Simultaneous Orthogonal Matching Pursuit Research Articles

Multi-Channel ECG Signals Compression Algorithm Using Simultaneous Orthogonal Matching Pursuit

Sparse decompression is a new theory for signal processing, having the advantage in that the base (dictionary) used in this theory is over-complete, and can reflect the nature of signa1. So the sparse decompression of signal can get sparse representation, which is very important in data compression. In this paper, a novel ECG compression method for multi-channel ECG signals was introduced based on the Simultaneous Orthogonal Matching Pursuit (S-OMP). The proposed method decomposes multi-channel ECG signals simultaneously into different linear expansions of the same atoms that are selected from a redundant dictionary, which is constructed by Hermite fuctions and Gobar functions in order to the best match the characteristic of the ECG waveform. Compression performance has been tested using a subset of multi-channel ECG records from the St.-Petersburg Institute of Cardiological Technics database, the results demonstrate that much less atoms are selected to present signals and the compression ratio of Multi-channel ECG can achieve better performance in comparison to Simultaneous Matching Pursuit (SMP).

Joint compressive spectrum sensing scheme in wideband cognitive radio networks

In this paper, a distributed compressive spectrum sensing scheme in wideband cognitive radio networks is investigated. An analog-to-information converters (AIC) RF front-end sampling structure is proposed which use parallel low rate analog to digital conversions (ADCs) and fewer storage units for wideband spectrum signal sampling. The proposed scheme uses multiple low rate congitive radios (CRs) collecting compressed samples through AICs distritbutedly and recover the signal spectrum jointly. A general joint sparsity model is defined in this scenario, along with a universal recovery algorithm based on simultaneous orthogonal matching pursuit (S-OMP). Numerical simulations show this algorithm outperforms current existing algorithms under this model and works competently under other existing models.

Color image fusion using sparse representation

It is hard to generate high quality images directly by camera because of some inherent limitations of camera when the scene contains objects at greatly varying distances or large local changes in illumination. Image fusion is an effective way to obtain high quality image in these situations. A novel color image fusion method based on sparse representation is proposed in this paper. Since it is observed that the geometrical structure among different color channels is similar, we apply the same overcomplete dictionary composed of the DCT, Haar wavelet, Gabor and Ridgelet dictionary to three color channels simultaneously. To speed up the simultaneous sparse representation of source images, we develop the simultaneous stagewise orthogonal matching pursuit algorithm. The proposed fusion method is applied to extend depth of field and dynamic range for color images. The experimental results show that our method outperforms other recent methods in terms of both visual effect and objective evaluation.

Plate impulse response spatial interpolation with sub-Nyquist sampling

Impulse responses of vibrating plates are classically measured on a fine spatial grid satisfying the Shannon–Nyquist spatial sampling criterion, and interpolated between measurement points. For homogeneous and isotropic plates, this study proposed a more efficient sampling and interpolation process, inspired by the recent paradigm of compressed sensing. Remarkably, this method can accommodate any star-convex shape and unspecified boundary conditions. Here, impulse responses are first decomposed as sums of damped sinusoids, using the Simultaneous Orthogonal Matching Pursuit algorithm. Finally, modes are interpolated using a plane wave decomposition. As a beneficial side effect, these algorithms can also be used to obtain the dispersion curve of the plate with a limited number of measurements. Experimental results are given for three different plates of different shapes and boundary conditions, and compared to classical Shannon interpolation.

Cooperative wideband spectrum sensing based on sequential compressed sensing

Compressed sensing offers a new wideband spectrum sensing scheme in Cognitive Radio (CR). A major challenge of this scheme is how to determinate the required measurements while the signal sparsity is not known a priori. This paper presents a cooperative sensing scheme based on sequential compressed sensing where sequential measurements are collected from the analog-to-information converters. A novel cooperative compressed sensing recovery algorithm named Simultaneous Sparsity Adaptive Matching Pursuit (SSAMP) is utilized for sequential compressed sensing in order to estimate the reconstruction errors and determinate the minimal number of required measurements. Once the fusion center obtains enough measurements, the reconstruction spectrum sparse vectors are then used to make a decision on spectrum occupancy. Simulations corroborate the effectiveness of the estimation and sensing performance of our cooperative scheme. Meanwhile, the performance of SSAMP and Simultaneous Orthogonal Matching Pursuit (SOMP) is evaluated by Mean-Square estimation Errors (MSE) and sensing time.

