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This paper considers the orthogonal observation matrix design of deterministic compressive sampling (CS). An observation matrix called the weighted truncated Hadamard-modulated wideband converter (WITH-MWC) is deterministically designed based on the truncated Hadamard matrix. This matrix can meet the restricted isometry property (RIP) condition with overwhelming probability by randomly or strategically extracting from a standard Hadamard matrix. Most compressed sampling systems are highly sensitive to noise. To reduce the adverse effects of noise interference, partial specific matrix elements are weighted according to the sparse characteristics of multiband signals, and the recovery probability is provably better than that of the original system and other deterministic observation matrices, especially in the low signal-to-noise ratio scenario. Compared to the random Gaussian and random Bernoulli matrices, WITH-MWC is much easier to implement in hardware. The simulations verify the above analysis. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the conditions for the exact or stable recovery of weighted k-sparse signals in weighted sparse phase retrieval in our previous work [11] from the weighted ℓ1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell _1$$\end{document} minimization to the weighted ℓq(0k-sparse signal from its noiseless phaseless measurements via the weighted ℓq(0k-sparse signal from its noisy phaseless measurements via the weighted ℓq(0

A key issue in compressive sampling is to construct a sensing matrix that is stable and easy to design in hardware. In this paper, a novel chaotic sensing matrix is proposed by establishing a connection between sensing architecture and chaotic sinusoidal iterator. Based on a chaining method with the volumetric argument, we show that the proposed sinusoidal chaotic sensing matrix yields the well-known restricted isometry property. Numerical experiments with time-sparse signals and natural images are reported to compare the sampling performance between chaotic sensing constructions and random ones. The obtained results indicate that the proposed chaotic matrix is always able to exhibit similar or superior performance with respect to its counterparts. Moreover, the proposed construction can be easily implemented on the field-programmable gate array environment. Our framework may guide other researchers to extend the proposed method for other chaotic systems as well. [ABSTRACT FROM AUTHOR]

A problem of recovering weighted sparse signals via weighted l1 minimization has recently drawn considerable attention with application to function interpolation. The weighted robust null space property (NSP) of order s and the weighted restricted isometry property (RIP) with the weighted 3s-RIP constant δw,3s have been proposed and proved to be sufficient conditions for guaranteeing stable recovery of weighted s-sparse signals. In this paper, we propose two new sufficient conditions, i.e., the weighted lq-robust NSP of order s and the weighted RIP with δw,2s. Different from the existing results, the weighted lq-robust NSP of order s is more general and weaker than the weighted robust NSP of order s, and the weighted RIP is characterized by δw,2s instead of δw,3s. Accordingly, the reconstruction error estimations based on the newly proposed recovery conditions are also derived, respectively. Moreover, we demonstrate that the weighted RIP with small δw,2s implies the weighted l1-robust NSP of order s. [ABSTRACT FROM AUTHOR]

Underdetermined blind source separation based on compressed sensing (CS) has already been proven to be an effective mechanism from an experimental viewpoint. In this study, we develop a theoretical result and show that, under a certain sparsity constraint for the restricted isometry property, the accuracy of CS when retrieving sources is guaranteed. This theoretical result can be regarded as a generalization of the blocked polynomial deterministic matrix theory and has been confirmed using numerical examples. [ABSTRACT FROM AUTHOR]

Pulse position modulation ultra-wideband (PPM-UWB) is a new technology developed for high-speed wireless communication. Nonetheless, the sampling of PPM-UWB communication signal is limited by its ultra-wide bandwidth. According to the compressed sensing (CS) theory, the original signal can theoretically be under-sampled by a projection matrix with fewer rows than columns. However, the multiplication of matrix and signal demands that the received signal should already be sampled completely. The random matrix cannot be realized using hardware, and the process of random under-sampling is also uncontrollable. To address these problems, we propose a practical under-sampling method for the PPM-UWB communication signal based on CS theory and analog-to-information conversion (AIC) technology. Random matrix is replaced with AIC in the CS measuring projection stage, and the entire structure of AIC can be constructed using hardware. Whether or not the system matrix of AIC can satisfy the restricted isometry property is verified with the Johnson-Lindenstrauss lemma. Finally, a detection platform is constructed for the PPM-UWB communication signal based on CS and AIC, and it is considered for implementation. Although the proposed method cannot guarantee the precise reconstruction of a target vector, it can still be applied to under-sample the PPM-UWB communication signal practically. An analysis of performance results demonstrates the validity and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

The construction of sensing matrix is a fundamental issue in compressed sensing (CS). This paper introduces a new deterministic construction, referred to as Toeplitzed structurally chaotic matrix (TSCM), which possesses the advantages of both random and structural sensing matrices. We derive the matrix by first multiplying an orthonormal matrix with a chaotic-based Toeplitz matrix, and then subsampling the resultant matrix to obtain the structural one. Theoretically, we show that the entries of the TSCM are asymptotically normally distributed with that of arbitrary sparsifying matrices, yielding low mutual coherence that guarantees faithful recovery. Moreover, the proposed scheme is implementation friendly and hardware efficient, since its entries have almost no randomness and are easy to generate. Extensive numerical results via Matlab suggest that the TSCM outperforms the state-of-the-art matrix schemes and demonstrate its promising potentials. [ABSTRACT FROM AUTHOR]

An approach is proposed for producing compressed sensing (CS) matrices via multidimensional pseudo-random sequences. The columns of these matrices are binary Gold code vectors where zeros are replaced by −1. This technique is mainly applied to restore sub-Nyquist-sampled sparse signals, especially image reconstruction using block CS. First, for the specific requirements of message length and compression ratio, a set Λ which includes all preferred pairs of m-sequences is obtained by a searching algorithm. Then a sensing matrix A is produced by using structured hardware circuits. In order to better characterize the correlation between any two columns of A, the average coherence is defined and the restricted isometry property (RIP) condition is described accordingly. This RIP condition has strong adaptability to different sparse signals. The experimental results show that with constant values of N and M, the sparsity bound of A is higher than that of a random matrix. Also, the recovery probability may have a maximum increase of 20 % in a noisy environment. [ABSTRACT FROM AUTHOR]

Compressed sensing ensures the accurate reconstruction of sparse signals from far fewer samples than required in the classical Shannon-Nyquist theorem. In this paper, a generalized hard thresholding pursuit (GHTP) algorithm is presented that can recover unknown vectors without the sparsity level information. We also analyze the convergence of the proposed algorithm. Numerical experiments are given for synthetic and real-world data to illustrate the validity and the good performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]