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Dynamic thresholding algorithm with memory for linear inverse problems

INVERSE PROBLEMS 2025年第1期41卷

作者： Sun, Zhong-Feng Zhao, Yun-Bin Zhou, Jin-Chuan Huang, Zheng-Hai Shandong Univ Technol Sch Math & Stat Zibo Shandong Peoples R China Chinese Univ Hong Kong Shenzhen Int Ctr Ind & Appl Math SRIBD Shenzhen Peoples R China Tianjin Univ Sch Math Tianjin Peoples R China

The relaxed optimal k-thresholding pursuit (ROTP) is a recent algorithm for linear inverse problems. This algorithm is based on the optimal k-thresholding technique which performs vector thresholding and error metric reduction simultaneously. Although ROTP can be used to solve small to medium-sized linear inverse problems, the computational cost of this algorithm is high when solving large-scale problems. By merging the optimal k-thresholding technique and iterative method with memory as well as optimization with sparse search directions, we propose the so-called dynamic thresholding algorithm with memory (DTAM), which iteratively and dynamically selects vector bases to construct the problem solution. At every step, the algorithm uses more than one or all iterates generated so far to construct a new search direction, and solves only the small-sized quadratic subproblems at every iteration. Thus the computational complexity of DTAM is remarkably lower than that of ROTP-type methods. It turns out that DTAM can locate the solution of linear inverse problems if the matrix involved satisfies the restricted isometry property. Experiments on synthetic data, audio signal reconstruction and image denoising demonstrate that the proposed algorithm performs comparably to several mainstream thresholding and greedy algorithms, and it works faster than the ROTP-type algorithms especially when the sparsity level of signal is relatively low.

关键词： linear inverse problems thresholding algorithm restricted isometry property signal reconstruction image denoising

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A thresholding algorithm for Willmore-type flows via fourth-order linear parabolic equation

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INTERFACES AND FREE BOUNDARIES 2025年第2期27卷 235-283页

作者： Ishii, Katsuyuki Kohsaka, Yoshihito Miyake, Nobuhito Sakakibara, Koya Kobe Univ Grad Sch Maritime Sci 5-1-1 Fukaeminami MachiHigashinada Ku Kobe 6580022 Japan Kyushu Univ Fac Math 744 MotookaNishi Ku Fukuoka 8190395 Japan Kanazawa Univ Inst Sci & Engn Fac Math & Phys Kakuma Machi Kanazawa 9201192 Japan RIKEN Interdisciplinary Theoret & Math Sci Program iTHEM 2-1 Hirosawa Wako 3510198 Japan

We propose a thresholding algorithm to Willmore-type flows in R-N. This algorithm is constructed based on the asymptotic expansion of the solution to the initial value problem for a fourth order linear parabolic partial differential equation whose initial data is the indicator function on the compact set Omega(0). The main results of this paper demonstrate that the boundary partial derivative Omega(t) of the new set Omega(t), generated by our algorithm, is included in O(t)-neighborhood of partial derivative Omega(0) for small t > 0 and that the normal velocity from partial derivative Omega(0) to partial derivative Omega(t) is nearly equal to the L-2-gradient of Willmore-type energy for small t > 0. Finally, numerical examples of planar curves governed by the Willmore flow are provided by using our thresholding algorithm.

关键词： thresholding algorithm Willmore-type energy gradient flow

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ADAPTIVE thresholding algorithm AND ITS HARDWARE IMPLEMENTATION

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PATTERN RECOGNITION LETTERS 1994年第2期15卷 141-150页

作者： YANG, JD CHEN, YS HSU, WH YUAN ZE INST TECHNOL DEPT ELECT ENGNTAYUAN 320TAIWAN NATL TSING HUA UNIV INST ELECT ENGNHSINCHU 300TAIWAN ACAD SINICA INST INFORMAT SCITAIPEI 115TAIWAN

This paper presents an adaptive raster-scan thresholding algorithm which can deal with an image acquired under imperfect illumination. A statistical measurement called LSSD (Largest Static State Difference) relating to the gray-level variation is found first, According to the measurement, the pixels are separated into static and transient states which are treated by two different procedures, respectively. A hardware implementation of this algorithm shows that the real-time requirement can be met. Experiments of applying this algorithm to extracting characters from documents confirmed that a reasonable binary image can be efficiently and effectively obtained from a gray-level image under various illuminations.

