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In order to explore some concrete metric relationship between the ‖ x ‖ 1 / ‖ x ‖ ∞ and ‖ x ‖ 0 , we introduce a wonderful triangle whose sides are composed of ‖ x ‖ 0 , ‖ x ‖ 1 and ‖ x ‖ ∞ for any non-zero vector x ∈ R n by delving into the iterative soft-thresholding operator in this paper. Based on the angle β of the triangle corresponding to the side whose length is ‖ x ‖ ∞ - ‖ x ‖ 1 / ‖ x ‖ 0 , we demonstrate that the sparsity of signal is generally meaningful within a certain exact interval [ 1 , 50 ] without regard to its dimension. Finally, we construct a feasible algorithm for solving ℓ 1 / ℓ ∞ minimization, which further illustrates that it is effective for sparse recovery. [ABSTRACT FROM AUTHOR]

Federated learning (FL) enables the full utilization of decentralized training without raw data. However, various attacks still threaten the training process of FL. To address these concerns, differential privacy (DP) and secure multi-party computation (SMC) are applied, but these methods may result in low accuracy and heavy training load. Moreover, the high communication consumption of FL in resource-constrained devices is also a challenging problem. In this paper, we propose a novel SMC algorithm for the FL (FL-IPFE) to protect the local gradients. It does not require a trusted third party (TTP) and is more suitable for FL. Furthermore, we propose a secure and efficient FL algorithm (SEFL), which applies compressed sensing (CS) and all-or-nothing transform (AONT) to minimize the number of transmitted and encrypted model updates. Additionally, our FL-IPFE is used to encrypt the last element of the preprocessed parameters for guaranteeing the security of the entire local model updates. Meanwhile, the issue of participant dropouts is also taken into account. Theoretical analyses demonstrate that our proposed algorithms can aggregate model updates with high security. Finally, experimental evaluation reveals that our SEFL possesses higher efficiency compared to other state-of-the-art works, while providing comparable model accuracy and strong privacy guarantees. [ABSTRACT FROM AUTHOR]

• We propose a new patch-based model via non-convex weighted Smoothly Clipped Absolute Deviation (SCAD) prior for compressive sensing. • We derive an effective algorithm to solve the model by using ADMM framework. • We show the convergence of the algorithm under mild conditions. • Numerical results on synthetic and real MR image reconstruction demonstrate that our method is promising. The nuclear norm-based convex surrogate of the rank function has been widely used in compressive sensing (CS) to exploit the sparsity of nonlocal similar patches in an image. However, this method treats different singular values equally and thus may produce a result far from the optimum one. In order to alleviate the limitations of the nuclear norm, different singular values should be treated differently. The reason is that large singular values can be used to retrieve substantial contents of an image, while small ones may contain noisy information. In this paper, we propose a model via non-convex weighted Smoothly Clipped Absolute Deviation (SCAD) prior. Our motivation is that SCAD shrinkage behaves like a soft shrinkage operator for small enough inputs, whereas for large enough ones, it leaves the input intact and behaves like hard shrinkage. For moderate input values, SCAD makes a good balance between soft shrinkage and hard shrinkage. Numerically, the alternating direction method of multiplier (ADMM) is adopted to split the original problem into several sub-problems with closed-form solutions. We further analyze the convergence of the proposed method under mild conditions. Various experimental results demonstrate that the proposed model outperforms many existing state-of-the-art CS methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel distributed compressed sensing based joint detection and tracking algorithm for multistatic radar system, which significantly reduces the computational load in a centralized fusion framework. For different receivers in the multistatic radar system, their corresponding sparse vectors, which are represented in state space, share the same locations of nonzero reflection coefficients. This fits the joint sparsity model 2 (JSM-2) in distributed compressed sensing. In this paper, a novel algorithm, named distributed general similar sensing matrix pursuit (DGSSMP) algorithm, is proposed to tackle the generalized JSM-2 model when each individual sensing matrix is different and with high coherence. In contrast to the classical greedy algorithms dealing with single subspace, the proposed DGSSMP algorithm has to tackle a union of different subspaces, with each subspace corresponding to a different sensing matrix for each individual receiver. The simulation results show that in the proposed distributed compressed sensing based joint detection and tracking framework, the proposed DGSSMP algorithm together with the track before detect (TBD) scheme can effectively distinguish true targets from clutter based on the information from multiple scans. [ABSTRACT FROM AUTHOR]

