Greedy Recovery Algorithm Research Articles

A new greedy sparse recovery algorithm for fast solving sparse representation

Kernel sparse representation-based classification (KSRC) in compressive sensing represents one of the most interesting research areas in pattern recognition and image processing. Nevertheless, KSRC is subjected to some shortcomings. KSRC is greedy in time to achieve an approximate solution of sparse representation based on $$\ell_{1}$$ -norm minimization. A diversity of greedy recovery algorithms have been tested in order to decrease computational complexity compared to the optimal $$\ell_{1}$$ -norm minimization while keeping a proved reconstruction accuracy. In this research, we suggest a new greedy recovery algorithm, called the fast reduced sampling matching pursuit (FRSMP). Unlike previous greedy recovery algorithms which applied too many or very few values per iteration, FRSMP selects a sufficient number of elements. Moreover, FRSMP performs the least square minimization iteratively through the Sherman–Morrison–Woodbury formula, to avoid large matrix inversion which results in a significant speedup. Experimental results with both noisy and noiseless data have shown that the proposed FRSMP method achieves a higher reconstruction accuracy at low reconstruction time compared to other greedy pursuit algorithms. Also, experiments on frequent face databases have proven that the KSRC-based FRSMP method shows reliable and higher recognition rate and computation time compared with other advanced sparse representation methods for face recognition.

Cross Validation Based Distributed Greedy Sparse Recovery for Multiview Through-the-Wall Radar Imaging

Multiview through-the-wall radar imaging (TWRI) can improve the imaging quality and target detection by exploiting the measurement data acquired from various views. Based on the established joint sparsity signal model for multiview TWRI, a cross validation (CV) based distributed greedy sparse recovery algorithm which combines the strengths of the CV technique and censored simultaneous orthogonal matching pursuit algorithm (CSOMP) is proposed in this paper. The developed imaging algorithm named by CV-CSOMP which separates the total measurements into reconstruction measurements and CV measurements is able to achieve the accurate imaging reconstruction and estimation of recovery error tolerance by the iterative CSOMP calculation. The proposed CV-CSOMP imaging algorithm not only can reduce the communication costs among radar units, but also can provide the desirable imaging performance without the prior information such as the sparsity or noise level. The experimental results have verified the validity and effectiveness of the proposed imaging algorithm.

Fast matching pursuit for wideband spectrum sensing in cognitive radio networks

Wideband spectrum sensing is one of the most challenging components of cognitive radio networks. It should be performed as fast and accurately as possible. Traditional wideband spectrum sensing techniques suffer from the requirement of analog-to-digital converters with very high sampling rates. Compressed sensing has been recently considered as a technique that may enable wideband spectrum sensing at a much lower sampling rate than that dictated by the Nyquist theorem. However, the complexity and speed of existing compressed sensing reconstruction techniques remained a barrier for such an application. In this paper, we introduce fast matching pursuit (FMP), a fast and accurate greedy recovery algorithm for compressed sensing. We show that the spectral data are sparse in the Haar wavelet and wavelet packet domains. We apply FMP to wideband spectrum sensing for cognitive radio networks. Our proposed algorithm is capable of reconstructing spectrum signals from samples at a rate of about 25% of the Nyquist rate, significantly faster than other related algorithms, at more than 99% probability of detection and less than 1% probability of false alarm.

Design and Implementation of Low-Power Analog-to-Information Conversion for Environmental Information Perception

Because sensing nodes typically have limited power resources, it is extremely important for signals to be acquired with high efficiency and low power consumption, especially in large-scale wireless sensor networks (WSNs) applications. An emerging signal acquisition and compression method called compressed sensing (CS) is a notable alternative to traditional signal processing methods and is a feasible solution for WSNs. In our previous work, we studied several data recovery algorithms and network models that use CS for compressive sampling and signal recovery. The results were validated on large data sets from actual environmental monitoring WSNs. In this paper, we focus on the hardware solution for signal acquisition and processing on separate end nodes. We propose the paradigm of an analog-to-information converter (AIC) based on CS theory. The system model consists of a modulation module, filtering module, and sampling module, and was simulated and analyzed in a MATLAB/Simulink 7.0 environment. Further, the hardware design and implementation of an improved digital AIC system is presented. We also study the performances of three different greedy data recovery algorithms and analyze the system power consumption. The experimental results show that, for normal environmental signals, the new system overcomes the Nyquist limit and exhibits good recovery performance with a low sampling frequency, which is suitable for environmental monitoring based on WSNs.

