Orthogonal Matching Pursuit Approach Research Articles

On the sparsity bound for the existence of a unique solution in compressive sensing by the Gershgorin theorem

Since compressive sensing deals with a signal reconstruction using a reduced set of measurements, the existence of a unique solution is of crucial importance. The most important approach to this problem is based on the restricted isometry property which is computationally unfeasible. The coherence index-based uniqueness criteria are computationally efficient, however, they are pessimistic. An approach to alleviating this problem has been recently introduced by relaxing the coherence index condition for the unique signal reconstruction using the orthogonal matching pursuit approach. This approach can be further relaxed and the sparsity bound improved if we consider only the solution existence rather than its reconstruction. One such improved bound for the sparsity limit is derived in this paper using the Gershgorin disk theorem.

Compressive sensing based PAPR reduction in OFDM systems: Modified orthogonal matching pursuit approach

Abstract Orthogonal frequency division multiplexing (OFDM) has been proposed to achieve high data rate transmission in wireless communications. The OFDM system usually suffers from the high envelope fluctuations called peak-to-average power ratio (PAPR). The high PAPR causes a signal clipping distortion, and consequently, the performance is degraded. To mitigate the PAPR, we introduce a new PAPR reduction approach using a compressive sensing approach at the transmitter side and an orthogonal matching pursuit (OMP) reconstruction algorithm at the receiver end. Numerical results show the significant reduction of the PAPR compared with the traditional OFDM system without degrading the bit error rate performance.

Multiple Batches of Motion History Images (MB-MHIs) for Multi-view Human Action Recognition

The recognition of human actions recorded in a multi-camera environment faces the challenging issue of viewpoint variation. Multi-view methods employ videos from different views to generate a compact view-invariant representation of human actions. This paper proposes a novel multi-view human action recognition approach that uses multiple low-dimensional temporal templates and a reconstruction-based encoding scheme. The proposed approach is based upon the extraction of multiple 2D motion history images (MHIs) of human action videos over non-overlapping temporal windows, constructing multiple batches of motion history images (MB-MHIs). Then, two kinds of descriptions are computed for these MHIs batches based on (1) a deep residual network (ResNet) and (2) histogram of oriented gradients (HOG) to effectively quantify a change in gradient. ResNet descriptions are average pooled at each batch. HOG descriptions are processed independently at each batch to learn a class-based dictionary using a K-spectral value decomposition algorithm. Later, the sparse codes of feature descriptions are obtained using an orthogonal matching pursuit approach. These sparse codes are average pooled to extract encoded feature vectors. Then, encoded feature vectors at each batch are fused to form a final view-invariant feature representation. Finally, a linear support vector machine classifier is trained for action recognition. Experimental results are given on three versions of a multi-view dataset: MuHAVi-8, MuHAVi-14, and MuHAVi-uncut. The proposed approach shows promising results when tested for a novel camera. Results on deep features indicate that action representation by MB-MHIs is more view-invariant than single MHIs.

Efficient Computation of MSE Lower Bounds via Matching Pursuit

The classes of large-error bounds that are based on the covariance inequality, in both Bayesian and non-Bayesian approaches, are characterized as projection-based bounds. Tightening of bounds in these classes involves high computational complexity due to multidimensional optimization procedure. Consequently, projection-based large-error bounds have little popularity, while small-error bounds are frequently preferred, although they are not necessarily tight. In this letter, we first introduce a unified formulation for Bayesian and non-Bayesian projection-based lower bounds and set a general framework, which allows for their approximation via a greedy-based method. This framework is then used to propose the use of optimized orthogonal matching pursuit approach for computing projection-based large-error bounds. We analyze the complexity of the proposed algorithm and show that it is significantly lower than the complexity of the conventional approach. Finally, we apply the algorithm for the problem of multitone estimation and show that for fixed computational resources, the Weiss–Weinstein bound implemented with the proposed algorithm, provides a tighter bound compared to conventional approaches.

