2,642 research outputs found
Recovery of Sparse Signals Using Multiple Orthogonal Least Squares
We study the problem of recovering sparse signals from compressed linear
measurements. This problem, often referred to as sparse recovery or sparse
reconstruction, has generated a great deal of interest in recent years. To
recover the sparse signals, we propose a new method called multiple orthogonal
least squares (MOLS), which extends the well-known orthogonal least squares
(OLS) algorithm by allowing multiple indices to be chosen per iteration.
Owing to inclusion of multiple support indices in each selection, the MOLS
algorithm converges in much fewer iterations and improves the computational
efficiency over the conventional OLS algorithm. Theoretical analysis shows that
MOLS () performs exact recovery of all -sparse signals within
iterations if the measurement matrix satisfies the restricted isometry property
(RIP) with isometry constant The recovery performance of MOLS in the noisy scenario is also
studied. It is shown that stable recovery of sparse signals can be achieved
with the MOLS algorithm when the signal-to-noise ratio (SNR) scales linearly
with the sparsity level of input signals
A* Orthogonal Matching Pursuit: Best-First Search for Compressed Sensing Signal Recovery
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 norm
due to sparsity, however it is not practical to solve the minimization
problem. Commonly used techniques include 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.Comment: accepted for publication in Digital Signal Processin
Improving A*OMP: Theoretical and Empirical Analyses With a Novel Dynamic Cost Model
Best-first search has been recently utilized for compressed sensing (CS) by
the A* orthogonal matching pursuit (A*OMP) algorithm. In this work, we
concentrate on theoretical and empirical analyses of A*OMP. We present a
restricted isometry property (RIP) based general condition for exact recovery
of sparse signals via A*OMP. In addition, we develop online guarantees which
promise improved recovery performance with the residue-based termination
instead of the sparsity-based one. We demonstrate the recovery capabilities of
A*OMP with extensive recovery simulations using the adaptive-multiplicative
(AMul) cost model, which effectively compensates for the path length
differences in the search tree. The presented results, involving phase
transitions for different nonzero element distributions as well as recovery
rates and average error, reveal not only the superior recovery accuracy of
A*OMP, but also the improvements with the residue-based termination and the
AMul cost model. Comparison of the run times indicate the speed up by the AMul
cost model. We also demonstrate a hybrid of OMP and A?OMP to accelerate the
search further. Finally, we run A*OMP on a sparse image to illustrate its
recovery performance for more realistic coefcient distributions
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