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检索条件"主题词=proximal algorithm"

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CALIBRATIONLESS OSCAR-BASED IMAGE RECONSTRUCTION IN COMPRESSED SENSING PARALLEL MRI 16

CALIBRATIONLESS OSCAR-BASED IMAGE RECONSTRUCTION IN COMPRESS...

引用

16th IEEE International Symposium on Biomedical Imaging (ISBI)

作者： El Gueddari, L. Ciuciu, P. Chouzenoux, E. Vignaud, A. Pesquet, J-C CEA NeuroSpin Bat 145 F-91191 Gif Sur Yvette France Univ Paris Saclay Parietal Team INRIA CEA Saclay Ile de France St Aubin France Univ Paris Saclay Cent Supelec CVN St Aubin France Paris Est Univ LIGM Champs Sur Marne France

ISBN: (纸本)9781538636411

Reducing acquisition time is a crucial issue in MRI especially in the high resolution context. Compressed sensing has faced this problem for a decade. However, to maintain a high signal-to-noise ratio (SNR), CS must be combined with parallel imaging. This leads to harder reconstruction problems that usually require the knowledge of coil sensitivity profiles. In this work, we introduce a calibrationless image reconstruction approach that no longer requires this knowledge. The originality of this work lies in using for reconstruction a group sparsity structure (called OSCAR) across channels that handles SNR inhomogeneities across receivers. We compare this reconstruction with other calibrationless approaches based on group LASSO and its sparse variation as well as with the auto-calibrated method called l(1)-ESPIRiT. We demonstrate that OSCAR outperforms its competitors and provides similar results to l(1)-ESPIRiT. This suggests that the sensitivity maps are no longer required to perform combined CS and parallel imaging reconstruction.

关键词： Compressed Sensing Parallel MRI Group Sparsity proximal algorithm

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Joint decomposition of multichannel signals with multimarginal optimal transport 32

Joint decomposition of multichannel signals with multimargin...

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32nd European Signal Processing Conference (EUSIPCO)

作者： Mallejac, Jean Idier, Jerome Soussen, Charles Li, Xiangyi Univ Paris Saclay CentraleSupelec CNRS L2S F-91192 Gif Sur Yvette France Nantes Univ Ecole Cent Nantes CNRS LS2N F-44000 Nantes France Aix Marseille Univ Cent Marseille CNRS Inst Fresnel F-13013 Marseille France

ISBN: (纸本)9789464593617;9798331519773

The joint decomposition of a sequence of signals is addressed, where each signal is coded within a predefined dictionary. We propose a convex variational formulation involving a regularization term based on optimal transport. The latter is designed so as to promote proximity between neighboring channels. Two kinds of regularization criteria are designed, corresponding to distinct cross-channel information on the transport of dictionary atoms from one channel to another. The resulting optimization problems are reformulated as quadratic programs and solved using a proximal algorithm. The proposed approach is analyzed for a multichannel deconvolution problem.

关键词： Inverse problem multichannel decomposition optimal transport proximal algorithm

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LEARNING COMPACT PARTIAL DIFFERENTIAL EQUATIONS FOR COLOR IMAGES WITH EFFICIENCY 44

LEARNING COMPACT PARTIAL DIFFERENTIAL EQUATIONS FOR COLOR IM...

引用

44th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Zhao, Zhenyu Hou, Chenping Lin, Bo Fang, Cong Natl Univ Def Technol Coll Liberal Arts & Sci Changsha Hunan Peoples R China Peking Univ Sch EECS Key Lab Machine Percept MOE Beijing Peoples R China

ISBN: (纸本)9781479981311

Learning Partial Differential Equations (LPDEs) from training data for particular tasks has been successfully applied to many image processing problems. In this paper, we aim to learn compact Partial Differential Equations (LCPDEs) for color image tasks by proposing a more effective algorithm. The LCPDEs system is formulated as a linear combination of fundamental differential invariants and simplified by omitting the PDE which works as an indicate function. We replace L2-norm with L1-norm to regularize the coefficients with respect to the invariants. As the objective function is non-smooth, we resort to proximal algorithm to optimize it, which ensures convergence in an at least sub-linear rate. Experiments demonstrate the advantages of the proposed method over other PDE-based methods in terms of both quality and efficiency.

