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In this article, a new projection neural network (PNN) for solving ${L_{\mathrm{1}}}$ -minimization problem is proposed, which is based on classic PNN and sliding mode control technique. Furthermore, the proposed network can be used to make sparse signal reconstruction and image reconstruction. First, a sign function is introduced into the PNN model to design fixed-time PNN (FPNN). Then, under the condition that the projection matrix satisfies the restricted isometry property (RIP), the stability and fixed-time convergence of the proposed FPNN are proved by the Lyapunov method. Finally, based on the experimental results of signal simulation and image reconstruction, the proposed FPNN shows the effectiveness and superiority compared with that of the existing PNNs. [ABSTRACT FROM AUTHOR]

In conventional sparse Space-Time Adaptive Processing (STAP) algorithms, the l 0 -norm is often used instead of the l 1 -norm to relax convexity constraints. The approach presented in this paper can be mathematically reformulated as a linear problem, which can be efficiently solved using various convex optimization techniques. While this method effectively circumvents the NP-Hard complexity associated with the l 0 -norm, it does come with certain potential challenges. For example, the observation matrix must meet the criteria of the Restricted Isometry Property (RIP) and other stringent conditions. In this research, a novel STAP algorithm is introduced, which is based on a non-convex penalty function. This innovative algorithm substitutes the traditional l 0 -norm with a custom-designed non-convex penalty function and is applied to the Direct Filter Processor (DFP), solved using the recursive least squares (RLS) algorithm. The resulting algorithm, known as g p -RLS, is demonstrated through Monte Carlo simulations to outperform other l 1 -based and reduced-rank STAP algorithms in terms of faster convergence, improved signal-to-clutter-plus-noise ratio (SCNR), and enhanced target detection performance. [ABSTRACT FROM AUTHOR]

Recently, many types of compressive sensing (CS) matrices have been constructed. Most of these constructions focus on the measurement of one-dimensional (1-D) signals. However, many practical applications involve the acquisition of two-dimensional (2-D) signals. One of the main difficulties in the direct application of a 1-D CS measurement system to the measurement of a 2-D signal is that the computational complexity and data storage increase sharply with increasing dimension. For the measurement of 2-D signals, the structures of block CS (BCS) and Kronecker CS (KCS) have been presented. By exploiting the sparsity of 2-D signals, we provide a new extended 2-D separable measurement structure in this work, which implements separate linear operations along each 2-D signal dimension. The new structure extends the traditional 2-D separable measurement operator via measuring each subset of the signal by different CS operators, and BCS and KCS can be unified into this structure. The lower bound of the restricted isometry constant of the extended 2-D separable matrix is identified. Simulation results demonstrate the validity of our proposed structure. The proposed structure reduces the complexity of implementation and storage, and provides a new construction for the measurement of 2-D sparse signals. [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]

Crowdsourcing has become the most appealing way to provide a plethora of labels at a low cost. Nevertheless, labels from amateur workers are often noisy, which inevitably degenerates the robustness of subsequent learning models. To improve the label quality for subsequent use, majority voting (MV) is widely leveraged to aggregate crowdsourced labels due to its simplicity and scalability. However, when crowdsourced labels are “heavily” noisy (e.g., 40% of noisy labels), MV may not work well because of the fact “garbage (heavily noisy labels) in, garbage (full aggregated labels) out.” This issue inspires us to think: if the ultimate target is to learn a robust model using noisy labels, why not provide partial aggregated labels and ensure that these labels are reliable enough for learning models? To solve this challenge by improving MV, we propose a coarse-to-fine label filtration model called double filter machine (DFM), which consists of a (majority) voting filter and a sparse filter serially. Specifically, the DFM refines crowdsourced labels from coarse filtering to fine filtering. In the stage of coarse filtering, the DFM aggregates crowdsourced labels by voting filter, which yields (quality-acceptable) full aggregated labels. In the stage of fine filtering, DFM further digs out a set of high-quality labels from full aggregated labels by sparse filter, since this filter can identify high-quality labels by the methodology of support selection. Based on the insight of compressed sensing, DFM recovers a ground-truth signal from heavily noisy data under a restricted isometry property. To sum up, the primary benefits of DFM are to keep the scalability by voting filter, while improve the robustness by sparse filter. We also derive theoretical guarantees for the convergence and recovery of DFM and reveal its complexity. We conduct comprehensive experiments on both the UCI simulated and the AMT crowdsourced datasets. Empirical results show that partial aggregated labels provided by DFM effectively improve the robustness of learning models. [ABSTRACT FROM AUTHOR]

