The detection bound of the probability of error in compressed sensing using Bayesian approach

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 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.

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 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

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.

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.

A new greedy algorithm for sparse recovery

Compressed Sensing (CS) has been considered a very effective means of reducing energy consumption at the energy-constrained wireless body sensor networks for monitoring the multi-lead Electrocardiogram (MECG) signals. This paper develops the compressed sensing theory for sparse modeling and effective multi-channel ECG compression. A basis matrix with Gaussian kernels is proposed to obtain the sparse representation of each channel, which showed the closest similarity to the ECG signals. Thereafter, the greedy orthogonal matching pursuit (OMP) method is used to obtain the sparse representation of the signals. After obtaining the sparse representation of each ECG signal, the compressed sensing theory could be used to compress the signals as much as possible. Following the compression, the compressed signal is reconstructed utilizing the greedy orthogonal matching pursuit (OMP) optimization technique to demonstrate the accuracy and reliability of the algorithm. Moreover, as the wavelet basis matrix is another sparsifying basis to sparse representations of ECG signals, the compressed sensing is applied to the ECG signals using the wavelet basis matrix. The simulation results indicated that the proposed algorithm with Gaussian basis matrix reduces the reconstruction error and increases the compression ratio.

An improved orthogonal matching pursuit method for denoising high-frequency ultrasonic detection signals of flip chips

Impulse detection using a shift-invariant dictionary and multiple compressions

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).

In this paper, we present improved performance compressed sensing (CS) based pulse Doppler radar. CS is an emerging sampling technique which uses very few number of samples to reconstruct original signal. Improvement in performance is achieved using Orthogonal Matching Pursuit (OMP) method with Fourier dictionary at low signal to noise ratio (SNR). OMP is an iterative and fast reconstruction method while Fourier dictionary is used to transform the original signal from time domain to Fourier domain. A significant reduction of sampling frequency by a factor of 360 is achieved at SNR as low as 10 dB, while preserving essential signal information. Low signal reconstruction error leads to good detection performance using Generalized Likelihood Ratio Test (GLRT), a detector based on ratio of probabilities of detection and false alarm. Simulation results demonstrate usefulness of the ideas presented.

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.

In this paper, we deal with the signal recovery problem in compressed sensing, that is, the problem of estimating the original signal from its linear measurements. Recovery algorithms can be mainly classified into two types, optimization based algorithms and statistical modeling based algorithms. Basis pursuit (BP) or basis pursuit denoising (BPDN) is one of the most widely used optimization based recovery algorithms, that minimizes the $\ell_{1}$ norm of the signal or its coefficients in some basis under the constraint that its linear transform is equal to or close to the observation signal. There are various extensions of those algorithms depending on the problem structure. When the original signal is an image, the objective function is often the sum of the $\ell_{1}$ norm of the coefficients of the signal in some basis and a total variation (TV) of the image. It can be considered that it requires the image to be sparse in both the specific transform domain and finite differences at the same time. In this paper, we propose a statistical model that represents those sparsities and the signal recovery algorithm based on the variational method. One of the advantages of the statistical approach is that we can utilize the posterior information of the original signal and it is known that it can be used to construct the compressed sensing measurements adaptively. The proposed recovery algorithm and adaptive construction of the compressed sensing measurements are validated on numerical experiments.