1,543 research outputs found
Perturbation Analysis of Orthogonal Matching Pursuit
Orthogonal Matching Pursuit (OMP) is a canonical greedy pursuit algorithm for
sparse approximation. Previous studies of OMP have mainly considered the exact
recovery of a sparse signal through and , where is a matrix with more columns than rows. In this paper,
based on Restricted Isometry Property (RIP), the performance of OMP is analyzed
under general perturbations, which means both and are
perturbed. Though exact recovery of an almost sparse signal is no
longer feasible, the main contribution reveals that the exact recovery of the
locations of largest magnitude entries of can be guaranteed under
reasonable conditions. The error between and solution of OMP is also
estimated. It is also demonstrated that the sufficient condition is rather
tight by constructing an example. When is strong-decaying, it is proved
that the sufficient conditions can be relaxed, and the locations can even be
recovered in the order of the entries' magnitude.Comment: 29 page
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
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