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Distributed primal-dual splitting algorithm for Multiblock Separable Optimization Problems

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2022年第8期67卷 4264-4271页

作者： Li, Huaqing Wu, Xiangzhao Wang, Zheng Huang, Tingwen Southwest Univ Chongqing Key Lab Nonlinear Circuits & Intelligen Coll Elect & Informat Engn Chongqing 400715 Peoples R China Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia Texas A&M Univ Sci Program Doha 23874 Qatar

This article considers the distributed structured optimization problem of collaboratively minimizing the global objective function composed of the sum of local cost functions. Each local objective function involves a Lipschitz-differentiable convex function, a nonsmooth convex function, and a linear composite nonsmooth convex function. For such problems, we derive the synchronous distributed primal-dual splitting (S-DPDS) algorithm with uncoordinated stepsizes. Meanwhile, we develop the asynchronous version of the algorithm in light of the randomized block-coordinate method (A-DPDS). Further, the convergence results show the relaxed range and concise form of the acceptable parameters, which indicates that the algorithms are conducive to the selection of parameters in practical applications. Finally, we demonstrate the efficiency of S-DPDS and A-DPDS algorithms by numerical experiments.

关键词： Optimization Convex functions Distributed algorithms Convergence Linear programming Couplings Simulation Asynchronous algorithm distributed optimization primal-dual splitting algorithm uncoordinated stepsizes

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Stable and Lightweight Deep primal-dual Unrolling for Constrained Image Restoration with Convolutional Sparse Coding

Stable and Lightweight Deep Primal-Dual Unrolling for Constr...

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2025 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2025

作者： Ueki, Takafumi Naganuma, Kazuki Ono, Shunsuke Dept. Computer Science Institute of Science Tokyo Tokyo Japan

ISBN: (纸本)9798350368741

This paper proposes an image restoration method using a convolutional sparse coding (CSC) unrolling network with a box constraint and total variation. Unlike conventional deep unrolling methods, the proposed method constructs an interpretable lightweight network with restoration stability. Specifically, we design a new constrained convex optimization problem that incorporates CSC, a box constraint, and total variation (TV). The box constraint ensures that the image values fall within a certain range, making the restoration process stable. In addition, combining total variation and CSC leads to high interpretability and representation with a small number of parameters. We develop an optimization algorithm based on the primal-dual splitting (PDS) method. Then, by unrolling the algorithm, we construct the proposed lightweight network. Experimental results demonstrate the superiority of the proposed method in image restoration accuracy and lightweightness of the proposed network in the number of parameters. © 2025 IEEE.

关键词： box constraint convolutional sparse coding deep unrolling Image restoration primal-dual splitting algorithm

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DETERMINED BLIND SOURCE SEPARATION VIA PROXIMAL splitting algorithm

DETERMINED BLIND SOURCE SEPARATION VIA PROXIMAL SPLITTING AL...

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

作者： Yatabe, Kohei Kitamura, Daichi Waseda Univ Dept Intermedia Art & Sci Tokyo Japan Univ Tokyo Dept Informat Phys & Comp Tokyo Japan

ISBN: (纸本)9781538646588

The state-of-the-art algorithms of determined blind source separation (BSS) methods based on the independent component analysis (ICA) have gained computational efficiency by the majorization-minimization (MM) principle with a price of losing flexibility. That is, replacing and comparing different source models are not easy in such MM-based framework because it requires efforts to derive a new algorithm each time when one changes the model. In this paper, a general framework for obtaining an ICA-based BSS algorithm is proposed so that a source model can easily be replaced because only a single line of the algorithm must be modified. A sparsity-based extension of the independent vector analysis and a low-rankness-based BSS model using the nuclear norm are also proposed to demonstrate the simplicity and easiness of the proposed framework.

