Scaled Heavy-Ball Acceleration of the Richardson-Lucy Algorithm for 3D Microscopy Image Restoration

Wang, Hongbin; Miller, Paul

doi:10.1109/tip.2013.2291324

Cited by 39 publications

(17 citation statements)

References 17 publications

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“…The Heavy-ball method uses previous iterates when computing the next, but in contrast to Nesterov's method it only uses the gradient at the current iterate. Extensions of the Heavy-ball method to constrained and distributed optimization problems have confirmed its performance benefits over the standard gradient-based methods [15][16][17].…”

mentioning

confidence: 91%

Global convergence of the Heavy-ball method for convex optimization

Ghadimi

Feyzmahdavian

Johansson

2015

2015 European Control Conference (ECC)

199

182

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This paper establishes global convergence and provides global bounds of the convergence rate of the Heavy-ball method for convex optimization problems. When the objective function has Lipschitz-continuous gradient, we show that the Cesáro average of the iterates converges to the optimum at a rate of O(1/k) where k is the number of iterations. When the objective function is also strongly convex, we prove that the Heavy-ball iterates converge linearly to the unique optimum.

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mentioning

confidence: 91%

Global convergence of the Heavy-ball method for convex optimization

Ghadimi

Feyzmahdavian

Johansson

2015

2015 European Control Conference (ECC)

199

182

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“…But is is possible to illustrate qualitatively the former results. In order to minimize the regularization functional, we have used Expectation-Minimization type iterative methods [16,15,22,45]. In each case investigated, we will study the decrease of the Kullback-Leibler functional as a function of the iterations.…”

Section: 2mentioning

confidence: 99%

Morozov principle for Kullback-Leibler residual term and Poisson noise

Sixou¹,

Hohweiller²,

Ducros³

2018

Inverse Problems &Amp; Imaging

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We study the properties of a regularization method for inverse problems corrupted by Poisson noise with Kullback-Leibler divergence as data term. The regularization parameter is chosen according to a Morozov type principle. We show that this method of choice of the parameter is well-defined. This a posteriori choice leads to a convergent regularization method. Convergences rates are obtained for this a posteriori choice of the regularization parameter when some source condition is satisfied.

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“…In their approach, the step size was adapted by a schedule based on second order statistics. Other works that have used the momentum term to accelerate convergence include object tracking by Le et al [33], image segmentation by Andersson et al [34], image deconvolution by Wang and Miller [35], and scene labelling and denoising by Domke [36].…”

Section: Related Workmentioning

confidence: 99%