Impulse detection using a shift-invariant dictionary and multiple compressions

In this paper, we consider the theoretical bound of the probability of error in compressed sensing (CS) with the Bayesian approach. In the detection problem, the signal is sparse and is reconstructed from a compressed measurement vector. Utilizing the oracle estimator in CS, we provide a theoretical bound of the probability of error when the noise in CS is white Gaussian noise (WGN). We show that without any additional information in CS, the probability of error obtained using the signal reconstructed by four recovery algorithms: the basis pursuit denoising (BPDN) algorithm, the Dantzig selector, the orthogonal matching pursuit (OMP) method and the compressive sampling matching pursuit (CoSaMP) algorithm is always larger than the derived theoretical bound. Simulation results demonstrate the effectiveness of our result.

In this paper, joint compressed sensing (CS)-based estimation of transmit power, geographical location and frequency bands of active primary users (PUs) using three reconstruction algorithms, orthogonal matching pursuit (OMP), compressive sampling matching pursuit (CoSaMP) and iterative hard thresholding (IHT) methods is investigated. In the first simulations, the performances of OMP, CoSaMP and IHT methods are evaluated in different signal to noise ratios (SNRs) and different values of sparsity. The first experiment demonstrates that OMP is the high performance reconstruction algorithm but it needs a bit higher complexity. Moreover, two scenarios for decision-making is considered in fusion center (FC) and respected simulation results for two cases, ideal and non-ideal lossy channels between secondary users (SUs) and fusion center, are represented. Second experiments show that decision-making based on integrated reconstruction is more efficient than averaging on three separate reconstructions in both ideal and lossy channels.

The upcoming wireless communication technologies increase the demand for spectrum, the dynamic spectrum allocation technique is a promising solution for the spectrum allocation. Spectrum sensing plays a key role in dynamic spectrum allocation, scanning through a wideband for the detection of spectrum holes which poses a problem of very high sampling rate and compressive sensing (CS) uses sub-Nyquist samples to addresses this problem. This paper proposes how orthogonal matching pursuit (OMP), compressive sampling matching pursuit (CoSaMP) and stage wise orthogonal matching pursuit (StOMP) signal reconstruction algorithms can be used for detection of spectrum holes. Simulation results reveal that the probability of detection of these algorithms is very high for the detection problem than for the estimation problem.KeywordsCognitive radioOrthogonal matching pursuitSpectrum sensingCompressive sensingWide band signal

The Compressive Sensing (CS) allows the acquisition of signals already compressed and the posterior reconstruction with much less number of measures than the minimum required by the Nyquist theorem. A subarea of CS which improves the performance at the reconstruction stage is named Model-Based CS. Some works have been developed within this subarea. However, most of them consider only the noise generated by sparse approximation, disregarding the noise generated by the quantization stage and its influence on efficiency and robustness of CS. The objective of this study is to investigate the influence of the noise generated by the quantization stage in Model-Based CS efficiency for images with different levels of sparsity and different distributions of coefficients in the frequency domain. In this work, the image acquisition stage is implemented using the partial Fourier matrix which results in a vector of measures. Then, different steps of uniform scalar quantization are added to this vector and the image reconstruction stage is performed using the Compressive Sampling Matching Pursuit (CoSaMP) on a quadtree model. PSNR and bits rate (BR) are then used to evaluate the efficiency of CoSaMP with quantization noise. The performance of this proposed Model-Based CS using different quantization steps were slightly better than other studies using the same model in terms of PSNR, but with the advantage of obtaining smaller values of bit rate (BR maior que 2 bpp).

