another at minimal cost. Cycle-consistent generative adversarial network (cycleGAN) is a recent extension of GAN to learn target distributions with less mode collapsing behavior. Although similar in that no supervised training is required, the algorithms look different, so the mathematical relationship between these approaches is not clear. In this article, we provide an important advance to unveil the missing link. Specifically, we reveal that a cycle-GAN architecture can be derived as a dual formulation of the optimal transport problem, if the PLS with a deep learning penalty is used as a transport cost between the two probability measures from measurements and unknown images. This suggests that cycleGAN can be considered as stochastic generalization of classical PLS approaches. Our derivation is so general that various types of cy-cleGAN architecture can be easily derived by merely changing the transport cost. As proofs of concept, this paper provides novel cycleGAN architecture for unsupervised learning in accelerated MRI and deconvolution microscopy problems, which confirm the efficacy and the flexibility of the theory. * Jong Chul Ye is the corresponding author of this paper.

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Section: Introductionmentioning

confidence: 99%

Optimal Transport Structure of CycleGAN for Unsupervised Learning for Inverse Problems

Sim

2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…Multi-frame may also be referred to as multichannel deconvolution [16] and is functionally equivalent. Most of these algorithms may be reduced to the alternating minimisation (AM) class of methods or otherwise Iterative Shrinkage [13,17]. AM methods subdivide the problem into several individual parts (usually two) and proceed by iteratively updating each of the parts assuming the other parts to be fixed and given by the previous iteration step, they have been well studied as a methodology for solving such inverse problems [18,19].…”

Section: Introductionmentioning

confidence: 99%

“…In Chan and Wong [21], the use is made of quadratic smoothness regularisers for both the image and PSFs. This type of regularisation tend to favour very smooth solutions [17] (as will be seen later). In order to avoid such smoothing the total variation (TV) for both the object and the PSFs has been elsewhere proposed as alternative regularisation (metrics) [17].…”

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confidence: 99%

“…Many different variations have been proposed in the last few decades, for the interested, the book [17] has an overview and (convergence) analysis of some numerical solutions to this problem based on alternating minimisation (AM). The convergence analysis in [17] is based on the following paper [21]. In Chan and Wong [21], the use is made of quadratic smoothness regularisers for both the image and PSFs.…”

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confidence: 99%

“…For completeness, following one major family of solutions to the BMFD problem; this problem of jointly estimating the object and the PSFs belonging to sets O and H has been alternatively formulated as a regularised least-squares cost function [16,17]:…”

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confidence: 99%

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Blind multi-frame deconvolution by tangential iterative projections (TIP)

et al. 2017

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Abstract:A methodology for retrieving the unknown object distribution and point-spread functions (PSFs) from a set of images acquired in the presence of temporal phase aberrations is presented in this paper. The method works by finding optimal complimentary linear filters for multi-frame deconvolution. The algorithm uses undemanding computational operations and few a priori, making it simple, fast and robust even at low signal-to-noise ratios. Results of numerical simulations and experimental tests are given as empirical proof, alongside comparisons with other algorithms found in the literature.

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