Greedy pursuits assisted basis pursuit for compressive sensing (original) (raw)

Greedy Pursuits Assisted Basis Pursuit for reconstruction of joint-sparse signals

Signal Processing, 2018

Distributed Compressive Sensing (DCS) is an extension of compressive sensing from single measurement vector problem to Multiple Measurement Vectors (MMV) problem. In DCS, several reconstruction algorithms have been proposed to reconstruct the joint-sparse signal ensemble. However, most of them are designed for signal ensemble sharing common support. Since the assumption of common sparsity pattern is very restrictive, we are more interested in signal ensemble containing both common and innovation components. With a goal of proposing an MMV-type algorithm that is robust to outliers (absence of common sparsity pattern), we propose Greedy Pursuits Assisted Basis Pursuit for Multiple Measurement Vectors (GPABP-MMV). It employs modified basis pursuit and MMV versions of multiple greedy pursuits. We also formulate the exact reconstruction conditions and the reconstruction error bound for GPABP-MMV. GPABP-MMV is suitable for a variety of applications including time-sequence reconstruction of video frames, reconstruction of ECG signals, etc.

A Survey of Compressive Sensing Based Greedy Pursuit Reconstruction Algorithms

—Conventional approaches to sampling images use Shannon theorem, which requires signals to be sampled at a rate twice the maximum frequency. This criterion leads to larger storage and bandwidth requirements. Compressive Sensing (CS) is a novel sampling technique that removes the bottleneck imposed by Shannon's theorem. This theory utilizes sparsity present in the images to recover it from fewer observations than the traditional methods. It joins the sampling and compression steps and enables to reconstruct with the only fewer number of observations. This property of compressive Sensing provides evident advantages over Nyquist-Shannon theorem. The image reconstruction algorithms with CS increase the efficiency of the overall algorithm in reconstructing the sparse signal. There are various algorithms available for recovery. These algorithms include convex minimization class, greedy pursuit algorithms. Numerous algorithms come under these classes of recovery techniques. This paper discusses the origin, purpose, scope and implementation of CS in image reconstruction. It also depicts various reconstruction algorithms and compares their complexity, PSNR and running time. It concludes with the discussion of the various versions of these reconstruction algorithms and future direction of CS-based image reconstruction algorithms.

A* orthogonal matching pursuit: Best-first search for compressed sensing signal recovery

Digital Signal Processing, 2012

Compressed sensing is a developing field aiming at reconstruction of sparse signals acquired in reduced dimensions, which make the recovery process under-determined. The required solution is the one with minimum ℓ 0 norm due to sparsity, however it is not practical to solve the ℓ 0 minimization problem. Commonly used techniques include ℓ 1 minimization, such as Basis Pursuit (BP) and greedy pursuit algorithms such as Orthogonal Matching Pursuit (OMP) and Subspace Pursuit (SP). This manuscript proposes a novel semi-greedy recovery approach, namely A* Orthogonal Matching Pursuit (A*OMP). A*OMP performs A* search to look for the sparsest solution on a tree whose paths grow similar to the Orthogonal Matching Pursuit (OMP) algorithm. Paths on the tree are evaluated according to a cost function, which should compensate for different path lengths. For this purpose, three different auxiliary structures are defined, including novel dynamic ones. A*OMP also incorporates pruning techniques which enable practical applications of the algorithm. Moreover, the adjustable search parameters provide means for a complexity-accuracy trade-off. We demonstrate the reconstruction ability of the proposed scheme on both synthetically generated data and images using Gaussian and Bernoulli observation matrices, where A*OMP yields less reconstruction error and higher exact recovery frequency than BP, OMP and SP. Results also indicate that novel dynamic cost functions provide improved results as compared to a conventional choice.

Sparsity adaptive matching pursuit algorithm for practical compressed sensing

2008

This paper presents a novel iterative greedy reconstruction algorithm for practical compressed sensing (CS), called the sparsity adaptive matching pursuit (SAMP). Compared with other state-of-the-art greedy algorithms, the most innovative feature of the SAMP is its capability of signal reconstruction without prior information of the sparsity. This makes it a promising candidate for many practical applications when the number of non-zero (significant) coefficients of a signal is not available. The proposed algorithm adopts a similar flavor of the EM algorithm, which alternatively estimates the sparsity and the true support set of the target signals. In fact, SAMP provides a generalized greedy reconstruction framework in which the orthogonal matching pursuit and the subspace pursuit can be viewed as its special cases. Such a connection also gives us an intuitive justification of trade-offs between computational complexity and reconstruction performance. While the SAMP offers a comparably theoretical guarantees as the best optimization-based approach, simulation results show that it outperforms many existing iterative algorithms, especially for compressible signals.