Highlights • Novel chaotic bipolar measurement matrix of general size for compressive sensing. • Proposed binarization measurement matrix based on chaotic bipolar sequence. • Comparative analysis carried out with the state-of-the-art measurement matrix. Abstract In this paper, a novel paradigm of constructing measurement matrices is proposed for compressive sensing. More precisely, the chaotic bipolar sequences ({ 1 , − 1 } elements) are utilized to build binarization measurement matrices of general size. By means of concentration inequalities together with covering argument, we show that our proposed bipolar matrices meet the restricted isometry property, which can ensure exact recovery from the linear samples. Moreover, numerical experiments illustrate that the proposed matrices outperform its counterparts, such as random Gaussian matrix. For practical applications, our proposed matrices are highly efficient for storage, multiplier and rapid data acquisition, and hardware realization. We hope that our framework reveals new directions for practitioners, as it attempts to put some of the chaos theory in perspective for practical compressive sensing applications. [ABSTRACT FROM AUTHOR]

For the existing compressed sensing greedy reconstruction algorithm, it is easy to fall into local optimum and overfitting problems. In this paper, we propose a new sparse recovery algorithm, called Parallel Matching pursuit (PMP), which searches the signal support set in both depth and breadth dimensions. PMP simultaneously examines multiple estimates of candidate support set in each iteration, and finally chooses the estimate that minimizes the reconstruction residual. Based on the restricted isometry property (RIP), sufficient conditions for PMP to reconstruct the signal are given to ensure that we can accurately recover any K -sparse signal from the measured value. Moreover, the recovery guarantee of the PMP algorithm is also provided for the case of noisy measurements. The performance of the PMP algorithm is evaluated by the signal reconstruction ability. Finally, numerical experiments verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of estimating a parameter matrix from observations which are affected by two types of noise components: (i) a sparse noise sequence which, whenever nonzero can have arbitrarily large amplitude (ii) and a dense and bounded noise sequence of “moderate” amount. This is termed a robust regression problem. To tackle it, a quite general optimization-based framework is proposed and analyzed. When only the sparse noise is present, a sufficient bound is derived on the number of nonzero elements in the sparse noise sequence that can be accommodated by the estimator while still returning the true parameter matrix. While almost all the restricted isometry-based bounds from the literature are not verifiable, our bound can be easily computed through solving a convex optimization problem. Moreover, empirical evidence tends to suggest that it is generally tight. If in addition to the sparse noise sequence, the training data are affected by a bounded dense noise, we derive an upper bound on the estimation error. [ABSTRACT FROM PUBLISHER]

A number of tree search based methods have recently been utilized for compressive sensing signal reconstruction. Among these methods, a heuristic algorithm named A* orthogonal matching pursuit (A*OMP) follows best-first search principle and employs dynamic cost model which makes sparse reconstruction exceptionally excellent. Since the algorithm performance of A*OMP relies heavily on preset parameters in the cost model and the estimation of these preset parameters requires a large number of experiments, there is room for improvement in A*OMP. In this paper, an improved algorithm referred to as Nonlinear Regression A*OMP (NR-A*OMP) is proposed which is built on the residue trend to avoid the estimation procedure. This method is inspired by the fact that the residue is correlated closely to the measurement matrix. The residue trend reflects the characteristics of nonlinear regression with the increasing of sparsity K . In addition, restricted isometry property (RIP) based general conditions are introduced to ensure the effectiveness and practicality of the algorithm. Numerical simulations demonstrate the superiority of NR-A*OMP in both reconstruction rate and normalized mean squared error. Results indicate that the performance of NR-A*OMP can become nearly equal to or even better than that of A*OMP with perfect preset parameters. [ABSTRACT FROM AUTHOR]

