We give some new results on sparse signal recovery in the presence of noise, for weighted spaces. Traditionally, were used dictionaries that have the norm equal to 1, but, for random dictionaries this condition is rarely satisfied. Moreover, we give better estimations then the ones given recently by Cai, Wang and Xu.

The emerging field of compressive Sensing enables the reconstruction of the signal from a small set of linear projections. Traditional compressive Sensing approaches deal with a single signal; while one can jointly reconstruct multiple signals via distributed compressive Sensing algorithm, which exploits both the inter-and intra-signal correlations via joint sparsity models. Since the wavelet coefficients of many signals is sparse, in this paper, the wavelet transform is used as sparsifying transform, and a new wavelet-based Bayesian distributed compressive Sensing algorithm is proposed, which takes into account the inter-scale dependencies among the wavelet coefficients via hidden Markov tree model, as well as the inter-signal correlations. This paper uses Bayesian procedure to statistically model this correlation via the prior distributions. Also, in this work, a type-1 joint sparsity model is used for jointly sparse signals, in which every sparse coefficient vector is considered as the sum of a common component and an innovation component. In order to jointly reconstruct multiple sparse signals, the centralized approach is used in distributed compressive Sensing, in which all the data is processed in the fusion center. Also, variational Bayes procedure is used to infer the posterior distributions of unknown variables. Simulation results demonstrate that the structure exploited within the wavelet coefficients provides superior performance in terms of average reconstruction error and structural similarity index.

The purpose of this paper is to exploit the Compressed Sensing theory in order to compress multi-lead ECG channels with a high compression ratio and minimum reconstruction error. In order to obtain the sparse representation of the ECG signals a basis matrix with Gaussian kernels which have the maximum resemblance with ECG signals, is constructed. Then using Orthogonal matching pursuit, algorithm which is a greedy/iterative optimization technique, the sparse representation is acquired.Finally, utilizing the Compressed Sensing theory is possible. In order to prove the accuracy of the algorithm the same optimization technique is used to reconstruct the Compressed signal. Using a wavelet basis is also common to obtain the sparse representation. The Compressed Sensing theory is also applied to the ECG signals for which their sparse representations have been obtained using a wavelet basis. The results show the superiority of the proposed method over the wavelet basis.

Speckle noise seriously degrades the quality of SAR images and complicates the image exploitation using automated image analysis techniques. Recently, the application of Compressed Sensing ((CS)) is explored in the SAR signal processing. In this paper, first, a linear model is derived for speckled SAR data. Then, using this model and the Compressed Sensing theory, a speckle reduction method is proposed. In the proposed method, the image backgrounds as well as the bright point targets are also reconstructed together with noise reduction. The important feature of the proposed method is the joint noise reduction simultaneous with the SAR image formation. Moreover, using simulated and real SAR images, the performance of the proposed method in noise reduction and preserving image features is evaluated and compared to the performance of some de-noising approaches.

Background and Objectives: Compressed Sensing ((CS)) of analog signals in shift-invariant spaces can be used to reduce the complexity of the matched-filter (MF) receiver, in which we can be approached the standard MF performance with fewer filters. But, with a small number of filters the performance degrades quite rapidly as a function of SNR. In fact, the (CS) matrix aliases all the noise components, therefore the noise increases in the Compressed measurements. This effect is referred to as noise folding. In this paper, an approach for compensating the noise folding effect is proposed. Methods: An approach for compensating of this effect is to use a sufficient number of filters. In this paper the aim is to reach the better performance with the same number of filter as in the previous work. This, can be approached using a weighting function embedded in the analog signal Compressed Sensing structure. In fact, using this weighting function we can remedy the effect of (CS) matrix on the noise variance. Results: Comparing with the approach based on using the sufficient number of filters to counterbalance the noise increase, experimental results show that with the same numbers of filters, in terms of probability of correct detection, the proposed approach remarkably outperforms the rival’s.Conclusion: Noise folding formation is the main factor in (CS)-based matched-filter receiver. The method previously presented to reduce this effect demanded using the sufficient number of filters which comes at a cost. In this paper we propose a new method based on using the weighting function embedded in the analog signal Compressed Sensing structure to achieve better performance.

