Article
Engineering, Electrical & Electronic
Thuong Nguyen Canh, Byeungwoo Jeon
Summary: This work introduces a novel sampling matrix RSRM, aiming to improve sensing and compressing efficiency while maintaining security. RSRM combines the advantages of frame-based and block-based sensing, achieving compressive measurements through random projection of multiple randomly sub-sampled signals, and satisfying the Restricted Isometry Property.
SIGNAL PROCESSING-IMAGE COMMUNICATION
(2021)
Article
Engineering, Electrical & Electronic
Yujia Xie, Xinhua Su, Huanmin Ge
Summary: Recently, non-convex and non-linear metrics have been used in compressed sensing to promote sparsity. This letter proposes an extension of the l(1)/l(2) minimization method for sparse recovery, using the l(1)/l(p) minimization method with p > 1. We establish sufficient conditions for the l(1)/l(p) minimization to recover sparse signals under the restricted isometry property (RIP). Additionally, we develop an effective algorithm to solve the l(1)/l(p) minimization problem. Experimental results show that the proposed method is comparable to state-of-the-art methods for sparse signal recovery.
IEEE SIGNAL PROCESSING LETTERS
(2023)
Article
Computer Science, Artificial Intelligence
Huanmin Ge, Wengu Chen, Michael K. Ng
Summary: The paper discusses the application and advantages of l(1) - l(2) regularization in signal and image processing, explores more precise conditions for the method, and proposes new analysis techniques and restricted isometry property to guarantee accurate and stable signal recovery.
SIAM JOURNAL ON IMAGING SCIENCES
(2021)
Article
Computer Science, Hardware & Architecture
Haiyang Zou, Wengang Zhao
Summary: In this paper, a scaled null space property method is proposed for sparse signal recovery. By scaling down the vectors in the null space of the sensing matrix, more relaxed RIP conditions are established, ensuring the bounded approximation recovery of sparse signals in bounded noisy environments.
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES
(2022)
Article
Automation & Control Systems
Yunyi Li, Yiqiu Jiang, Hengmin Zhang, Jianxun Liu, Xiangling Ding, Guan Gui
Summary: Compressive sensing (CS) based computed tomography (CT) image reconstruction aims to reduce radiation risk by using sparse-view projection data. However, it is challenging to achieve satisfactory image quality from incomplete projections. This paper proposes an L 1 / 2-regularized nonlocal self-similarity (NSS) denoiser based CT reconstruction model that combines with low-rank approximation and group sparse coding (GSC) framework. Experimental results on clinical CT images show that the proposed approach outperforms popular approaches.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Electrical & Electronic
Junlin Li, Wei Zhou, Xiuting Li
Summary: In this paper, we study a broad class of nonconvex and nonsmooth composition optimization problems and propose a proximal alternating partially linearized minimization (PAPLM) algorithm to solve them. The effectiveness and superior performance of the proposed algorithm are demonstrated through theoretical analysis and numerical experiments.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2023)
Article
Multidisciplinary Sciences
Ginkyu Choi, Soon-Mo Jung
Summary: The paper proves the generalized Hyers-Ulam stability of isometries, particularly focusing on stability for restricted domains. It specifically demonstrates the stability of the orthogonality equation and uses this result to show the stability of two other equations on restricted domains. These functional equations are symmetric, remaining the same even if the roles of variables x and y are exchanged.
Article
Automation & Control Systems
Amir Moslemi
Summary: Compressive sensing is applied to reduce the number of samples required for classification in representation learning. A novel approach is presented where image pixels are treated as sensors to identify the optimal sensors in feature space. Spatial sensor locations are learned to identify discriminative information regions within images. L1-2 minimization, RRQR and SVM are used for sparse minimization, feature space extraction and discrimination vector acquiring. The proposed method is evaluated on four experiments and outperforms a state-of-art technique.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2023)
Article
Engineering, Electrical & Electronic
Michael Koller, Wolfgang Utschick
Summary: This paper introduces a learning-based algorithm to obtain a measurement matrix for compressive sensing-related recovery problems. The algorithm focuses on matrices with a constant modulus constraint and aims to distribute points on a low-dimensional hypersphere uniformly to combat measurement noise. Numerical experiments show that the algorithm performs better than traditional random matrices, and a method adapted to the constant modulus constraint is also proposed.