关键词： Partial differential equations L1-norm regularization proximal algorithm Color images

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STRUCTURED SUPPORT EXPLORATION FOR MULTILAYER SPARSE MATRIX FACTORIZATION

STRUCTURED SUPPORT EXPLORATION FOR MULTILAYER SPARSE MATRIX ...

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

作者： Quoc-Tung Le Gribonval, Remi Univ Lyon ENS Lyon UCBL CNRSInriaLIP F-69342 Lyon 07 France

ISBN: (纸本)9781728176055

Matrix factorization with sparsity constraints plays an important role in many machine learning and signal processing problems such as dictionary learning, data visualization, dimension reduction. Among the most popular tools for sparse matrix factorization are proximal algorithms, a family of algorithms based on proximal operators. In this paper, we address two problems with the application of proximal algorithms to sparse matrix factorization. On the one hand, we analyze a weakness of proximal algorithms in sparse matrix factorization: the premature convergence of the support. A remedy is also proposed to address this problem. On the other hand, we describe a new tractable proximal operator called Generalized Hungarian Method, associated to so-called k-regular matrices, which are useful for the factorization of a class of matrices associated to fast linear transforms. We further illustrate the effectiveness of our proposals by numerical experiments on the Hadamard Transform and magnetoencephalography matrix factorization.

关键词： Matrix factorization Sparsity Support Exploration Hungarian Method proximal algorithm

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New Demiclosedness Principles for (Firmly) Nonexpansive Operators 1

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Workshop on Computational and Analytical Mathematics

作者： Bauschke, Heinz H. Univ British Columbia Dept Math Kelowna BC V1V 1V7 Canada

ISBN: (数字)9781461476214

ISBN: (纸本)9781461476214;9781461476207

The demiclosedness principle is one of the key tools in nonlinear analysis and fixed point theory. In this note, this principle is extended and made more flexible by two mutually orthogonal affine subspaces. Versions for finitely many (firmly) nonexpansive operators are presented. As an application, a simple proof of the weak convergence of the Douglas-Rachford splitting algorithm is provided.

关键词： Demiclosedness principle Douglas-Rachford algorithm Firmly nonexpansive mapping Maximal monotone operator Nonexpansive mapping proximal algorithm Resolvent Splitting algorithm

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A Triple Stabilized Bundle Method for Constrained Nonconvex Nonsmooth Optimization 6th

A Triple Stabilized Bundle Method for Constrained Nonconvex ...

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6th International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA)

作者： Dembele, Andre Ndiaye, Babacar M. Ouorou, Adam Degla, Guy Univ Abomey Calavi Inst Math & Phys Sci Porto Novo Benin Univ Cheikh Anta Diop Dakar Lab Math Decis & Numer Anal Dakar 45087 Senegal Orange Labs Res Ave Republ F-92320 Chatillon France

ISBN: (纸本)9783030383640;9783030383633

In this paper, we provide an exact reformulation of Nonsmooth Constrained optimization Problems (NCP) using the Moreau-Yosida regularization. This reformulation allows the transformation of (NCP) to a sequence of convex programs of which solutions are feasible for (NCP). This sequence of solutions of auxiliary programs converges to a local solution of (NCP). Assuming Slater constraint qualification and basing on an exact penalization, our reformulation combined with a nonconvex proximal bundle method provides a local solution of (NCP). Our bundle method allows a strong update of the level set, may reduce significantly the number of null-steps and gives a new stopping criterion. Finally, numerical simulations are carried out.

关键词： proximal algorithm Bundle method Nonconvex optimization Nonsmooth optimization Reformulation

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Monotone Operator Methods for Nash Equilibria in Non-potential Games 1

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Workshop on Computational and Analytical Mathematics

作者： Briceno-Arias, Luis M. Combettes, Patrick L. Univ Chile Ctr Math Modeling CNRS UMI 2807 Dept Math Santiago Chile Univ Tecn Federico Santa Maria Santiago Chile UPMC Univ Paris 06 Lab Jacques Louis Lions UMR CNRS 7598 F-75005 Paris France

ISBN: (数字)9781461476214

ISBN: (纸本)9781461476214;9781461476207

We observe that a significant class of Nash equilibrium problems in non-potential games can be associated with monotone inclusion problems. We propose splitting techniques to solve such problems and establish their convergence. Applications to generalized Nash equilibria, zero-sum games, and cyclic proximation problems are demonstrated.