This paper proposes an efficient image reconstruction for compressive sensing (CS) that combines the Lifting Wavelet Transform (LWT) using Symlet 8 (sym8) wavelets with three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). Unlike the conventional Discrete Wavelet Transform (DWT) which relies on computationally intensive convolution operations the LWT provides a faster sparse representation while preserving the sparsity crucial for CS. The proposed approach leverages a key insight: among the four subbands produced by the LWT namely the approximation (CA) and the detail coefficients (LH, HL, HH) only the latter three are inherently sparse. Therefore, compressive sensing is applied exclusively to these detail subbands, while the CA subband is left uncompressed to retain essential low-frequency information. Experiments were conducted on both a natural test image (Lena) and a medical MRI scan, across image resolutions ranging from 200×200 to 512×512 pixels and sampling rates from 10% to 80%. Performance was assessed using the Structural Similarity Index (SSIM) and reconstruction time. Results consistently demonstrate that ALISTA significantly outperforms SP and CoSaMP in both reconstruction fidelity and computational efficiency. At an 80% sampling rate, ALISTA achieves SSIM values of 0.99346 for Lena and 0.98 for the MRI image, compared to approximately 0.97 and 0.94, respectively, for the other two methods. Furthermore, ALISTA maintains remarkably low reconstruction times under 4 seconds even for 512×512-pixel images. These findings confirm that the ALISTA + LWT/sym8 combination offers the best trade-off between image quality and speed, exhibiting robustness across different image types and scales.

This paper proposes an efficient image reconstruction for compressive sensing (CS) that combines the Lifting Wavelet Transform (LWT) using Reverse Biorthogonal 6.8 (rbio6.8) wavelets with three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). Unlike the conventional Discrete Wavelet Transform (DWT) which relies on computationally intensive convolution operations the LWT provides a faster sparse representation while preserving the sparsity crucial for CS. The proposed approach leverages a key insight: among the four subbands produced by the LWT namely the approximation (CA) and the detail coefficients (LH, HL, HH) only the latter three are inherently sparse. Therefore, compressive sensing is applied exclusively to these detail subbands, while the CA subband is left uncompressed to retain essential low-frequency information. Experiments were conducted on both a natural test image (Lena) and a medical MRI scan, across image resolutions ranging from 200×200 to 512×512 pixels and sampling rates from 10% to 80%. Performance was assessed using the Structural Similarity Index (SSIM) and reconstruction time. Results consistently demonstrate that ALISTA significantly outperforms SP and CoSaMP in both reconstruction fidelity and computational efficiency. At an 80% sampling rate, ALISTA achieves SSIM values of 0.99314 for Lena and 0.97688 for the MRI image, compared to approximately 0.97402 and 0.93577, respectively, for the other two methods. Furthermore, ALISTA maintains remarkably low reconstruction times under 4 seconds even for 512×512-pixel images. These findings confirm that the ALISTA + LWT/rbio6.8 combination offers the best trade-off between image quality and speed, exhibiting robustness across different image types and scales.

In most scenes of through-the-wall imaging (TWI), the observation zone is spares. So the radar signals could be processed using Compressive Sensing (CS) technique. Existing greedy algorithms for CS, such as orthogonal Matching Pursuit (OMP) algorithm and Compressive Sampling Matching pursuit (CoSaMP), suffer from artifacts and low resolution respectively. To cover the shortage of existing algorithms, a modified Compressive Sampling Matching Pursuit algorithm is proposed. By using the orthogonality among selected basis-signals and backtracking strategy for basis-signals reevaluation, the proposed algorithm could reconstruct radar signal. Then the image of observation zone could be got using Delay and Sum (DAS) beamforming method. Measurement results demonstrate the effectiveness of the proposed algorithm.

Most signals can be represented sparsely in a basis. Recently, Compressive Sensing Theorem which offers convex optimization algorithms based on l 1 -minimization for sparse signal recovery is often being used. In this paper, some of the iterative signal recovery algorithms alternative to l 1 -minimization solution which are Orthogonal Matching Pursuit (OMP), Compressive Sampling Matching Pursuit (CoSaMP), Iterative Hard Thresholding (IHT) and Lipschitz Iterative Hard Theresholding (LIHT) are compared in noisy and noiseless conditions with various tests. Iterative algorithms alternative to the l 1 optimization method with similar performance are verified. OMP algorithm that works at higher true reconstruction rates in noisy and noiseless conditions can be preferred instead of convex optimization methods.