On the number of iterations for convergence of CoSaMP and Subspace Pursuit algorithms

In compressive sensing, one important parameter that characterizes the various greedy recovery algorithms is the iteration bound which provides the maximum number of iterations by which the algorithm is guaranteed to converge. In this letter, we present a new iteration bound for the compressive sampling matching pursuit (CoSaMP) algorithm by certain mathematical manipulations including formulation of appropriate sufficient conditions that ensure passage of a chosen support through the two selection stages of CoSaMP, “Augment” and “Update”. Subsequently, we extend the treatment to the subspace pursuit (SP) algorithm. The proposed iteration bounds for both CoSaMP and SP algorithms are seen to be improvements over their existing counterparts, revealing that both CoSaMP and SP algorithms converge in fewer iterations than suggested by results available in literature. • Presents new iteration bounds for CoSaMP and subspace pursuit (SP) algorithms. • Proposed bounds are lesser than their counterparts existing in literature. • The reduction is significant for moderately large K , i.e., system sparsity. • New results on convergence behavior of CoSaMP and SP algorithms presented.

RMP: Reduced-set matching pursuit approach for efficient compressed sensing signal reconstruction

Compressed sensing enables the acquisition of sparse signals at a rate that is much lower than the Nyquist rate. Compressed sensing initially adopted ℓ1 minimization for signal reconstruction which is computationally expensive. Several greedy recovery algorithms have been recently proposed for signal reconstruction at a lower computational complexity compared to the optimal ℓ1 minimization, while maintaining a good reconstruction accuracy. In this paper, the Reduced-set Matching Pursuit (RMP) greedy recovery algorithm is proposed for compressed sensing. Unlike existing approaches which either select too many or too few values per iteration, RMP aims at selecting the most sufficient number of correlation values per iteration, which improves both the reconstruction time and error. Furthermore, RMP prunes the estimated signal, and hence, excludes the incorrectly selected values. The RMP algorithm achieves a higher reconstruction accuracy at a significantly low computational complexity compared to existing greedy recovery algorithms. It is even superior to ℓ1 minimization in terms of the normalized time-error product, a new metric introduced to measure the trade-off between the reconstruction time and error. RMP superior performance is illustrated with both noiseless and noisy samples.

Achieving Autonomous Compressive Spectrum Sensing for Cognitive Radios

Compressive sensing (CS) technologies present many advantages over other existing approaches for implementing wideband spectrum sensing in cognitive radios (CRs), such as reduced sampling rate and computational complexity. However, there are two significant challenges: 1) choosing an appropriate number of sub-Nyquist measurements, and 2) deciding when to terminate the greedy recovery algorithm that reconstructs wideband spectrum. In this paper, an autonomous compressive spectrum sensing (ACSS) framework is presented that enables a CR to automatically choose the number of measurements while guaranteeing the wideband spectrum recovery with a small predictable recovery error. This is realized by the proposed measurement infrastructure and the validation technique. The proposed ACSS can find a good spectral estimate with high confidence by using only a small testing subset in both noiseless and noisy environments. Furthermore, a sparsity-aware spectral recovery algorithm is proposed to recover the wideband spectrum without requiring knowledge of the instantaneous spectral sparsity level. Such an algorithm bridges the gap between CS theory and practical spectrum sensing. Simulation results show that ACSS can not only recover the spectrum using an appropriate number of measurements, but can also considerably improve the spectral recovery performance compared with existing CS approaches. The proposed recovery algorithm can autonomously adopt a proper number of iterations, therefore solving the problems of under-fitting or over-fitting which commonly exist in most greedy recovery algorithms.

Improved Analysis for Subspace Pursuit Algorithm in Terms of Restricted Isometry Constant

In the context of compressed sensing (CS), both Subspace Pursuit (SP) and Compressive Sampling Matching Pursuit (CoSaMP) are very important iterative greedy recovery algorithms which could reduce the recovery complexity greatly comparing with the well-known $\ell_1$-minimization. Restricted isometry property (RIP) and restricted isometry constant (RIC) of measurement matrices which ensure the convergency of iterative algorithms play key roles for the guarantee of successful reconstructions. In this paper, we show that for the $s$-sparse recovery, the RICs are enlarged to $\delta_{3s}<0.4859$ for SP and $\delta_{4s}<0.5$ for CoSaMP, which improve the known results significantly. The proposed results also apply to almost sparse signal and corrupted measurements.