Limited-memory scaled gradient projection methods for real-time image deconvolution in microscopy

Porta, Federica; Zanella, Riccardo; Zanghirati, Gaetano; Zanni, Luca

doi:10.1016/j.cnsns.2014.08.035

Cited by 13 publications

(16 citation statements)

References 37 publications

(68 reference statements)

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“…• the Ritz-like values proposed by Fletcher [17] for a steepest descent method in the case of unconstrained optimization and recently extended to the SGP algorithm applied to a general constrained problem (1) [41,42].…”

Section: Edge Preserving Image Restorationmentioning

confidence: 99%

New convergence results for the scaled gradient projection method

Bonettini

Prato

2015

Inverse Problems

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Abstract. The aim of this paper is to deepen the convergence analysis of the scaled gradient projection (SGP) method, proposed by Bonettini et al. in a recent paper for constrained smooth optimization. The main feature of SGP is the presence of a variable scaling matrix multiplying the gradient, which may change at each iteration. In the last few years, an extensive numerical experimentation showed that SGP equipped with a suitable choice of the scaling matrix is a very effective tool for solving large scale variational problems arising in image and signal processing. In spite of the very reliable numerical results observed, only a weak, though very general, convergence theorem is provided, establishing that any limit point of the sequence generated by SGP is stationary. Here, under the only assumption that the objective function is convex and that a solution exists, we prove that the sequence generated by SGP converges to a minimum point, if the scaling matrices sequence satisfies a simple and implementable condition. Moreover, assuming that the gradient of the objective function is Lipschitz continuous, we are also able to prove the O(1/k) convergence rate with respect to the objective function values. Finally, we present the results of a numerical experience on some relevant image restoration problems, showing that the proposed scaling matrix selection rule performs well also from the computational point of view.

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Section: Edge Preserving Image Restorationmentioning

confidence: 99%

New convergence results for the scaled gradient projection method

Bonettini

Prato

2015

Inverse Problems

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“…Future work will include the analysis of the proposed method on real experimental images, where there is a limited number of observations and the sampling frequency is reduced. It is also contemplated to consider another formulation of the model by doing change of variables and designing suitable optimization methods, possibly exploiting the Fletcher step size adapted to the constrained case [12,13].…”

Section: Discussionmentioning

confidence: 99%

Phase estimation in differential-interference-contrast (DIC) microscopy

Bautista

Rebegoldi

Blanc‐Féraud

et al. 2016

2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI)

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We present a gradient-based optimization method for the estimation of a specimen's phase function from polychromatic DIC images. The method minimizes the sum of a nonlinear least-squares discrepancy measure and a smooth approximation of the total variation. A new formulation of the gradient and a recent updating rule for the choice of the step size are both exploited to reduce computational time. Numerical simulations on two computer-generated objects show significant improvements, both in efficiency and accuracy, with respect to a more standard choice of the step size.

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“…Future work will concern the application of the proposed strategies to real acquisitions and the reformulation of the minimization problem in terms of the specimen's transmission function e −iφ . This would lead to a standard regularized least-squares problem restricted to a nonconvex feasible set, which would require a generalization of the (VM)ILA approach able to account for nonconvex projections and to exploit the steplength selection rule proposed by Fletcher [25] in the presence of constraints [45,46].…”

Section: Discussionmentioning

confidence: 99%

A comparison of edge-preserving approaches for differential interference contrast microscopy

et al. 2017

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Abstract. In this paper we address the problem of estimating the phase from color images acquired with differential-interference-contrast microscopy. In particular, we consider the nonlinear and nonconvex optimization problem obtained by regularizing a least-squares-like discrepancy term with an edge-preserving functional, given by either the hypersurface potential or the total variation one. We investigate the analytical properties of the resulting objective functions, proving the existence of minimum points, and we propose effective optimization tools able to obtain in both the smooth and the nonsmooth case accurate reconstructions with a reduced computational demand.AMS classification scheme numbers: 65K05, 90C30, 90C90

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Limited-memory scaled gradient projection methods for real-time image deconvolution in microscopy

Cited by 13 publications

References 37 publications

New convergence results for the scaled gradient projection method

New convergence results for the scaled gradient projection method

Phase estimation in differential-interference-contrast (DIC) microscopy

A comparison of edge-preserving approaches for differential interference contrast microscopy

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