A Quasi-Orthogonal Matching Pursuit Algorithm for Compressive Sensing (original) (raw)

Reconstruction of Compressive Sensing Signal Using Orthogonal Matching Pursuit Algorithm

This paper represents the reconstruction of sampled signal in CS by using OMP algorithm. We have used the concept of compressive sensing for sub Nyquist sampling of sparse signal. Compressive sensing reconstruction methods have complex algorithms of l1 optimisation to reconstruct a signal sampled at sub nyquist rate. But out of those algorithm OMP algorithm is fast and computationally efficient. To prove the concept of CS implementation, we have simulated OMP algorithm for recovery of sparse signal of length 256 with sparsity 8.

Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise

—We consider the orthogonal matching pursuit (OMP) algorithm for the recovery of a high-dimensional sparse signal based on a small number of noisy linear measurements. OMP is an iterative greedy algorithm that selects at each step the column, which is most correlated with the current residuals. In this paper, we present a fully data driven OMP algorithm with explicit stopping rules. It is shown that under conditions on the mutual incoherence and the minimum magnitude of the nonzero components of the signal, the support of the signal can be recovered exactly by the OMP algorithm with high probability. In addition, we also consider the problem of identifying significant components in the case where some of the nonzero components are possibly small. It is shown that in this case the OMP algorithm will still select all the significant components before possibly selecting incorrect ones. Moreover, with modified stopping rules, the OMP algorithm can ensure that no zero components are selected.

Orthogonal Matching Pursuit with Thresholding and its Application in Compressive Sensing

IEEE Transactions on Signal Processing, 2015

Greed is good. However, the tighter you squeeze, the less you have. In this paper, a less greedy algorithm for sparse signal reconstruction in compressive sensing, named orthogonal matching pursuit with thresholding is studied. Using the global 2-coherence , which provides a "bridge" between the well known mutual coherence and the restricted isometry constant, the performance of orthogonal matching pursuit with thresholding is analyzed and more general results for sparse signal reconstruction are obtained. It is also shown that given the same assumption on the coherence index and the restricted isometry constant as required for orthogonal matching pursuit, the thresholding variation gives exactly the same reconstruction performance with significantly less complexity.

Extensions to Orthogonal Matching Pursuit for Compressed Sensing

2011 National Conference on Communications (NCC), 2011

Compressed Sensing (CS) provides a set of mathematical results showing that sparse signals can be exactly reconstructed from a relatively small number of random linear measurements. A particularly appealing greedy-approach to signal reconstruction from CS measurements is the so called Orthogonal Matching Pursuit (OMP). We propose two modifications to the basic OMP algorithm, which can be handy in different situations.

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.

Signal Recovery from Random Measurements via Extended Orthogonal Matching Pursuit

IEEE Transactions on Signal Processing, 2015

Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP) are two well-known recovery algorithms in compressed sensing. To recover a d-dimensional m-sparse signal with high probability, OMP needs O (m ln d) number of measurements, whereas BP needs only O m ln d m number of measurements. In contrary, OMP is a practically more appealing algorithm due to its superior execution speed. In this piece of work, we have proposed a scheme that brings the required number of measurements for OMP closer to BP. We have termed this scheme as OMPα, which runs OMP for (m + αm)-iterations instead of m-iterations, by choosing a value of α ∈ [0, 1]. It is shown that OMPα guarantees a high probability signal recovery with O m ln d αm +1 number of measurements. Another limitation of OMP unlike BP is that it requires the knowledge of m. In order to overcome this limitation, we have extended the idea of OMPα to illustrate another recovery scheme called OMP∞, which runs OMP until the signal residue vanishes. It is shown that OMP∞ can achieve a close to 0-norm recovery without any knowledge of m like BP. Theorem 1 (Theorem 1 of [2]). Let N ≥ C 1 m ln d m , and Φ has N × d Gaussian i.i.d entries. The following statement is true with probability exceeding 1 − e −c1N. It is possible

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.

Least Support Orthogonal Matching Pursuit Algorithm With Prior Information

Journal of Applied Computer Science Methods, 2014

This paper proposes a new fast matching pursuit technique named Partially Known Least Support Orthogonal Matching Pursuit (PKLS-OMP) which utilizes partially known support as a prior knowledge to reconstruct sparse signals from a limited number of its linear projections. The PKLS-OMP algorithm chooses optimum least part of the support at each iteration without need to test each candidate independently and incorporates prior signal information in the recovery process. We also derive sufficient condition for stable sparse signal recovery with the partially known support. Result shows that inclusion of prior information weakens the condition on the sensing matrices and needs fewer samples for successful reconstruction. Numerical experiments demonstrate that PKLS-OMP performs well compared to existing algorithms both in terms of reconstruction performance and execution time.