Rank Awareness in Joint Sparse Recovery

This paper revisits the sparse multiple measurement vector (MMV) problem, where the aim is to recover a set of jointly sparse multichannel vectors from incomplete measurements. This problem is an extension of single channel sparse recovery, which lies at the heart of compressed sensing. Inspired by the links to array signal processing, a new family of MMV algorithms is considered that highlight the role of rank in determining the difficulty of the MMV recovery problem. The simplest such method is a discrete version of MUSIC which is guaranteed to recover the sparse vectors in the full rank MMV setting, under mild conditions. This idea is extended to a rank aware pursuit algorithm that naturally reduces to Order Recursive Matching Pursuit (ORMP) in the single measurement case while also providing guaranteed recovery in the full rank setting. In contrast, popular MMV methods such as Simultaneous Orthogonal Matching Pursuit (SOMP) and mixed norm minimization techniques are shown to be rank blind in terms of worst case analysis. Numerical simulations demonstrate that the rank aware techniques are significantly better than existing methods in dealing with multiple measurements.

Channel estimation based on distributed compressed sensing in amplify-and-forward relay networks

In orthogonal frequency-division multiplexing (OFDM) amplify-and-forward (AF) relay networks, in order to exploit diversity gains over frequency-selective fading channels, the receiver needs to acquire the knowledge of channel state information (CSI). In this article, based on the recent methodology of distributed compressed sensing (DCS), a novel channel estimation scheme is proposed. The joint sparsity model 2 (JSM-2) in DCS theory and simultaneous orthogonal matching pursuit (SOMP) are both introduced to improve the estimation performance and increase the spectral efficiency. Simulation results show that compared with current compressed sensing (CS) methods, the estimation error of our scheme is reduced dramatically in high SNR region while the pilot number is still kept small.

Pixel-level image fusion with simultaneous orthogonal matching pursuit

Pixel-level image fusion integrates the information from multiple images of one scene to get an informative image which is more suitable for human visual perception or further image-processing. Sparse representation is a new signal representation theory which explores the sparseness of natural signals. Comparing to the traditional multiscale transform coefficients, the sparse representation coefficients can more accurately represent the image information. Thus, this paper proposes a novel image fusion scheme using the signal sparse representation theory. Because image fusion depends on local information of source images, we conduct the sparse representation on overlapping patches instead of the whole image, where a small size of dictionary is needed. In addition, the simultaneous orthogonal matching pursuit technique is introduced to guarantee that different source images are sparsely decomposed into the same subset of dictionary bases, which is the key to image fusion. The proposed method is tested on several categories of images and compared with some popular image fusion methods. The experimental results show that the proposed method can provide superior fused image in terms of several quantitative fusion evaluation indexes.

Average Case Analysis of Multichannel Sparse Recovery Using Convex Relaxation

This paper considers recovery of jointly sparse multichannel signals from incomplete measurements. Several approaches have been developed to recover the unknown sparse vectors from the given observations, including thresholding, simultaneous orthogonal matching pursuit (SOMP), and convex relaxation based on a mixed matrix norm. Typically, worst case analysis is carried out in order to analyze conditions under which the algorithms are able to recover any jointly sparse set of vectors. However, such an approach is not able to provide insights into why joint sparse recovery is superior to applying standard sparse reconstruction methods to each channel individually. Previous work considered an average case analysis of thresholding and SOMP by imposing a probability model on the measured signals. Here, the main focus is on analysis of convex relaxation techniques. In particular, the mixed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> approach to multichannel recovery is investigated. Under a very mild condition on the sparsity and on the dictionary characteristics, measured for example by the coherence, it is shown that the probability of recovery failure decays exponentially in the number of channels. This demonstrates that most of the time, multichannel sparse recovery is indeed superior to single channel methods. The probability bounds are valid and meaningful even for a small number of signals. Using the tools developed to analyze the convex relaxation technique, also previous bounds for thresholding and SOMP recovery are tightened.

Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit

A simultaneous sparse approximation problem requests a good approximation of several input signals at once using different linear combinations of the same elementary signals. At the same time, the problem balances the error in approximation against the total number of elementary signals that participate. These elementary signals typically model coherent structures in the input signals, and they are chosen from a large, linearly dependent collection.The first part of this paper proposes a greedy pursuit algorithm, called simultaneous orthogonal matching pursuit (S-OMP), for simultaneous sparse approximation. Then it presents some numerical experiments that demonstrate how a sparse model for the input signals can be identified more reliably given several input signals. Afterward, the paper proves that the S-OMP algorithm can compute provably good solutions to several simultaneous sparse approximation problems.The second part of the paper develops another algorithmic approach called convex relaxation, and it provides theoretical results on the performance of convex relaxation for simultaneous sparse approximation.