Compressive sensing is a technique that can sample compressible signals below the traditional rate. One of fundamental problems in compressive sensing is the sparse signal recovery. Recently, alternating projection method was proposed for this kind of recovery. Two sufficient conditions for the recovery guarantee of the method were also given. In this paper, we establish another sufficient condition for the recovery guarantee of alternating projection method in terms of the restricted isometry constants and singular values of the measurement matrix, it is a useful improvement on one of the existing two conditions. The famous Weyl inequality, Cauchy interlace theorem and partition skills of involved matrices are utilized. The requirement for the measurement matrix is lowered. Thus, this improvement allows more measurement matrices to be used for alternating projection method. This can enhance the applicability of the method. [ABSTRACT FROM AUTHOR]

Sparsity prior is a powerful tool for compressive sensing reconstruction (CSR) of hyperspectral image (HSI). However, conventional HSI-CSR strategies are not tuned to extracting refine spatial and spectral sparsity prior. Moreover, these CSR techniques are weak in preserving edges and suppressing artifacts. To alleviate these issues, this paper represents a first effort to characterize the spatial and spectral knowledge using the structure-based sparsity prior. Specifically, we introduce the nonlocal low-rank matrix recovery model and the hyper-Laplacian prior to encode the spatial and spectral structured sparsity, respectively. The key advantage of the proposed method, termed as hyper-Laplacian regularized nonlocal low-rank matrix recovery (HyNLRMR), is to adopt insightful property, namely the nonlocal self-similarity across the spatial domain and the consistency along the spectral domain. Then, the alternative direction multiplier method (ADMM) is designed to effectively implement the proposed algorithm. Experimental results on various HSI datasets verify that the proposed algorithm can significantly outperform existing state-of-the-art HSI-CSR methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel image encryption scheme based on a chaotic system and compressed sensing for multiple application scenarios. It is a dedicated scheme for JPEG format that makes full use of the characteristics of DCT data. The proposed scheme generates a key from a plain image with random noise, which is then used to generate the parameters needed in the scheme through using a new chaotic system structure. This structure employs data segmentation for the DCT data of a plain image and processes sparse data and non-sparse data separately: it permutes non-sparse data, and applies permutation and compressed sensing to sparse data. By merging the processed data and performing efficient confusion, we obtain the final encrypted data. The reverse operation is image decryption, and partial decryption can be performed quickly since sparse data is not required. Such partial decryption can be used for multiple applications, such as copyright protection platforms and machine learning based on private data. Simulation experiments and a performance analysis show that the key generation method and efficient confusion of our scheme can improve the security of image encryption. Furthermore, the data segmentation and reconstruction algorithm based on a cyclic matrix can greatly improve decryption efficiency. • A novel and efficient image encryption scheme based on chaotic system and compressed sensing is proposed. • Taking the hash value of plain image with random noise as the key is introduced. • Circulant matrix is used to accelerate the efficiency of data recovery. • Data segmentation is applied to accelerate the efficiency of our scheme, and it can fit more application scenarios. [ABSTRACT FROM AUTHOR]

Highlights • Two simple and efficient correntropy-based adaptation algorithms, l0-MCC and MB-l0-MCC, are proposed for robust CS reconstruction. • A novel and comprehensive theoretical analysis on convergence of l0-MCC is given. • Experiment results demonstrate that the proposed algorithms achieve superior performance as compared to existing state-of-the-art robust reconstruction algorithms in many aspects. Abstract Robust compressive sensing (CS) aims to recover the sparse signals from noisy measurements perturbed by non-Gaussian (i.e., heavy-tailed) noises, where traditional CS reconstruction algorithms may perform poorly owing to utilizing the l 2 error norm in optimization. In this paper, we propose a novel maximum correntropy adaptation approach for robust CS reconstruction. The task is formulated as a l 0 regularized maximum correntropy criterion (l 0 -MCC) optimization problem and is solved by adaptive filtering approach. The proposed l 0 -MCC algorithm has a simple algorithm structure and can adaptively estimate the sparsity. It can efficiently alleviate the negative impact of noise in the presence of large outliers. Moreover, a novel theoretical analysis on convergence of l 0 -MCC is also performed. Furthermore, a mini-batch-based l 0 -MCC (MB- l 0 -MCC) algorithm is developed to speed up the convergence. Comparison with existing robust CS reconstruction algorithms is conducted via simulations, showing that the proposed methods can achieve better performance than existing state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Abstract Since noise is an inevitable factor in real-world applications, designing robust image recovery technologies is crucial for the application of a compressive sensing (CS) system. However, current CS approaches rarely consider noise, or they only consider the noise generated in the process of transmission. Almost all CS approaches will breakdown when the original image is corrupted by noise due to natural or artificial factors, especially non-Gaussian noise. In this paper, we propose a nonconvex m-estimator-based robust image CS approach to recover the original clean images from the compressed measurements of their corrupted versions. We simultaneously conduct reconstructing and denoising in a unified framework. We also use a weighted schatten- p norm to better exploit the nonlocal low-rank property. In addition, we developed an efficient iterative scheme based on the half-quadratic theory and the alternating direction method of multipliers to solve the resulting nonconvex optimization problem. The experimental results show that the proposed algorithm can recover the clean images accurately when the original images are corrupted by non-Gaussian noise. [ABSTRACT FROM AUTHOR]