Massive Multiple-Input Multiple-Output (mMIMO) is a promising approach for the next generation wireless telecommunication systems. In these systems, having a suitable approach for channel estimation is mandatory in order to increase the data rate and spectral efficiency. Distributed Compressed Sensing (D(CS)) is prominent in extracting joint sparse channel state information ((CS)I). Here, we have utilized Alternating Direction Method of Multipliers (ADMM) approach to generate quasi-orthogonal pilot sequences, in order to improve the channel estimation approach based on D(CS) approach. In simulation results, it is represented that ADMM-based pilot sequences are very powerful in extracting (CS)I of the joint sparse channel ensembles.

In this paper, the compressive Sensing ((CS)) method is used in the through the wall radar imaging (TWRI) to reduce the measurement points and data acquisition time, consequently. In fact, the large required amount of measurement points is considered as one of the main challenges in TWRI which can be mitigated by this proposed method. The diffraction tomography (DT) method is the most efficient conventional method used in TWRI process. By exploiting the advantages of the (CS) and non-uniform fast Fourier transform (NUFFT), the effectiveness and speediness of the DT method is significantly increased. Simulations and the results of experiments have verified the validity of the proposed imaging method.

In this paper, sparse representation of EEG signal is used to automatically classify sleep stages. In this regard, two general sparse representation trends are proposed to classify 4-class sleep stages. The first proposed method is based on sparse principal component analysis (SPCA) which uses different features including time, frequency, and time-frequency features applied to support vector machine (SVM) classifier. The second proposed method is based on sparse representation-based classifier (SRC) which uses orthogonal matching pursuit (OMP) algorithm to obtain sparse coding of the EEG signal. In order to evaluate the effectiveness of the proposed algorithms, their performance is compared with the conventional SVM classification based on PCA method using time, frequency, and time-frequency features. The study is carried out on EEG signal from Physionet international database. Simulation results show on the average 8. 36% and 8. 26% improvement of the first proposed method in terms of classification accuracy compared to the PCA and deep learning methods, respectively, while the second proposed method has achieved the running time of 118% and 72% faster than the existing PCA and deep learning methods, respectively.

The problem of sparse signal reconstruction from the well-known Compressed Sensing measurement is considered in this paper. The measured signal is assumed to be corrupted with white Gaussian noise with zero mean and known variance. Based on detection theory, two iterative algorithms are developed for detection and estimation of nonzero elements of sparse signal. The principle of the proposed methods is based on applying composite multiple hypothesis test to the underlying problem at each iteration. Simulation results show the satisfactory performance of the proposed algorithms in sparse signal recovery. The proposed approach has the potential of being applied to other models for noise and signal.

The analysis of gene sequences is fundamentally important for exploring biological functions. Recently, the cost of gene sequencing has dropped sharply, thereby resulting in the production of considerable genomic data. However, the costs of saving, processing, and transferring these data are rising. At present, processing this massive volume of information is done by character based method which is highly time-consuming. Alternative methods challenge these problems in the realm of signal processing. Accordingly, the signal outlook to the genome, signal processing of the genome and compression of the genome are presently hot issues which are practically in demand. Compression reduces the cost, memory space, bandwidth for exchange, and the time required for analysis. In this study, the character genes were firstly represented as signals. Then, these genomic signals were Compressed by Compressed Sensing. Consequently, they were reconstructed by bayesian learning method. Adopted criteria for reconstruction were PRD and NMSE, respectively. Then, signals were selected with a compression rate of 75% for comparison. Meanwhile, the same cluster analysis was run with character based method. The results indicated that the time needed for signal based method was considerably lower than the character based method.