Correct Support Recovery Research Articles

A blind stopping condition for orthogonal matching pursuit with applications to compressive sensing radar

Orthogonal matching pursuit (OMP) is a popular greedy algorithm because of its simplicity and low computational cost. In the application of OMP, one of the most important issue is to design a stopping condition according to some prior information, such as sparsity and noise level. In this paper, we provide a blind stopping condition for OMP in the presence of Gaussian noise. We theoretically analyze the stopping condition in terms of the mutual incoherence and the minimum component signal-to-noise ratio (SNR), with which OMP can stop with correct support recovery. Different from other alternatives, the proposed stopping condition can be explicitly determined regardless of prior information. So it is much suitable for practical applications. In the application of compressive sensing pulse-Doppler radar, we further analyze the support recovery performance of the proposed condition. By separately recovering the targets belonging to different Doppler frequencies, we remarkably reduce the requirement on the minimum component SNR of all targets, and thus our stopping condition is applicable to low SNR scenes. Numerical results illustrate that the proposed condition has comparable performance to the alternative with a priori information.

Adaptive multi-penalty regularization based on a generalized Lasso path

For many algorithms, parameter tuning remains a challenging task, which becomes tedious in a multi-parameter setting. Multi-penalty regularization, successfully used for solving undetermined sparse regression problems of unmixing type, is one of such examples. We propose a novel algorithmic framework for an adaptive parameter choice in multi-penalty regularization with focus on correct support recovery. By extending ideas on regularization paths, we provide an efficient procedure for the construction of regions containing structurally similar solutions, i.e., solutions with the same sparsity and sign pattern, over the range of parameters. Combined with a model selection criterion, regularization parameters are chosen in a data-adaptive manner. Another advantage of our algorithm is that it provides an overview on the solution stability over the parameter range. We provide a numerical analysis of our method and compare it to the state-of-the-art algorithms for compressed sensing problems to demonstrate the robustness and power of the proposed algorithm.

Preconditioning for Orthogonal Matching Pursuit with Noisy and Random Measurements: The Gaussian Case

The success of orthogonal matching pursuit (OMP) in the sparse signal recovery heavily depends on its ability for correct support recovery. Based on a support recovery guarantee for OMP expressed in terms of the mutual coherence, and a result about the concentration of the extreme singular values of a Gaussian random matrix, this paper proposes a preconditioning method for increasing the recovery rate of OMP from random and noisy measurements. Compared to several existing preconditionings, the proposed method can reduce the mutual coherence with a proven high probability. Simultaneously, the proposed preconditioning can also succeed with a high probability in providing slight signal-to-noise ratio reduction, which is empirically shown to be less severe than that caused by a recently suggested technique for the noisy case. The simulations show the advantages of the proposed preconditioning over other currently relevant ones in terms of both the performance improvement for OMP, and computation time.

Predecision for Wideband Spectrum Sensing With Sub-Nyquist Sampling

Built on compressed sensing theories, sub-Nyquist spectrum sensing (SNSS) has emerged as a promising solution to the wideband spectrum sensing problem. However, most of the existing SNSS methods do not distinguish if primary users (PUs) are present or absent in the concerned spectrum band and directly pursue support recovery of the PUs. This may lead to a high false alarm rate and a waste of computational cost. To address the issue, we propose a predecision algorithm, referred to as the pairwise channel energy ratio (PCER) detector, to determine the presence or absence of PUs prior to signal support recovery. The proposed detector is based on the popular modulated wideband converter (MWC) framework for SNSS, which has several advantages over other SNSS approaches. The PCER test statistic is constructed from compressed samples obtained by the MWC. The decision threshold and the detection probability are derived in closed form following the Neyman–Pearson criterion. Numerical results are presented to verify the theoretical calculation. The proposed PCER detection method is shown to be able to detect the existence of PUs in a wide range of signal-to-noise ratio, while being robust to noise uncertainty and does not need the prior knowledge of the PU signals. Additionally, our results show that the use of the PCER detector leads to a significant improvement of the correct support recovery rate of the PU signals.

A Subspace Projection-Based Joint Sparse Recovery Method for Structured Biomedical Signals

Sparse signal processing has shown a significant promise for the reconstruction of biomedical signals, which possess well-defined sparsity structures in an appropriate transform domain. In this paper, a reconstruction algorithm is proposed based on the multiple-measurement-vector model using the hidden sparsity and correlation structure of biomedical signals. This incorporates subspace filtering over the partial supports, initialized by the sparse Bayesian learning framework along with a maximum projection-based support-estimation technique. The proposed method outperforms the conventional algorithms with respect to correct support recovery rate and needs fewer measurements. The robustness is studied by employing real-world biomedical signals. The experimental results using multichannel fetal-electrocardiogram signals and respiratory signals, collected from the Physiobank database, show that the proposed technique is an improved method in terms of reconstruction quality and compression rate.