关键词： thresholding algorithm LARGEST STATIC STATE DIFFERENCE SEGMENTATION

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Sparse signal recovery by accelerated _q (0<q<1) thresholding algorithm

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2017年第12期94卷 2481-2491页

作者： Zhang, Yong Ye, Wan-Zhou Zhang, Jian-Jun Shanghai Univ Coll Sci Dept Mat Shanghai 200444 Peoples R China

The nonconvex regularization, which has superiority on sparsity-inducing over the convex counterparts, has been proposed in many areas of engineering and science. In this paper, we present an accelerated regularization thresholding algorithm for sparse signal recovery, which can be viewed as an extension of the well-known Nesterov's accelerated gradient method from convex optimization to nonconvex case. It has shown numerically that the proposed algorithm keeps fast convergence, and also maintains high recovery precision. Extensive numerical experiments have been to demonstrate the effectiveness of the proposed algorithm. It is also mentioned that the proposed algorithm has much faster convergence and higher recovery precision in sparse signal recovery over the commonly non-accelerated thresholding algorithm.

关键词： Compressed sensing sparse signal recovery thresholding algorithm l(q) regularization nonlinear optimization 68W40 45Q05 90C30

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A thresholding algorithm for sparse recovery via Laplace norm

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SIGNAL IMAGE AND VIDEO PROCESSING 2019年第2期13卷 389-395页

作者： Wang, Qian Qu, Gangrong Han, Guanghui Tianjin Univ Commerce Sch Sci Tianjin Peoples R China Beijing Jiaotong Univ Sch Sci Beijing Peoples R China BCMIIS Beijing Peoples R China

The last decade has witnessed rapidly growing interest in the studies of compressed sensing. p norm, an approximation to 0 norm, can be used to recover a sparse signal from underdetermined linear systems. In comparison with p norm, another approximation called Laplace norm is a closer approximation to 0 norm. The thresholding algorithm is a simple and efficient iterative process to solve the regularization problem. In this paper, we derive the thresholding point and a quasi-analytic thresholding representation for the Laplace regularization, and then a thresholding algorithm for the Laplace regularization is proposed. The numerical results show that the proposed algorithm has higher recovery rate than the p thresholding algorithms. This thresholding representation can be easily incorporated into the iterative thresholding framework to provide a tool for sparsity problems.

关键词： Compressed sensing Sparse signal Regularization model thresholding algorithm Signal processing

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A new iterative firm-thresholding algorithm for inverse problems with sparsity constraints

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APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 2013年第1期35卷 151-164页

作者： Voronin, Sergey Woerdeman, Hugo J. Princeton Univ Program Appl & Computat Math Princeton NJ 08544 USA Drexel Univ Dept Math Philadelphia PA 19104 USA

In this paper we propose a variation of the soft-thresholding algorithm for finding sparse approximate solutions of the equation Ax = b, where as the sparsity of the iterate increases the penalty function changes. In this approach, sufficiently large entries in a sparse iterate are left untouched. The advantage of this approach is that a higher regularization constant can be used, leading to a significant reduction of the total number of iterations. Numerical experiments for sparse recovery problems, also with noisy data, are included. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Inverse problem Sparsity thresholding algorithm Firm thresholding Compressed sensing

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Performance Guarantees of the thresholding algorithm for the Cosparse Analysis Model

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IEEE TRANSACTIONS ON INFORMATION THEORY 2013年第3期59卷 1832-1845页

作者： Peleg, Tomer Elad, Michael Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel Technion Israel Inst Technol Dept Comp Sci IL-32000 Haifa Israel

