Space Variant Blind Image Restoration

Hadj, Saïma Ben; Blanc‐Féraud, Laure; Aubert, Gilles

doi:10.1137/130945776

Cited by 18 publications

(7 citation statements)

References 43 publications

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“…This approach is not adequate for MMF systems due to the presence of radial variations. Blind and semi-blind image restoration methods have also been proposed [17,18], but spatial variations in MMF systems can be readily measured without additional instrumentation, thus substantially simplifying the computational task. Machine learning methods also have the potential to model a spatially variant PSF and perform deconvolution in this context [18].…”

Section: Introductionmentioning

confidence: 99%

Deconvolution for multimode fiber imaging: modeling of spatially variant PSF

Turcotte¹,

Sutu²,

Schmidt³

et al. 2020

Biomed. Opt. Express

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Focusing light through a step-index multimode optical fiber (MMF) using wavefront control enables minimally-invasive endoscopy of biological tissue. The point spread function (PSF) of such an imaging system is spatially variant, and this variation limits compensation for blurring using most deconvolution algorithms as they require a uniform PSF. However, modeling the spatially variant PSF into a series of spatially invariant PSFs reopens the possibility of deconvolution. To achieve this we developed svmPSF: an open-source Java-based framework compatible with ImageJ. The approach takes a series of point response measurements across the field-of-view (FOV) and applies principal component analysis to the measurements' co-variance matrix to generate a PSF model. By combining the svmPSF output with a modified Richardson-Lucy deconvolution algorithm, we were able to deblur and regularize fluorescence images of beads and live neurons acquired with a MMF, and thus effectively increasing the FOV.

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Section: Introductionmentioning

confidence: 99%

Deconvolution for multimode fiber imaging: modeling of spatially variant PSF

Turcotte¹,

Sutu²,

Schmidt³

et al. 2020

Biomed. Opt. Express

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“…This model is used in the recent papers [HHS10,HSH11,BBA12]. In the EFF model the blur operator K has the form…”

Section: The Efficient Filter Flow Modelmentioning

confidence: 99%

Primal-Dual Decomposition by Operator Splitting and Applications to Image Deblurring

O’Connor¹,

Vandenberghe²

2014

SIAM J. Imaging Sci.

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Professor Lieven Vandenberghe, ChairWe present primal-dual decomposition algorithms for convex optimization problems with cost functions f (x)+g(Ax), where f and g have inexpensive proximal operators and A can be decomposed as a sum of structured matrices. The methods are based on the Douglas-Rachford splitting algorithm applied to various splittings of the primal-dual optimality conditions. We discuss applications to image deblurring problems with non-quadratic data fidelity terms, different types of convex regularization, and simple convex constraints. In these applications, the primal-dual splitting approach allows us to handle general boundary conditions for the blurring operator. We also give a domain decomposition approach to image deblurring, where the blur operator may use a different blur kernel for each image patch, and at each iteration all patches are processed in parallel. Numerical results indicate that the primal-dual splitting methods compare favorably with the alternating direction method of multipliers, the Douglas-Rachford algorithm applied to a reformulated primal problem, and the Chambolle-Pock primal-dual algorithm.A key property exploited in most image deblurring methods is spatial invariance of the blurring operator, which makes it possible to use the fast Fourier transform (FFT) when solving linear equations involving the operator. In this thesis we extend this approach to two popular models for space-varying blurring operators, the Nagy-O'Leary model and the Efficient Filter Flow model. We show how splitting methods derived from the Douglasii Rachford algorithm can be implemented with a low complexity per iteration, dominated by a small number of FFTs.iii The dissertation of Daniel Verity O'Connor is approved.

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“…-It is easy to show that J d is continuous and convex -It has been proved in [11], in the case where H is a convolution operator, that:…”

Section: Optimization Problem Formulationmentioning

confidence: 99%

“…1 is the ℓ 1 norm. TIRF operator (1) satisfies the conditions used in [11] and then (3) holds which implies that J d is coercive.…”

Section: Optimization Problem Formulationmentioning

confidence: 99%

Sparse reconstruction from Multiple-Angle Total Internal Reflection fluorescence Microscopy

Soubies

Blanc‐Féraud

Schaub

et al. 2014

2014 IEEE International Conference on Image Processing (ICIP)

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Super-resolution microscopy techniques allow to overstep the diffraction limit of conventional optics. Theses techniques are very promising since they give access to the visualisation of finer structures which is of fundamental importance in biology. In this paper we deal with Multiple-Angle Total Internal Reflection Microscopy (MA-TIRFM) which allows to reconstruct 3D sub-cellular structures of a single layer of ∼ 300 nm behind the glass coverslip with a high axial resolution. The 3D volume reconstruction from a set of 2D measurements is an ill-posed inverse problem and a regularization is essential. Our aim in this work is to propose a new reconstruction method for sparse structures robust to Poisson noise and background fluorescence. The sparse property of the solution can be seen as a regularization using the 'ℓ 0 norm'. In order to solve this combinatorial problem, we propose a new algorithm based on smoothed 'ℓ 0 norm' allowing minimizing a non convex energy, composed of the Kullback-Leibler divergence data term and the ℓ 0 regularization term, in a Graduated Non Convexity framework.

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Space Variant Blind Image Restoration

Cited by 18 publications

References 43 publications

Deconvolution for multimode fiber imaging: modeling of spatially variant PSF

Deconvolution for multimode fiber imaging: modeling of spatially variant PSF

Primal-Dual Decomposition by Operator Splitting and Applications to Image Deblurring

Sparse reconstruction from Multiple-Angle Total Internal Reflection fluorescence Microscopy

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