In order to improve signal reconstruction accuracy, a CoSaMP (Compressive Sampling Matching Pursuit) algorithm based on peak signal to noise ratio is proposed in allusion to the disadvantages of CoSaMP algorithm. Firstly, the discrete cosine wave transform is improved to initially estimate the signal sparseness; secondly, the optimum iteration number is determined according to the peak signal to noise ratio to gradually approach to the real sparseness of the signal for signal reconstruction; finally, the simulation experiment is adopted to analyze the algorithm performance. The result shows: compared with CoSaMP algorithm and other improved CoSaMP algorithms, the proposed algorithm can not only obtain more ideal reconstruction effect, but also improve the reconstruction success probability and reduce the reconstruction time, thus having higher reconstruction efficiency.

The early defects in bearings tend to result in periodic impacts and, thus, cause impulse components in vibration signals. However, these fault features are always submerged and distorted by the heavy noise. A new method called sparse regularization (SR)-based adjacent signal difference (SR-ASD) is proposed to extract fault features from bearing vibration signals. Impulsive sparse retention term and adjacent difference sparse retention term are proposed to extract the impulsive features based on the characteristic of the fault signal. They are capable of preserving the impulsive features and eliminating noise by retaining the sparsity of the signal and its difference, respectively. The adaptive setup of regularization parameters is developed to enhance the effect of noise removal according to the characteristics of the vibration signal. Majorization-minimization (MM) is adopted to solve the optimization problem of the objective in SR-ASD. Experimental results on simulation signals and bearing vibration signals illustrate that SR-ASD can effectively eliminate noise interference and then extract fault features of vibration signals. SR-ASD outperforms other typical methods on fault feature extraction from vibration signals.

A new greedy algorithm for sparse recovery

The measurements of delay and Doppler (DD) spreading in underwater acoustic channels (UACs) have multiple applications, including communications as well as the development of a dynamic UAC simulator. However, these measurements suffer from the difficulties of fast time variations and large data sets. This paper addresses an efficient compressed sensing (CS) method to solve these problems. First, the DD spreading in UACs is studied by using a doubly spread model; second, the least-square criterion is implemented and its limit is analyzed. Subsequently, the matching pursuit (MP) method is applied to the problem by exploiting the sparsity of the DD model-based UACs. Although the MP method improves the performance of the LS method, it has unavoidable deficiencies, e.g., the redundant selections of bases that lead to a limited measurement of DD spreading. Thus, this paper proposes an improved version by inserting a projection matrix. The projected MP (PMP) method adopts QR decomposition for an efficient computation. Finally, at-sea data-based comparisons among the abovementioned three methods are conducted to verify the superiority of the PMP method.

Compressed Sensing (CS), as a new rapidly growing research field, promises to effectively recover a sparse signal at the rate of below Nyquist rate. This revolutionary technology strongly relies on the sparsity of the signal and incoherency between sensing basis and representation basis. Exact recovery of a sparse signal will be occurred in a situation that the signal of interest sensed randomly and the measurements are also taken based on sparsity level and log factor of the signal dimension. In this paper, compressed sensing method is proposed to reduce the noise and reconstruct the image signal. Noise reduction and image reconstruction are formulated in the theoretical framework of compressed sensing using Basis Pursuit (BP) and Compressive Sampling Matching Pursuit (CoSaMP) algorithm when random measurement matrix is utilized to acquire the data. In this research we have evaluated the performance of our proposed image enhancement methods using the quality measure peak signal-to-noise ratio (PSNR).

A duplexer is necessary, but unfavourable for a frequency-division duplexing (FDD) base station, due to its bulky size, high cost and design challenges. In order to relax the performance requirement of such device, the transmitter (TX) leakage needs to be suppressed. The state-of-the-art solutions failed to provide a wideband solution for cancelling the TX leakage at RF frequency, due to the lack of delay optimization. Aiming to provide high delay estimation accuracy, this paper presents a modelling technique which is based on the compressed sampling matching pursuit (CoSaMP) algorithm for compressed sampling (CS). As a result, by using the proposed modelling technique, cancellation systems, particularly the ones that are based on the analog finite impulse response (FIR) filter structure, can be implemented to achieve wideband suppressing at RF frequencies.

Compressive sensing based multiuser detector for massive MBM MIMO uplink