3,283 research outputs found
Coherence-Based Performance Guarantees of Orthogonal Matching Pursuit
In this paper, we present coherence-based performance guarantees of
Orthogonal Matching Pursuit (OMP) for both support recovery and signal
reconstruction of sparse signals when the measurements are corrupted by noise.
In particular, two variants of OMP either with known sparsity level or with a
stopping rule are analyzed. It is shown that if the measurement matrix
satisfies the strong coherence property, then with
, OMP will recover a -sparse signal with high
probability. In particular, the performance guarantees obtained here separate
the properties required of the measurement matrix from the properties required
of the signal, which depends critically on the minimum signal to noise ratio
rather than the power profiles of the signal. We also provide performance
guarantees for partial support recovery. Comparisons are given with other
performance guarantees for OMP using worst-case analysis and the sorted one
step thresholding algorithm.Comment: appeared at 2012 Allerton conferenc
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
This paper demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with nonzero entries in dimension given random linear measurements of that signal. This is a massive improvement over previous results, which require measurements. The new results for OMP are comparable with recent results for another approach called Basis Pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems
Relaxed Recovery Conditions for OMP/OLS by Exploiting both Coherence and Decay
We propose extended coherence-based conditions for exact sparse support
recovery using orthogonal matching pursuit (OMP) and orthogonal least squares
(OLS). Unlike standard uniform guarantees, we embed some information about the
decay of the sparse vector coefficients in our conditions. As a result, the
standard condition (where denotes the mutual coherence and
the sparsity level) can be weakened as soon as the non-zero coefficients
obey some decay, both in the noiseless and the bounded-noise scenarios.
Furthermore, the resulting condition is approaching for strongly
decaying sparse signals. Finally, in the noiseless setting, we prove that the
proposed conditions, in particular the bound , are the tightest
achievable guarantees based on mutual coherence
Projection-Based and Look Ahead Strategies for Atom Selection
In this paper, we improve iterative greedy search algorithms in which atoms
are selected serially over iterations, i.e., one-by-one over iterations. For
serial atom selection, we devise two new schemes to select an atom from a set
of potential atoms in each iteration. The two new schemes lead to two new
algorithms. For both the algorithms, in each iteration, the set of potential
atoms is found using a standard matched filter. In case of the first scheme, we
propose an orthogonal projection strategy that selects an atom from the set of
potential atoms. Then, for the second scheme, we propose a look ahead strategy
such that the selection of an atom in the current iteration has an effect on
the future iterations. The use of look ahead strategy requires a higher
computational resource. To achieve a trade-off between performance and
complexity, we use the two new schemes in cascade and develop a third new
algorithm. Through experimental evaluations, we compare the proposed algorithms
with existing greedy search and convex relaxation algorithms.Comment: sparsity, compressive sensing; IEEE Trans on Signal Processing 201
Computational Methods for Sparse Solution of Linear Inverse Problems
The goal of the sparse approximation problem is to approximate a target signal using a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available. Many fundamental questions in electrical engineering, statistics, and applied mathematics can be posed as sparse approximation problems, making these algorithms versatile and relevant to a plethora of applications
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