The cosparse analysis model for signals assumes that the signal of interest can be multiplied by an analysis dictionary, leading to a sparse outcome. This model stands as an interesting alternative to the more classical synthesis-based sparse representation model. In this paper, we propose a theoretical study of the performance guarantee of the thresholding algorithm for the pursuit problem in the presence of noise. Our analysis reveals two significant properties of, which govern the pursuit performance: the first is the degree of linear dependencies between sets of rows in, depicted by the cosparsity level. The second property, termed the restricted orthogonal projection property, is the level of independence between such dependent sets and other rows in. We show how these dictionary properties are meaningful and useful, both in the theoretical bounds derived and in a series of experiments that are shown to align well with the theoretical prediction.

关键词： Analysis model linear dependencies probability of success restricted orthogonal projection property (ROPP) sparse representations thresholding algorithm

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Fully Parallel Implementation of Otsu Automatic Image thresholding algorithm on FPGA

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SENSORS 2021年第12期21卷 4151-4151页

作者： Barros, Wysterlanya K. P. Dias, Leonardo A. Fernandes, Marcelo A. C. Univ Fed Rio Grande do Norte Lab Machine Learning & Intelligent Instrumentat nPITI IMD BR-59078970 Natal RN Brazil Univ Birmingham Ctr Cyber Secur & Privacy Sch Comp Sci Birmingham B15 2TT W Midlands England Univ Fed Rio Grande do Norte Dept Comp & Automat Engn BR-59078970 Natal RN Brazil

This work proposes a high-throughput implementation of the Otsu automatic image thresholding algorithm on Field Programmable Gate Array (FPGA), aiming to process high-resolution images in real-time. The Otsu method is a widely used global thresholding algorithm to define an optimal threshold between two classes. However, this technique has a high computational cost, making it difficult to use in real-time applications. Thus, this paper proposes a hardware design exploiting parallelization to optimize the system's processing time. The implementation details and an analysis of the synthesis results concerning the hardware area occupation, throughput, and dynamic power consumption, are presented. Results have shown that the proposed hardware achieved a high speedup compared to similar works in the literature.

关键词： FPGA image segmentation thresholding algorithm Otsu's method

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An inverse problem of finding a time-dependent parameter in a bilinear heat equation

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JOURNAL OF INVERSE AND ILL-POSED PROBLEMS 2025年

作者： El Mezegueldy, Redouane Ouakrim, Youssef Ouzahra, Mohamed Univ Sidi Mohamed Ben Abdellah Ecole Normale Super MASI Lab Fes Morocco

This paper investigates the inverse problem of estimating an unknown bilinear control u, applied locally in a reaction-diffusion equation. Our goal is to achieve a temperature profile close to a desired reference at the final time. We formulate the problem as an optimal control framework and analyze the existence, optimality conditions and stability of the solution with respect to the data. An algorithm and some numerical experiments are proposed to show the effectiveness of our approach in steering the system towards a desired state.

关键词： Reaction-diffusion equation inverse problem time-dependent control bilinear control thresholding algorithm

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Fast pairwise nearest neighbor based algorithm for multilevel thresholding

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JOURNAL OF ELECTRONIC IMAGING 2003年第4期12卷 648-659页

作者： Virmajoki, O Fränti, P Univ Joensuu Dept Comp Sci FIN-80101 Joensuu Finland

We propose a fast pairwise nearest neighbor (PNN)-based O(N log N) time algorithm for multilevel nonparametric thresholding, where N denotes the size of the image histogram. The proposed PNN-based multilevel thresholding algorithm is considerably faster than optimal thresholding. On a set of 8 to 16 bits-per-pixel real images, experimental results also reveal that the proposed method provides better quality than the Lloyd-Max quantizer alone. Since the time complexity of the proposed thresholding algorithm is log linear, it is applicable in real-time image processing applications. (C) 2003 SPIE and IST.

关键词： .log time thresholds between-class maximizing quantizer Fast pairwise thresholding algorithm optimal thresholding

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