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This paper considers efficient sampling of simultaneously sparse and correlated (S&C) signals for automotive radar application. We propose an implementable sampling architecture for the acquisition of S&C at a sub-Nyquist rate. We prove a sampling theorem showing exact and stable reconstruction of the acquired signals even when the sampling rate is smaller than the Nyquist rate by orders of magnitude. Quantitatively, our results state that an ensemble M signals, composed of a-priori unknown latent R signals, each bandlimited to W / 2 but only S -sparse in the Fourier domain, can be reconstructed exactly from compressive sampling only at a rate R S log α ⁡ W samples per second. When R ≪ M and S ≪ W , this amounts to a significant reduction in sampling rate compared to the Nyquist rate of MW samples per second. This is the first result that presents an implementable sampling architecture and a sampling theorem for the compressive acquisition of S&C signals. We resort to a two-step algorithm to recover sparse and low-rank (S&L) matrix from a near optimal number of measurements. This result then translates into a signal reconstruction algorithm from a sub-Nyquist sampling rate. [ABSTRACT FROM AUTHOR]

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]

A novel signal compression and reconstruction procedure suitable for guided wave based structural health monitoring (SHM) applications is presented. The proposed approach combines the wavelet packet transform and frequency warping to generate a sparse decomposition of the acquired dispersive signal. The sparsity of the signal in the considered representation is exploited to develop data compression strategy based on the Best-Basis Compressive sensing (CS) theory. The proposed data compression strategy has been compared with the transform encoder based on the Embedded Zerotree (EZT), a well known data compression algorithm. These approaches are tested on experimental Lamb wave signals obtained by acquiring acoustic emissions in a 1 m 2 aluminum plate with conventional piezoelectric sensors. The performances of the two methods are analyzed by varying the compression ratio in the range 40–80%, and measuring the discrepancy between the original and the reconstructed signal. Results show the improvement in signal reconstruction with the use of the modified CS framework with respect to transform-encoders such as the EZT algorithm with Huffman coding. [ABSTRACT FROM AUTHOR]

Time-frequency distributions (TFD) provide a set of powerful tools for the non-stationary signal analysis. Although TFD overcomes signal representation limitations, the most commonly used TFDs generate unwanted artefacts, also called the cross-terms, which make the TFD application less feasible for noise-corrupted real-life signals. In this paper, we investigate the advantages of the TFD sparsity by using the compressive sensing based methods. We propose a sparse reconstruction algorithm which reconstructs a TFD from a small sub-set of samples taken from the signal ambiguity function. The proposed algorithm is based on the iterative shrinkage algorithm which performance and robustness have been improved by utilizing the short-term and narrow-band Rényi entropies. Furthermore, we have circumvented the limitations of global concentration measure by coupling it with the measure based on the local Rényi entropy. The introduced concentration measures have been used as objective functions in a multi-objective meta-heuristic optimization of the proposed algorithm parameters, resulting in high-resolution TFDs while avoiding disjunctions within signal components. The obtained results have been compared to the state-of-the-art sparse reconstruction algorithms, for both noisy synthetic and real-life signals. • TFD sparsity by using compressive sensing based methods has been investigated. • Sparse reconstruction has been augmented with the local Rényi entropy. • The algorithm parameters have been optimized using meta-heuristic optimization. • A TFD with a highly concentrated auto-terms has been achieved. [ABSTRACT FROM AUTHOR]

The compressive sensing theory enables reconstruction of sparse or compressible signals at reduced sampling rate. Recent studies have shown that stable signal reconstruction is possible even if each measurement is quantized to one bit. In conventional compressive sensing framework, the signal can be sparsely represented by some discrete atoms. In many applications however, signals are sparse in a continuous parameter space, e.g., radar imaging. A commonly used method is to discretize the continuous parameter into grid points and build a dictionary to characterize the sparsity. However, the true targets may not coincide with the predefined grid points. This off-grid problem always leads to a mismatched basis matrix, which results in degradation of the performance. In this paper, a parameter perturbation method, based on 1-bit compressive sensing is proposed to deal with the off-grid problem. Especially for adjacent targets in the adjoining grids, a self-checking mechanism is proposed to further discriminate the adjacent targets located within the proximity of adjoining grids. In the proposed algorithm, the available grid points in the dictionary are adaptively updated to approach the true targets. The convergence of the algorithm can be theoretically guaranteed, and numerical experiments demonstrate that the proposed algorithm can be effectively applied to range profile and synthetic aperture radar imaging. Simulations indicate that the proposed algorithm outperforms the state-of-the-art techniques over a wide range of signal-to-noise ratio levels. [ABSTRACT FROM AUTHOR]