Analysis-based sparse reconstruction with synthesis-based solvers

TL;DR

This paper introduces the Analysis-By-Synthesis (ABS) approach, converting analysis sparse reconstruction into a synthesis problem with constraints, enabling the use of existing algorithms for analysis recovery.

Contribution

It presents a novel method that transforms analysis sparse recovery into a synthesis problem, allowing existing algorithms to be applied directly for analysis reconstruction.

Findings

ABS approach is a viable analysis reconstruction method

Allows use of synthesis algorithms for analysis problems

Comparable performance to recent analysis algorithms

Abstract

Analysis based reconstruction has recently been introduced as an alternative to the well-known synthesis sparsity model used in a variety of signal processing areas. In this paper we convert the analysis exact-sparse reconstruction problem to an equivalent synthesis recovery problem with a set of additional constraints. We are therefore able to use existing synthesis-based algorithms for analysis-based exact-sparse recovery. We call this the Analysis-By-Synthesis (ABS) approach. We evaluate our proposed approach by comparing it against the recent Greedy Analysis Pursuit (GAP) analysis-based recovery algorithm. The results show that our approach is a viable option for analysis-based reconstruction, while at the same time allowing many algorithms that have been developed for synthesis reconstruction to be directly applied for analysis reconstruction as well.