Undersampled Phase Retrieval with Outliers.

This paper proposes a general framework for reconstructing sparse images from undersampled (squared)-magnitude data corrupted with outliers and noise. This phase retrieval method uses a layered approach, combining repeated minimization of a convex majorizer (surrogate for a nonconvex objective function), and iterative optimization of that majorizer using a preconditioned variant of the alternating direction method of multipliers (ADMM). Since phase retrieval is nonconvex, this implementation uses multiple initial majorization vectors. The introduction of a robust 1-norm data fit term that is better adapted to outliers exploits the generality of this framework. The derivation also describes a normalization scheme for the regularization parameter and a known adaptive heuristic for the ADMM penalty parameter. Both 1D Monte Carlo tests and 2D image reconstruction simulations suggest the proposed framework, with the robust data fit term, reduces the reconstruction error for data corrupted with both outliers and additive noise, relative to competing algorithms having the same total computation.

Compressed sensing of ECG signal for wireless system with new fast iterative method

Recent experiments in wireless body area network (WBAN) show that compressive sensing (CS) is a promising tool to compress the Electrocardiogram signal ECG signal. The performance of CS is based on algorithms use to reconstruct exactly or approximately the original signal. In this paper, we present two methods work with absence and presence of noise, these methods are Least Support Orthogonal Matching Pursuit (LS-OMP) and Least Support Denoising-Orthogonal Matching Pursuit (LSD-OMP). The algorithms achieve correct support recovery without requiring sparsity knowledge. We derive an improved restricted isometry property (RIP) based conditions over the best known results.The basic procedures are done by observational and analytical of a different Electrocardiogram signal downloaded them from PhysioBankATM.Experimental results show that significant performance in term of reconstruction quality and compression rate can be obtained by these two new proposed algorithms, and help the specialist gathering the necessary information from the patient in less time if we use Magnetic Resonance Imaging (MRI) application, or reconstructed the patient data after sending it through the network.

Strong recovery conditions for least support orthogonal matching pursuit in noisy case

A least support denoising-orthogonal matching pursuit (LSD-OMP) algorithm to reconstruct the sparse signal using less number of iterations from noisy measurements is presented. The algorithm achieves correct support recovery without requiring sparsity knowledge. An improved restricted isometry property-based condition is derived over the best-known results. Experimental results demonstrate that the LSD-OMP achieves good performance on recovering sparse signals, outperforming the latest state-of-the art method in terms of reconstructed signal-to-noise ratio and running time.

Sufficient conditions for generalized Orthogonal Matching Pursuit in noisy case

In compressive sensing, generalized Orthogonal Matching Pursuit (gOMP) algorithm generalizes OMP algorithm by selecting N(N≥1) atoms in each iteration. In this paper, we propose restricted isometry constant based sufficient conditions for gOMP algorithm to correctly recover the support of significant components of signal when both measurement dictionary and measurement signal are contaminated with noise. Bound of estimation error is also derived. Upper bound of restricted isometry constant could be relaxed if the original sparse signal is strong decaying. When sparsity of original sparse signal is unavailable, we give a stopping criterion of gOMP algorithm to ensure correct support recovery.

Sparse Spatial Spectral Estimation: A Covariance Fitting Algorithm, Performance and Regularization

In this paper, the sparse spectrum fitting (SpSF) algorithm for the estimation of directions-of-arrival (DOAs) of multiple sources is introduced, and its asymptotic consistency and effective regularization under both asymptotic and finite sample cases are studied. Specifically, through the analysis of the optimality conditions of the method, we prove the asymptotic, in the number of snapshots, consistency of SpSF estimators of the DOAs and the received powers of uncorrelated sources in a sparse spatial spectra model. Along with this result, an explicit formula of the best regularization parameter of SpSF estimator with infinitely many snapshots is obtained. We then build on these results to investigate the problem of selecting an appropriate regularization parameter for SpSF with finite snapshots. An automatic selector of such regularization parameter is presented based on the formulation of an upper bound on the probability of correct support recovery of SpSF, which can be efficiently evaluated by Monte Carlo simulations. Simulation results illustrating the effectiveness and performance of this selector are provided, and the application of SpSF to direction-finding for correlated sources is discussed.