Article
Mathematics, Applied
Manxia Cao, Wei Huang, Shuaijun Lv
Summary: This paper investigates the recovery conditions and guarantees of the weighted l(p) minimization method with multiple different weights. The study reveals that the recovery conditions for the weighted l(p) minimization method with non-uniform weights are weaker than those with a single weight when p is within the range of (0, 0.8]. Furthermore, the weighted l(p) minimization method with non-uniform weights demonstrates better upper limits for recovery error in the presence of noise compared to the method with a single weight. Numerical experiments on synthetic signals validate the findings, and the results are applied to the recovery of sparse signals using a redundant dictionary.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Computer Science, Information Systems
Yamin Ru, Fang Li, Faming Fang, Guixu Zhang
Summary: In this paper, a model based on non-convex weighted Smoothly Clipped Absolute Deviation (SCAD) prior is proposed to address the issue of unequal treatment of singular values in the nuclear norm method. Through numerical experiments and theoretical analysis, the effectiveness and convergence of the proposed method are demonstrated.
INFORMATION SCIENCES
(2022)
Article
Remote Sensing
Shijin Li, Shubi Zhang, Yandong Gao, Tao Li, Jiazheng Han, Qiang Chen, Yansuo Zhang, Yu Tian
Summary: In this paper, a time series phase unwrapping algorithm using LP-norm optimization compressive sensing is proposed, which can accurately unwrap phase information in the case of intense noise and steep deformation gradients, improving the accuracy of deformation interpretation.
INTERNATIONAL JOURNAL OF APPLIED EARTH OBSERVATION AND GEOINFORMATION
(2023)
Article
Computer Science, Artificial Intelligence
Mehmet Yamac, Ugur Akpinar, Erdem Sahin, Moncef Gabbouj, Serkan Kiranyaz
Summary: Efforts in compressive sensing (CS) literature can be categorized into finding a measurement matrix that preserves compressed information effectively and finding a reliable reconstruction algorithm. While traditional CS methods use random matrices and iterative optimizations, recent deep learning-based solutions accelerate recovery and improve accuracy. However, jointly learning the entire measurement matrix remains challenging. This work introduces a separable multi-linear learning method for the CS matrix, which improves performance compared to block-wise CS, especially at low measurement rates.
IEEE TRANSACTIONS ON IMAGE PROCESSING
(2023)
Article
Mathematics, Applied
Yunbin Zhao, Zhiquan Luo
Summary: This paper analyzes the performance of two mainstream compressed sensing algorithms, Iterative Hard Thresholding (IHT) and Compressive Sampling Matching Pursuit (CoSaMP), and explores the possibility of improving their performance bounds.
SCIENCE CHINA-MATHEMATICS
(2023)
Article
Mathematics, Applied
Simone Brugiapaglia, Sjoerd Dirksen, Hans Christian Jung, Holger Rauhut
Summary: This paper studies sparse recovery with structured random measurement matrices and improves upon existing results for the null space and restricted isometry properties. The main novelty lies in a new upper bound for the expectation of the supremum of a Bernoulli process associated with a restricted isometry constant. The results are then applied to prove new performance guarantees for the CORSING method in numerical approximation techniques for partial differential equations based on compressive sensing.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2021)
Article
Mathematics, Applied
Tian-Yi Zhou, Xiaoming Huo
Summary: This paper investigates the learning ability of deep convolutional neural networks (DCNNs) under both underparameterized and overparameterized settings. The study establishes the learning rates of underparameterized DCNNs without restrictions on parameter or function variable structure. Furthermore, it demonstrates that by adding well-defined layers to a non-interpolating DCNN, some interpolating DCNNs can maintain the good learning rates.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2024)
Article
Mathematics, Applied
Amine Laghrib, Lekbir Afraites
Summary: This paper proposes a new PDE-based image denoising model that effectively deals with images contaminated by multiplicative noise. The model takes into account the gray level information by introducing a gray level indicator function in the diffusion coefficient, and has shown promising theoretical and numerical results.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2024)
Article
Mathematics, Applied
Hartmut Fuehr, Irina Shafkulovska