Highlights • A collaborative block compressed sensing (CBCS) framework is proposed where the local structure information and perceptual nonlocal similarity are considered to better characterize the structural details and maintain the smoothness of the pixels. • The combination of the syntheses and analysis sparse coding is applied in the formulated CBCS, which could better explore the sparsity of the signal. • An efficient iterative appraoch based on Multi-criteria Nash equilibrium techinique is proposed to solve the reconstruction problem, resulting in a better performance than the compared state-of-the-art BCS methods. Abstract In the past decade, image reconstruction based on compressed sensing (CS) has attracted great interest from researchers in signal processing. Due to the tremendous amount of information that an image contains, block compressed sensing (BCS) is often applied to divide an entire image into non-overlapping sub-blocks, treating all sub-blocks separately. However, an independent reconstruction ignores the correlation between adjacent sub-blocks and results in quality degradation, both in objective and subjective assessments. To obtain a satisfactory reconstructed image, this paper proposes a collaborative BCS (CBCS) framework with dual-domain sparse representation, where local structural information (LSI) and non-local pixel similarity are jointly considered. During a reconstruction, a local data-adaptive kernel regressor is introduced to extract the local image structure, which helps build a correlation of pixels between adjacent sub-blocks and preserves the details of an image. At the same time, a perceptually non-local similarity (PNLS), based on the human visual system, is used to improve visual quality. In addition, we employed both an analysis model and a synthesis model to further enhance sparseness and to formulate a dual-domain sparse representation based BCS reconstruction problem. Finally, an efficient, iterative approach, based on the multi-criteria Nash equilibrium technique, is proposed to solve this problem. Experimental results on benchmark images demonstrate that the proposed method can achieve competitive results both in both numerical and visual comparisons with some state-of-the-art BCS algorithms. [ABSTRACT FROM AUTHOR]

A central problem in compressed sensing (CS) is the design of measurement matrices. Compared with the conventional random matrices, sparse binary matrices have some attractive properties, such as lower storage/encoding cost and easy hardware implementation. In this paper, we formulate the construction of sparse binary measurement matrices from an optimization standpoint. A new algorithm is presented to construct arbitrary-size sparse binary measurement matrices through relaxing the resultant optimization model to an incremental integer programming problem. The proposed method in general outputs sparse binary matrices with optimal mutual coherence. In addition, we prove that the constructed matrices can be almost completely incoherent with the conventional wavelet dictionary. Extensive simulation results show that the sparse binary matrices constructed by the proposed algorithm significantly outperform Gaussian random matrices, random sparse binary matrices and two well-performing deterministic sparse binary matrices. [ABSTRACT FROM AUTHOR]

Joint sparsity has attracted considerable attention in recent years in many fields including sparse signal recovery in compressive sensing, statistics, and machine learning. Traditional convex models with joint sparsity suffer from the suboptimal performance though enjoying tractable computation. In this paper, we propose a new non-convex joint sparsity model, and develop a corresponding multi-stage adaptive convex relaxation algorithm. This method extends the idea of iterative support detection (ISD) from the single vector estimation to the multi-vector estimation by considering the joint sparsity prior. We provide some preliminary theoretical analysis including convergence analysis and a sufficient recovery condition. Numerical experiments from both compressive sensing and multi-task feature learning show the better performance of the proposed method in comparison with several state-of-the-art alternatives. Moreover, we demonstrate that the extension of ISD from the single vector to multi-vector estimation is not trivial. While ISD does not well reconstruct the single channel sparse Bernoulli signal, it does achieve significantly improved performance when recovering the multi-channel sparse Bernoulli signal thanks to its ability of natural incorporation of the joint sparsity structure. [ABSTRACT FROM AUTHOR]

