Compressive Spectrum Sensing for Wideband Signals Using Improved Matching Pursuit Algorithms

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.

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.

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 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.

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.

Impulse detection using a shift-invariant dictionary and multiple compressions

Multiphase flow measurements, based on tomographic imaging techniques, have made substantial progress in the past several years. In particular, ultrasonic tomographic reconstruction has shown its high potential in accurately measuring fluid fractions in a flow cross-section based on direct flow measurements. These types of measurements are very attractive as the system is nonradioactive, has direct contact to fluid, yet without flow obstruction. An ultrasonic tomographic multiphase flow meter (UTM) is being developed to capture the fluid flow rates and phase compositions in producing oil wells. The UTM aims to generate cross-sectional images of the flow inside the pipe. To recover these images, complex computations and high processing time are required, based on a limited amount of available data. For this purpose, compressive sensing (CS) reconstruction methods have shown great potential in overcoming the mentioned data quality and quantity issues. CS builds upon the fact that one can recover certain data of interest from potentially very few measurements. Many CS algorithms have been proposed in the literature. In this paper, we seek to find a suitable algorithm by comparing different CS algorithms in terms of the resulting recovered image quality. Specifically, we survey three algorithms in CS, namely basis pursuit, iterative soft thresholding (IST), and orthogonal matching pursuit (OMP). We also compare the results of the CS algorithms to that of a least-square based conventional algorithm. The numerical results show the superiority of CS recovery algorithms over the conventional approach, both qualitatively and quantitatively. The results also suggest that high image quality could potentially be achieved with less complex CS algorithms, i.e., the IST and OMP algorithms. As presented in the paper, our goal is to adapt CS reconstruction algorithms for images generated by the UTM, for the purpose of accurate quantification of oil, gas, and water phase fractions produced from different wells.

Several interference mitigation strategies can be used in LTE networks to meet the consumers' increasing need for faster data speeds. Dynamic Spectrum Allocation (DSA), which maintains spectrum in a converged radio system and distributes it across all participating radio terminals, is one of the most promising solutions. However, the fundamental obstacle to achieving increased network capacities is increased inter-cell interference. The aim of this paper is to analyse the effectiveness of a newly proposed DSA technique by comparing its bit error rate (BER) and throughput (TP) with a typical uplink LTE configuration. To maximise throughput in a heterogeneous network, the suggested DSA technique utilises the Nash Bargaining Solution (NBS) scheme, a cooperative game theory that could correlate with the bit error rate. The software tool GNU Radio, which offers signal-processing blocks to develop softwaredefined radios and signal-processing systems, was used to create the setups. After the simulations were performed, the BER values were recorded and compared, while the TP values were established and computed appropriately. According to the results, the uplink (UL-LTE) architecture with DSA has an improved TP and a lower BER value. As a result, spectral efficiency can also be improved.

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.

QoS-aware distributed spectrum sharing for heterogeneous wireless cognitive networks

In this paper, we present a novel method for the acquisition and compression of hyperspectral images based on two concepts - distributed source coding and compressive sensing. Compressive sensing (CS) is a signal acquisition method that samples at sub Nyquist rates which is possible for signals that are sparse in some transform domain. Distributed source coding (DSC) is a method to encode correlated sources separately and decode them together in an attempt to shift complexity from the encoder to the decoder. Distributed compressive sensing (DCS) is a new framework suggested for jointly sparse signals which we apply to the correlated bands of hyperspectral images. We compressively sense each band of the hyperspectral image individually and can then recover the bands separately or using a joint recovery method. We use the Orthogonal Matching Pursuit (OMP) for individual recovery and Simultaneous Orthogonal Matching Pursuit (SOMP) for joint decoding and compare the two methods. The latter is shown to perform consistently better showing that the Distributed Compressive Sensing method that exploits the joint sparsity of the hyperspectral image is much better than individual recovery.

A new greedy algorithm for sparse recovery

Design and realization of random measurement scheme for compressed sensing (CS) are presented in this paper, and lower limits of the measurement number are achieved when the precise reconstruction is realized. Four kinds of random measurement matrices are designed according to the constraint conditions of random measurement. The performance is tested employing the algorithm of stagewise orthogonal matching pursuit (StOMP). Results of the experiment show that lower limits of the measurement number are much better than the results described in Refs.[13–15]. When the ratios of measurement to sparsity are 3.8 and 4.0, the mean relative errors of the reconstructed signals are 8.57 × 10−13 and 2.43 × 10−14, respectively, which confirms that the random measurement scheme of this paper is very effective.