Summary: In this article, we study the mapping properties of metaplectic operators on modulation spaces and provide a full characterization of the pairs for which the operator is well-defined and bounded. We also show that these two properties are equivalent and imply that the operator is a Banach space automorphism. Furthermore, we provide a simple criterion to determine the transferability of well-definedness and boundedness for polynomially bounded weight functions.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2024)
Article
Mathematics, Applied
Jinjun Li, Zhiyi Wu
Summary: We prove that the Beurling dimensions of the spectra for a class of Moran spectral measures are between 0 and their upper entropy dimensions. Moreover, for such a Moran spectral measure, we show that the Beurling dimension for the spectra of the measure has the intermediate value property. Furthermore, we prove that the set of the spectra whose Beurling dimensions are equal to any fixed value in 0 and the upper entropy dimension has the cardinality of the continuum.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2024)
Article
Mathematics, Applied
M. M. Castro, F. A. Gruenbaum, I. Zurrian
Summary: This article introduces the existence of commuting differential operators for families of exceptional orthogonal polynomials, which can be found and exploited. The concept of Fourier Algebras is used, and the application of the result is illustrated through two examples.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2024)
Article
Mathematics, Applied
Anton Kutsenko, Sergey Danilov, Stephan Juricke, Marcel Oliver
Summary: This paper discusses the relations between the expansion coefficients of a discrete random field analyzed with different hierarchical bases. The focus is on comparing Walsh-Rademacher basis and trigonometric Fourier basis, and it is proven that the rate of spectral decay computed in one basis can be translated to the other in a statistical sense. Explicit expressions for this translation on quadrilateral meshes are provided, and numerical examples are used to illustrate the results.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2024)
Article
Mathematics, Applied
Albert Chua, Matthew Hirn, Anna Little
Summary: In this paper, we generalize and study finite depth wavelet scattering transforms. We provide norms for these operators and prove their continuity and invariance under specific conditions.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2024)
Article
Mathematics, Applied
Hung-Hsu Chou, Carsten Gieshoff, Johannes Maly, Holger Rauhut
Summary: In deep learning, over-parameterization is commonly used and leads to implicit bias. This paper analyzes the dynamics of gradient descent and provides insights into implicit bias. The study also explores time intervals for early stopping and presents empirical evidence for implicit bias in various scenarios.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2024)
Article
Mathematics, Applied
Elena Cordero, Gianluca Giacchi
Summary: This article introduces metaplectic Gabor frames as a natural extension of Gabor frames within the framework of metaplectic Wigner distributions. The authors develop the theory of metaplectic atoms and prove an inversion formula for metaplectic Wigner distributions on Rd. The discretization of this formula yields metaplectic Gabor frames. The study also reveals the relationship between shift-invertible metaplectic Wigner distributions and rescaled short-time Fourier transforms, providing a new characterization of modulation and Wiener amalgam spaces.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2024)
Article
Mathematics, Applied
Ryan Vaughn, Tyrus Berry, Harbir Antil
Summary: In this paper, we propose a new method to solve elliptic and parabolic partial differential equations (PDEs) with boundary conditions using a finite collection of points sampled from a Riemannian manifold embedded in a Euclidean space. Unlike traditional methods that rely on triangulations, our approach defines quadrature formulas on the unknown manifold using only sample points. Our main result is the consistency of the variational diffusion maps graph Laplacian as an estimator of the Dirichlet energy on the manifold, which improves upon previous results and justifies the relationship between diffusion maps and the Neumann eigenvalue problem. Additionally, we derive the first uniform asymptotic expansion of the diffusion maps kernel integral operator for manifolds with boundary using semigeodesic coordinates. By combining various estimators, we demonstrate how to impose Dirichlet and Neumann conditions for common PDEs based on the Laplacian.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2024)
Article
Mathematics, Applied
Tal Shnitzer, Hau-Tieng Wu, Ronen Talmon
Summary: This paper proposes an operator-based approach for spatiotemporal analysis of multivariate time-series data. The approach combines manifold learning, Riemannian geometry, and spectral analysis techniques to extract different dynamic modes.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2024)