The analog-to-information convertor (AIC) is a successful practice of compressive sensing (CS) theory in the analog signal acquisition. This paper presents a multi-narrowband signals sampling and reconstruction model based on AIC and block sparsity. To overcome the practical problems, the block sparsity is divided into uniform block and non-uniform block situations, and the block restricted isometry property and sub-sampling limit in different situations are analyzed respectively in detail. Theoretical analysis proves that using the block sparsity in AIC can reduce the restricted isometric constant, increase the reconstruction probability and reduce the sub-sampling rate. Simulation results show that the proposed model can complete sub-sampling and reconstruction for multi-narrowband signals. This paper extends the application range of AIC from the finite information rate signal to the multi-narowband signals by using the potential relevance of support sets. The proposed receiving model has low complexity and is easy to implement, which can promote the application of CS theory in the radar receiver to reduce the burden of analog-todigital convertor (ADC) and solve bandwidth limitations of ADC. [ABSTRACT FROM AUTHOR]

In compressed sensing (CS), sparse or compressible signals can be reconstructed with fewer samples than the Nyquist–Shannon theorem requires. Over the past ten years, CS has developed into a relatively mature theory and this brand-new technique has been widely used in many fields such as image processing, wireless communication and medical imaging. In this paper, we propose a new model for signal compression and reconstruction based on semi-tensor product, called STP-CS, which is a generalization of traditional CS. Like traditional CS, we investigate some reconstruction conditions of STP-CS in terms of the spark, the coherence and the restricted isometry property (RIP). The experimental results show that STP-CS has the flexibility to choose a lower-dimensional sensing matrix for signal compression and reconstruction. [ABSTRACT FROM AUTHOR]

Nonlinear regression A⁎ orthogonal matching pursuit (NR-A⁎OMP), as a new algorithm, has been proposed for recovering the sparse signal in the filed of compressed sensing. In this paper, we consider the general perturbed model y ˜ = Φ x + b , Φ ˜ = Φ + E , where x is K -sparse and E is the perturbation matrix. Assume that the matrix Φ ˜ satisfies the RIP of order K ⋆ with δ K ⋆ < B K + B (K ⁎ = max ⁡ { 2 K , K + B }), then under the suitable constraint on min t ∈ T ⁡ | x t | , NR-A⁎OMP can recover the support of K -sparse signal x , where B is the number of child paths for each candidate in the algorithm. Compared with the existing results, we showed that the theoretical conclusion in the text is more relaxed. In the noiseless case, we also presented a condition which guaranteed that NR-A⁎OMP can not recover the support in K iterations by a counterexample. Besides, we also considered the theoretical analysis of NR-A⁎OMP when b is a Gaussian noise. [ABSTRACT FROM AUTHOR]

This paper analyzes the performance of the orthogonal matching pursuit (OMP) algorithm in recovering sparse signals from noisy measurement. Considering the fact that some matrices satisfy some restricted isometry properties (RIPs) but not the coherence condition, a superior RIP-based condition is proposed, which means that if the measurement matrix satisfies δk+1 < 1/(2 + √k) and the minimum component signal-to-noise ratio (MCSNR) is bounded, the OMP algorithm can exactly identify the support of the original sparse signal within k iterations. Finally, the theoretical results are verified by numerical simulations concerning different values of MCSNR and noise levels. [ABSTRACT FROM AUTHOR]

This paper discusses the block sparse signal recovery when the partial prior support information is available. A high order block RIP condition for our proposed weighted ℓ 2 / ℓ 1 − 2 minimization is established, which in absence of support information is proved to improve the previous one. We demonstrate that the obtained recovery condition is weaker than the analogous one for ℓ 2 / ℓ 1 − 2 minimization if at least 50% of the estimated block support information is accurate, and the corresponding recovery error estimate is also better. In addition, a series of numerical experiments are carried out to show the excellent recovery performance of the weighted ℓ 2 / ℓ 1 − 2 minimization. [ABSTRACT FROM AUTHOR]

Traditional phase retrieval methods for sparse signals are not able to achieve optimal performance when dealing with special-structured signals such as block-sparse signals. In this paper, we focus on the phase retrieval for block k -sparse signal x ∈ C N , with uniform block size d. Taking advantage of the block-sparse property, an algorithm, called block compressed phase retrieval via lifting (BCPRL), is proposed. The algorithm is not complicated as it combines the classical convex optimization approach for phase retrieval, with the l 2 , 1 -minimization for recovery of block sparsity. The analysis with restricted isometry property (RIP) proves that the sample complexity for successful recovery of our algorithm is about d time less than that of conventional sparsity. Simulation results verify that our method provides desirable performance for both block-sparse and conventional sparse signals. [ABSTRACT FROM AUTHOR]