Abstract
In this paper, the Feasibility Pump is adapted for the problem of sparse representations of signals affected by Gaussian noise. This adaptation is tested and then compared to Orthogonal Matching Pursuit (OMP) and the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The feasibility pump recovers the true support much better than the other two algorithms and, as the SNR decreases and the support size increases, it has a smaller recovery and representation error when compared with its competitors. It is observed that, in order for the algorithm to be efficient, a regularization parameter and a weight term for the error are needed.
Highlights
Problem FormulationThe Feasibility Pump (FP), proposed in References [1,2], is an Mixed Integer Programming (MIP) algorithm that alternates between solving the problem with relaxed integer constraints and the one satisfying the integer requirements
In this paper, the Feasibility Pump is adapted for the problem of sparse representations of signals affected by Gaussian noise
Rather than attempting to find the sparsest solution, it is easier to bound the number of nonzero elements by a given threshold K and so the sparse representation can be found by solving the optimization problem minimize ky − Dx k2 x ∈Rn subject to k x k0 ≤ K
Summary
The Feasibility Pump (FP), proposed in References [1,2], is an MIP algorithm that alternates between solving the problem with relaxed integer constraints and the one satisfying the integer requirements. This is done until a point is reached that satisfies all the constraints, even though it might be not optimal, or for a prescribed number of iterations. The case in which the l1 norm is used for the representation error was analyzed and a modification of the Feasibility Pump algorithm for this problem was presented in Reference [12].
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