1 research outputs found
Fast Reconstruction Algorithm for Perturbed Compressive Sensing Based on Total Least-Squares and Proximal Splitting
We consider the problem of finding a sparse solution for an underdetermined
linear system of equations when the known parameters on both sides of the
system are subject to perturbation. This problem is particularly relevant to
reconstruction in fully-perturbed compressive-sensing setups where both the
projected measurements of an unknown sparse vector and the knowledge of the
associated projection matrix are perturbed due to noise, error, mismatch, etc.
We propose a new iterative algorithm for tackling this problem. The proposed
algorithm utilizes the proximal-gradient method to find a sparse total
least-squares solution by minimizing an l1-regularized Rayleigh-quotient cost
function. We determine the step-size of the algorithm at each iteration using
an adaptive rule accompanied by backtracking line search to improve the
algorithm's convergence speed and preserve its stability. The proposed
algorithm is considerably faster than a popular previously-proposed algorithm,
which employs the alternating-direction method and coordinate-descent
iterations, as it requires significantly fewer computations to deliver the same
accuracy. We demonstrate the effectiveness of the proposed algorithm via
simulation results