Sparse representation‐based quasi‐clean speech construction for speech quality assessment under complex environments

A non-intrusive speech quality assessment method for complex environments was proposed. In the proposed approach, a new sparse representation-based speech reconstruction algorithm was presented to acquire the quasi-clean speech from the noisy degraded signal. Firstly, an over-complete dictionary of the clean speech power spectrum was learned by the K-singular value decomposition algorithm. Then in the sparse representation stage, the stopping residue error was adaptively achieved according to the estimated cross-correlation and the noise spectrum which was adjusted by a posteriori SNR-weighted factor, and the orthogonal matching pursuit approach was applied to reconstruct the clean speech spectrum from the noisy speech. The quasi-clean speech was considered as the reference to a modified PESQ perceptual model, and the mean opinion score of the noisy degraded speech was achieved via the distortions estimation between the quasi-clean speech and the degraded speech. Experimental results show that the proposed approach obtains a correlation coefficient of 0.925 on NOIZEUS complex environment database, which is 99% similar to the performance of the intrusive standard ITU-T PESQ, and 7.1% outperforms non-intrusive standard ITU-T P.563.

Compressed sensing of roller bearing fault based on multiple down-sampling strategy

Roller bearings are essential components of rotating machinery and are often exposed to complex operating conditions, which can easily lead to their failures. Thus, to ensure normal production and the safety of machine operators, it is essential to detect the failures as soon as possible. However, it is a major challenge to maintain a balance between detection efficiency and big data acquisition given the limitations of sampling theory. To overcome these limitations, we try to preserve the information pertaining to roller bearing failures using a sampling rate far below the Nyquist sampling rate, which can ease the pressure generated by the large-scale data. The big data of a faulty roller bearing’s vibration signals is firstly reduced by a down-sample strategy while preserving the fault features by selecting peaks to represent the data segments in time domain. However, a problem arises in that the fault features may be weaker than before, since the noise may be mistaken for the peaks when the noise is stronger than the vibration signals, which makes the fault features unable to be extracted by commonly-used envelope analysis. Here we employ compressive sensing theory to overcome this problem, which can make a signal enhancement and reduce the sample sizes further. Moreover, it is capable of detecting fault features from a small number of samples based on orthogonal matching pursuit approach, which can overcome the shortcomings of the multiple down-sample algorithm. Experimental results validate the effectiveness of the proposed technique in detecting roller bearing faults.

Compressed-sensing-based content-driven hierarchical reconstruction: Theory and application to C-arm cone-beam tomography.

This paper addresses the reconstruction of x-ray cone-beam computed tomography (CBCT) for interventional C-arm systems. Subsampling of CBCT is a significant issue with C-arms due to their slow rotation and to the low frame rate of their flat panel x-ray detectors. The aim of this work is to propose a novel method able to handle the subsampling artifacts generally observed with analytical reconstruction, through a content-driven hierarchical reconstruction based on compressed sensing. The central idea is to proceed with a hierarchical method where the most salient features (high intensities or gradients) are reconstructed first to reduce the artifacts these features induce. These artifacts are addressed first because their presence contaminates less salient features. Several hierarchical schemes aiming at streak artifacts reduction are introduced for C-arm CBCT: the empirical orthogonal matching pursuit approach with the ℓ0 pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the ℓ1-norm constraint of compressed sensing, for reconstructing sparse vessels over a nonsparse background; homotopy with total variation (TV); and a novel empirical extension to nonlinear diffusion (NLD). Such principles are implemented with penalized iterative filtered backprojection algorithms. For soft-tissue imaging, the authors compare the use of TV and NLD filters as sparsity constraints, both optimized with the alternating direction method of multipliers, using a threshold for TV and a nonlinear weighting for NLD. The authors show on simulated data that their approach provides fast convergence to good approximations of the solution of the TV-constrained minimization problem introduced by the compressed sensing theory. Using C-arm CBCT clinical data, the authors show that both TV and NLD can deliver improved image quality by reducing streaks. A flexible compressed-sensing-based algorithmic approach is proposed that is able to accommodate for a wide range of constraints. It is successfully applied to C-arm CBCT images that may not be so well approximated by piecewise constant functions.

Backward-Optimized Orthogonal Matching Pursuit Approach

A recursive approach for shrinking coefficients of an atomic decomposition is proposed. The corresponding algorithm evolves so as to provide at each iteration a) the orthogonal projection of a signal onto a reduced subspace and b) the index of the coefficient to be disregarded in order to construct a coarser approximation minimizing the norm of the residual error.

Optimized orthogonal matching pursuit approach

An adaptive procedure for signal representation is proposed. The representation is built up through functions (atoms) selected from a redundant family (dictionary). At each iteration, the algorithm gives rise to an approximation of a given signal, which is guaranteed (1) to be the orthogonal projection of a signal onto the subspace generated by the selected atoms and (2) to minimize the norm of the corresponding residual error. The approach is termed optimized orthogonal matching pursuit because it improves upon the earlier proposed matching pursuit and orthogonal matching pursuit approaches.