A number of recent works have emphasized the prominent role played by the Kurdyka-Aojasiewicz inequality for proving the convergence of iterative algorithms solving possibly nonsmooth/nonconvex optimization problems. ...
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A number of recent works have emphasized the prominent role played by the Kurdyka-Aojasiewicz inequality for proving the convergence of iterative algorithms solving possibly nonsmooth/nonconvex optimization problems. In this work, we consider the minimization of an objective function satisfying this property, which is a sum of two terms: (i) a differentiable, but not necessarily convex, function and (ii) a function that is not necessarily convex, nor necessarily differentiable. The latter function is expressed as a separable sum of functions of blocks of variables. Such an optimization problem can be addressed with the Forward-Backward algorithm which can be accelerated thanks to the use of variable metrics derived from the majorize-minimize principle. We propose to combine the latter acceleration technique with an alternating minimization strategy which relies upon a flexible update rule. We give conditions under which the sequence generated by the resulting Block Coordinate Variable Metric Forward-Backward algorithm converges to a critical point of the objective function. An application example to a nonconvex phase retrieval problem encountered in signal/image processing shows the efficiency of the proposed optimization method.
The sample mean is one of the most fundamental concepts in statistics. Properties of the sample mean that are well-defined in Euclidean spaces become unclear in graph spaces. This paper proposes conditions under which...
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The sample mean is one of the most fundamental concepts in statistics. Properties of the sample mean that are well-defined in Euclidean spaces become unclear in graph spaces. This paper proposes conditions under which the following properties are valid: existence, uniqueness, and consistency of means, the midpoint property, necessary conditions of optimality, and convergence results of mean algorithms. The theoretical results address common misconceptions about the graph mean in graph edit distance spaces, serve as a first step towards a statistical analysis of graph spaces, and result in a theoretically well-founded mean algorithm that outperformed six other mean algorithms with respect to solution quality on different graph datasets representing images and molecules. (C) 2016 Elsevier Ltd. All rights reserved.
We present a mixture cure model with the survival time of the "uncured" group coming from a class of linear transformation models, which is an extension of the proportional odds model This class of model. fi...
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We present a mixture cure model with the survival time of the "uncured" group coming from a class of linear transformation models, which is an extension of the proportional odds model This class of model. first proposed by Dabrowska and Doksum ( 988). which we term "generalized proportional odds model," is well suited for the mixture cure model setting due to a clear separation between long-term and short-term effects A standard expectation-maximization algorithm can he employed to locate the nonparametric likelihood estimators which are shown to he consistent and semiparametric efficient However. there are difficulties in the M-step due to the nonparametric component We overcome these difficulties by proposing two different algorithms The first is to employ an majorize-minimize (MM) algorithm in the M-step instead of the usual Newton-Raphson method, and the other is based on an alternative form to express the model as a proportional hazards frailty model The two new algorithms are compared in a simulation study with an existing estimating equation approach by DJ and Ying (2004) The MM algorithm provides both computational stability and efficiency A case study of leukemia dam is conducted to illustrate the proposed procedures
We discuss in this paper the influence of line search on the performances of interior point algorithms applied for constrained signal restoration. Interior point algorithms ensure the fulfillment of the constraints th...
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ISBN:
(纸本)9781457705700
We discuss in this paper the influence of line search on the performances of interior point algorithms applied for constrained signal restoration. Interior point algorithms ensure the fulfillment of the constraints through the minimization of a criterion augmented with a barrier function. However, the presence of the barrier function can slow down the convergence of iterative descent algorithms when general-purpose line search procedures are employed. We recently proposed a line search algorithm, based on a majorization-minimization approach, which allows to handle the singularity introduced by the barrier function. We present here a comparative study of various line search strategies for the resolution of a sparse signal restoration problem with both primal and primal-dual interior point algorithms.
In multichannel imaging, several observations of the same scene acquired in different spectral ranges are available. Very often, the spectral components are degraded by a blur modelled by a linear operator and an addi...
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ISBN:
(纸本)9781479923410
In multichannel imaging, several observations of the same scene acquired in different spectral ranges are available. Very often, the spectral components are degraded by a blur modelled by a linear operator and an additive noise. In this paper, we address the problem of recovering the image components in a wavelet domain by adopting a variational approach. Our contribution is twofold. First, an appropriate multivariate penalty function is derived from a novel joint prior model of the probability distribution of the wavelet coefficients located at the same spatial position in a given subband through all the channels. Secondly, we address the challenging issue of computing the Maximum A Posteriori estimate by using a majorize-minimize optimization strategy. Simulation tests carried out on multispectral satellite images show that the proposed method outperforms conventional techniques.
Purpose: To accelerate denoising of magnitude diffusion-weighted images subject to joint rank and edge constraints. Methods: We extend a previously proposed majorize-minimize method for statistical estimation that inv...
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Purpose: To accelerate denoising of magnitude diffusion-weighted images subject to joint rank and edge constraints. Methods: We extend a previously proposed majorize-minimize method for statistical estimation that involves noncentral chi distributions to incorporate joint rank and edge constraints. A new algorithm is derived which decomposes the constrained noncentral chi denoising problem into a series of constrained Gaussian denoising problems each of which is then solved using an efficient alternating minimization scheme. Results: The performance of the proposed algorithm has been evaluated using both simulated and experimental data. Results from simulations based on ex vivo data show that the new algorithm achieves about a factor of 10 speed up over the original Quasi-Newton-based algorithm. This improvement in computational efficiency enabled denoising of large datasets containing many diffusion-encoding directions. The denoising performance of the new efficient algorithm is found to be comparable to or even better than that of the original slow algorithm. For an in vivo high-resolution Q-ball acquisition, comparison of fiber tracking results around hippocampus region before and after denoising will also be shown to demonstrate the denoising effects of the new algorithm. Conclusion: The optimization problem associated with denoising noncentral chi distributed diffusion-weighted images subject to joint rank and edge constraints can be solved efficiently using a majorize-minimize-based algorithm. (C) 2015 Wiley Periodicals, Inc.
In multichannel imaging, several observations of the same scene acquired in different spectral ranges are available. Very often, the spectral components are degraded by a blur modelled by a linear operator and an addi...
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ISBN:
(纸本)9781479923427
In multichannel imaging, several observations of the same scene acquired in different spectral ranges are available. Very often, the spectral components are degraded by a blur modelled by a linear operator and an additive noise. In this paper, we address the problem of recovering the image components in a wavelet domain by adopting a variational approach. Our contribution is twofold. First, an appropriate multivariate penalty function is derived from a novel joint prior model of the probability distribution of the wavelet coefficients located at the same spatial position in a given subband through all the channels. Secondly, we address the challenging issue of computing the Maximum A Posteriori estimate by using a majorize-minimize optimization strategy. Simulation tests carried out on multispectral satellite images show that the proposed method outperforms conventional techniques.
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