Reconstruction algorithm in compressed sensing based on maximum a posteriori estimation
Abstract
We propose a systematic method for constructing a sparse data reconstruction algorithm in compressed sensing at a relatively low computational cost for general observation matrix. It is known that the cost of l1-norm minimization using a standard linear programming algorithm is O(N^3). We show that this cost can be reduced to O(N^2) by applying the approach of posterior maximization. Furthermore, in principle, the algorithm from our approach is expected to achieve the widest successful reconstruction region, which is evaluated from theoretical argument. We also discuss the relation between the belief propagation-based reconstruction algorithm introduced in preceding works and our approach.
Cite
@article{arxiv.1311.0095,
title = {Reconstruction algorithm in compressed sensing based on maximum a posteriori estimation},
author = {Koujin Takeda and Yoshiyuki Kabashima},
journal= {arXiv preprint arXiv:1311.0095},
year = {2014}
}
Comments
11 pages, 5 figures, proceedings of ELC International Meeting on "Inference, Computation, and Spin Glasses" (ICSG2013), Sapporo, Japan