关键词： Monotone operator Nash equilibrium Potential game proximal algorithm Splitting method Zero-sum game

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A Convex Optimization Approach for Image Resolution Enhancement from Compressed Representations

A Convex Optimization Approach for Image Resolution Enhancem...

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18th International Conference on Digital Signal Processing (DSP)

作者： Gaetano, Raffaele Pesquet-Popescu, Beatrice Chaux, Caroline Telecom ParisTech Paris France Univ Aix Marseille CNRS LATP UMR 7353 Marseille France

ISBN: (纸本)9781467358057

Quality of experience in future home devices is foreseen to drastically increase, with the increase in image resolution. Displays with a horizontal resolution of 4K pixels are already appearing, and 8K Super-HiVision has already been demonstrated. Currently, only spatial upsampling of conventional HD format is performed to match the resolution of such displays. In this paper, we propose a novel method for high-quality up-conversion of legacy visual content in order to fit the screen resolution. More precisely, by assuming that we have various versions of the same image at standard resolution, encoded with different parameters, we try to reconstruct the high resolution image with higher quality than a simple interpolation. To this end, we adopt a variational formulation of the problem and construct a convex constrained criterion that incorporates both a fidelity term (linked to the acquisition process) and some a priori information. A recent primal-dual proximal algorithm is used to solve the associated minimization problem and simulation results show the good performance and behavior of the proposed approach.

关键词： super-resolution convex optimization proximal algorithm

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An Efficient Waveform Design Method with Spectral Coexistence and Pulse-like Autocorrelation Function

An Efficient Waveform Design Method with Spectral Coexistenc...

引用

IEEE Radar Conference (RadarConf)

作者： Zhang, Cut Pei, Jifang Zhang, Yujie Zhang, Yin Huo, Weibo Huang, Yulin Yang, Jianyu Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 611731 Peoples R China

ISBN: (纸本)9798350329216;9798350329209

Spectrum coexistence capability is particularly important for radar systems in complex electromagnetic environments, since it can suppress interference arising from signals in the common frequency band. In this paper, a unimodular waveform design method based on the Karush-Kuhn-Tucker (KKT) conditions is proposed to design transmit waveforms with spectral coexistence and pulse-like autocorrelation function. First, we construct the joint optimization problem as a stopband minimization problem subject to energy spectral density (ESD) and amplitude constraints. Subsequently, the constructed optimization problem is decomposed into multiple subproblems with a single constraint. In particular, we solve the coupling variables by analyzing the KKT conditions for the coupling subproblem. The proposed method achieves simultaneous optimization of spectral coexistence and pulse-like autocorrelation by constructing a new optimization framework and introducing a proximal algorithm, which also reduces the computational complexity and improves the efficiency of waveform design. Numerical simulation results demonstrate the effectiveness of the proposed method in terms of runtime and waveform characteristics.

关键词： Unimodular waveform spectral coexistence autocorrelation joint optimization proximal algorithm

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DUAL CONSTRAINED TV-BASED REGULARIZATION

DUAL CONSTRAINED TV-BASED REGULARIZATION

引用

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

作者： Couprie, Camille Talbot, Hugues Pesquet, Jean-Christophe Najman, Laurent Grady, Leo Univ Paris Est Lab Informat Gaspard Monge Champs Sur Marne France Siemens Corp Res Dept Imaging Analyt & Informat Princeton NJ USA

ISBN: (纸本)9781457705397

algorithms based on the minimization of the Total Variation are prevalent in computer vision. They are used in a variety of applications such as image denoising, compressive sensing and inverse problems in general. In this work, we extend the TV dual framework that includes Chambolle's and Gilboa-Osher's projection algorithms for TV minimization in a flexible graph data representation by generalizing the constraint on the projection variable. We show how this new formulation of the TV problem may be solved by means of a fast parallel proximal algorithm, which performs better than the classical TV approach for denoising, and is also applicable to inverse problems such as image deblurring.

关键词： proximal algorithm inverse problems image denoising convex optimization image restoration

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