As a natural extension of Compressive Sensing and the requirement of some practical problems, Phaseless Compressive Sensing (PCS) has been introduced and studied recently. Many theoretical results have been obtained for PCS with the aid of its convex relaxation. Motivated by successful applications of nonconvex relaxed methods for solving Compressive Sensing, in this paper, we try to investigate PCS via its nonconvex relaxation. Specifically, we relax PCS in the real context by the corresponding ℓ p -minimization with p ∈ (0, 1). We show that there exists a constant p * ∈ (0, 1] such that for any fixed p ∈ (0, p *), every optimal solution to the ℓ p -minimization also solves the concerned problem; and derive an expression of such a constant p * by making use of the known data and the sparsity level of the concerned problem. These provide a theoretical basis for solving this class of problems via the corresponding ℓ p -minimization. [ABSTRACT FROM AUTHOR]

3D shape retrieval is always a challenging research topic because of complex geometric structural variations involved. Although many feature extraction and retrieval algorithms have been proposed, they generally only use single 3D model descriptor hence cannot obtain better retrieval performance. In this paper, we propose a new 3D shape retrieval framework based on compressive sensing (CS) and multi-feature fusion (MFF). Firstly, we extract three new features including the CS Chebyshev ray (CSCR) feature, the CS spatial hierarchical (CSSH) feature and the Extended Gaussian sphere (EGS) feature. Actually, CSCR, CSSH and EGS respectively represent the volume tensor, the layered detail and the statistical space distribution on the model surface of a 3D model. To make the best use of these features, a supervised learning is used to determine the weighting coefficients for these features. Finally, the features and their corresponding weighting coefficients are used to determine the similarity of 3D models in the multi-feature fusion (MFF) framework for 3D shape retrieval. For performance assessment, two publicly available datasets that contain 3D models with large geometric variations are used, including ModelNet-10 and PSB datasets. Comprehensive experimental results have demonstrated the efficacy of the proposed method for 3D shape retrieval. [ABSTRACT FROM AUTHOR]

In order to attain better reconstruction quality from compressive sensing (CS) of images, exploitation of the dependency or correlation patterns among the transform coefficients commonly has been employed. In this paper, we study a new image sensing technique, called compressive image sensing (CIS), with computational complexity O ( m 2 ), where m denotes the length of a measurement vector y = ϕ x , which is sampled from the signal x of length n via the sampling matrix ϕ with dimensionality m × n . CIS is basically a variation on compressive sampling. The contributions of CIS include: (i) reconstruction speed is extremely fast due to a closed-form solution being derived; (ii) certain reconstruction accuracy is preserved because significant components of x can be reconstructed with higher priority via an elaborately designed ϕ ; and (iii) in addition to conventional 1D sensing, we also study 2D separate sensing to enable simultaneous acquisition and compression of large-sized images. [ABSTRACT FROM AUTHOR]

This paper proposes the Bayesian approach to signal detection in compressed sensing (CS) using compressed measurements directly. A general expression of the probability of error is obtained where the prior probabilities of hypotheses could be equal or unequal and the additive noise is assumed to be uncorrelated Gaussian noise with possibly unequal variances. Upper and lower bounds of the probability of error are also derived using the restricted isometry property (RIP) constant and then the more computationally feasible mutual coherence of a given sampling matrix in CS. When the difference between the prior probabilities is sufficiently small and the signal to noise ratio is relatively large, an approximate but simpler expression of the probability of error is obtained. Furthermore, a new bound of the probability of error is derived in terms of a piecewise function. Numerical simulations are also provided to illustrate the new theoretical results. [ABSTRACT FROM AUTHOR]

Compressed sensing (CS) has stirred great interests in many fields of science, due to its ability to capture most information of compressible signals at a rate significantly below the Nyquist rate. Reconstructing the signal from random measurements is an important topic in CS. In this paper, a new algorithm— Incomplete variables Truncated Conjugate Gradient method (ITCG) is proposed to reconstruct the signal by solving a programming with ℓ 1 norm. By adjusting the parameters of ITCG, two specific algorithms are presented, i.e. ITCG-vs for very sparse reconstruction and ITCG-nvs for not very sparse reconstruction. To make full use of the sparse nature of signals, ITCG can reconstruct them efficiently. The experiments show that the two algorithms of ITCG (especially ITCG-nvs) are much faster than competing methods in sparse reconstruction. In addition, it has been shown that ITCG-vs can converge after finite iterations under some decent conditions. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach for the fault diagnosis of induction motors. The invariant character vectors of fault signals are first extracted from the training samples. A single-class support vector machine (SC-SVM) is then used to detect the occurrence of faults, and the obtained invariant character vectors are employed as the desired references to classify the faults associated with the nearest neighbor classifier. The new diagnosis algorithm is validated for an induction motor (Y132S-4), which has shown excellent performance. [ABSTRACT FROM AUTHOR]