Modified adaptive basis pursuits for recovery of correlated sparse signals

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2014

In Distributed Compressive Sensing (DCS), correlated sparse signals refer to as an ensemble of signals characterized by presenting a sparse correlation. If one signal is known apriori, the remaining signals in the ensemble can be reconstructed using l1-minimization with far fewer measurements compared to separate CS reconstruction. Reconstruction of such correlated signals is possible via Modified-CS and Regularized-Modified-BP but these methods are greatly influenced by the support set of the known signal which also includes locations irrelavant to the target signal. While recovering each signal, prior to Modified-CS or Regularized-Modified-BP, we propose an adaptation step to retain only the sparse locations significant to that signal. We call our proposed methods as Modified-Adaptive-BP and Regularized-Modified-Adaptive-BP. Theoretical guarantees and experimental results show that our proposed method provides efficient recovery compared to that of the Modified-CS and its regularized version.

Compressed sensing signal recovery via A* Orthogonal Matching Pursuit

Reconstruction of sparse signals acquired in reduced dimensions requires the solution with minimum 0 norm. As solving the 0 minimization directly is unpractical, a number of algorithms have appeared for finding an indirect solution. A semi-greedy approach, A* Orthogonal Matching Pursuit (A*OMP), is proposed in [1] where the solution is searched on several paths of a search tree. Paths of the tree are evaluated and extended according to some cost function, for which novel dynamic auxiliary cost functions are suggested. This paper describes the A*OMP algorithm and the proposed cost functions briefly. The novel dynamic auxiliary cost functions are shown to provide improved results as compared to a conventional choice. Reconstruction performance is illustrated on both synthetically generated data and real images, which show that the proposed scheme outperforms well-known CS reconstruction methods.

Sparse Signals Reconstruction via Adaptive Iterative Greedy Algorithm

International Journal of Computer Applications, 2014

Compressive sensing(CS) is an emerging research field that has applications in signal processing, error correction, medical imaging, seismology, and many more other areas. CS promises to efficiently reconstruct a sparse signal vector via a much smaller number of linear measurements than its dimension. In order to improve CS reconstruction performance, this paper present a novel reconstruction greedy algorithm called the Enhanced Orthogonal Matching Pursuit (E-OMP). E-OMP falls into the general category of Two Stage Thresholding(TST)-type algorithms where it consists of consecutive forward and backward stages. During the forward stage, E-OMP depends on solving the least square problem to select columns from the measurement matrix. Furthermore, E-OMP uses a simple backtracking step to detect the previous chosen columns accuracy and then remove the false columns at each time. From simulations it is observed that E-OMP improve the reconstruction performance better than Orthogonal Matching Pursuit (OMP) and Regularized OMP (ROMP).

Theory and Applications of Compressive Sensing

This thesis develops algorithms and applications for compressive sensing, a topic in signal processing that allows reconstruction of a signal from a limited number of linear combinations of the signal. New algorithms are described for common remote sensing problems including superresolution and fusion of images. The algorithms show superior results in comparison with conventional methods. We describe a method that uses compressive sensing to reduce the size of image databases used for content based image retrieval. The thesis also describes an improved estimator that enhances the performance of Matching Pursuit type algorithms, several variants of which have been developed for compressive sensing recovery.

Compressed sensing signal recovery via forward–backward pursuit

Digital Signal Processing, 2013

Recovery of sparse signals from compressed measurements constitutes an ℓ 0 norm minimization problem, which is unpractical to solve. A number of sparse recovery approaches have appeared in the literature, including ℓ 1 minimization techniques, greedy pursuit algorithms, Bayesian methods and nonconvex optimization techniques among others. This manuscript introduces a novel two stage greedy approach, called the Forward-Backward Pursuit (FBP). FBP is an iterative approach where each iteration consists of consecutive forward and backward stages. The forward step first expands the support estimate by the forward step size, while the following backward step shrinks it by the backward step size. The forward step size is larger than the backward step size, hence the initially empty support estimate is expanded at the end of each iteration. Forward and backward steps are iterated until the residual power of the observation vector falls below a threshold. This structure of FBP does not necessitate the sparsity level to be known a priori in contrast to the Subspace Pursuit or Compressive Sampling Matching Pursuit algorithms. FBP recovery performance is demonstrated via simulations including recovery of random sparse signals with different nonzero coefficient distributions in noisy and noise-free scenarios in addition to the recovery of a sparse image.

A COMPARATIVE STUDY OF SOME GREEDY PURSUIT ALGORITHMS FOR SPARSE APPROXIMATION

2009

Solving an under-determined system of equations for the sparsest solution has attracted considerable attention in recent years. Among the two well known approaches, the greedy algorithms like matching pursuits (MP) are simpler to implement and can produce satisfactory results under certain conditions. In this paper, we compare several greedy algorithms in terms of the sparsity of the solution vector and the approximation accuracy. We present two new greedy algorithms based on the recently proposed complementary matching pursuit (CMP) and the sensing dictionary framework, and compare them with the classical MP, CMP, and the sensing dictionary approach. It is shown that in the noise-free case, the complementary matching pursuit algorithm performs the best among these algorithms.