关键词： Independence-based separation frequency domain independent component analysis (FDICA) independent vector analysis (IVA) primal-dual splitting algorithm proximity operator

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GRADIENT-DOMAIN IMAGE DECOMPOSITION FOR IMAGE RECOVERY

GRADIENT-DOMAIN IMAGE DECOMPOSITION FOR IMAGE RECOVERY

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IEEE International Conference on Image Processing (ICIP)

作者： Watanabe, Makoto Kyochi, Seisuke Ono, Shunsuke Univ Kitakyushu Dept Informat & Media Engn 1-1 Wakamatsu Kitakyushu Fukuoka 8080135 Japan Tokyo Inst Technol Imaging Sci & Engn Lab Midori Ku Yokohama Kanagawa 2268503 Japan

ISBN: (纸本)9781479983391

This paper aims to introduce a convex prior based on gradient-domain image decomposition (GID) for image recovery. As a useful class of convex priors, total variation (TV) and its variants have been widely investigated. Among them, total generalized variation (TGV) is paid much attention recently, because it provides rich visual quality around edges and gradation regions in recovered images. This paper gives a general perspective: the TGV can be regarded as a GID and thus can be extended to more general formulation. Specifically, by introducing some priors promoting desired properties on gradient components which cannot be treated efficiently by the TGV, the restored image would attain better visual quality. As a practical instance, we incorporate block nuclear norm (BNN), which can characterize local low rankness, into the GID framework to keep the visual quality of well-patterned textures. Consequently, the GID provides better subjective visual quality and less reconstruction error in missing pixel recovery, than the TGV-based and the TV/BNN-based regularization methods.

关键词： Convex optimization Image recovery Total generalized variation Gradient-domain image decomposition primal-dual splitting algorithm

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Static-Scene Constrained Optimization for Matrix/Tensor-Decomposition-free Foreground-Background Separation 48

Static-Scene Constrained Optimization for Matrix/Tensor-Deco...

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48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023

作者： Naganuma, Kazuki Ono, Shunsuke Tokyo Institute of Technology Kanagawa Japan

ISBN: (纸本)9781728163277

We propose an efficient foreground-background separation (FBS) method for (possibly noisy) video data. Most existing FBS methods model the background as a low-rank component. However, this approach is computationally expensive because it requires matrix/tensor decomposition of high-dimensional videos. In this paper, we first introduce a new background model, named static scene constraint (SSC), to FBS. SSC plays a role in accurately capturing the static background by keeping the temporal gradient of the background component to zero. In addition, SSC is formulated as a convex constraint using differences in the temporal direction, which eliminates the need for matrix/tensor decomposition in optimization and significantly reduces the computational cost compared to existing low-rank-based background models. Second, we formulate the FBS problem as a convex optimization problem involving SSC and develop an efficient solver based on a preconditioned primal-dual splitting algorithm, which can automatically determine the appropriate stepsizes based on problem structure. Finally, we demonstrate the efficiency and effectiveness of our method compared with state-of-the-art FBS methods through experiments using infrared and electron microscope videos. © 2023 IEEE.

关键词： electron microscope data Foreground-background separation gradient constraint infrared data primal-dual splitting algorithm

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Determined Blind Source Separation via Proximal splitting algorithm

Determined Blind Source Separation via Proximal Splitting Al...

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Kohei Yatabe Daichi Kitamura Departrnent of Intermedia Art and Science Waseda University Tokyo Japan Department of Information Physics and Computing The University of Tokyo Tokyo Japan

ISBN: (纸本)9781538646595

关键词： Independence-based separation frequency domain independent component analysis (FDICA) independent vector analysis (IVA) primal-dual splitting algorithm proximity operator Blind source separation algorithms single line Vector Analysis Independent component analysis Source separation Frameworks

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GRADIENT-DOMAIN IMAGE DECOMPOSITION FOR IMAGE RECOVERY

GRADIENT-DOMAIN IMAGE DECOMPOSITION FOR IMAGE RECOVERY

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IEEE International Conference on Image Processing

作者： Makoto Watanabe Seisuke Kyochi Shunsuke Ono Dept. of Information and Media Engineering The University of Kitakyushu Imaging Science and Engineering Laboratory Tokyo Institute of Technology

ISBN: (纸本)9781479983407

关键词： Convex optimization Image recovery Total generalized variation Gradient-domain image decomposition primal-dual splitting algorithm group identification number images Convex function Train A Grande Vitesse thoracic gas volume reconstruction error Visualization decomposition

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