Analysis and Synthesis Prior Greedy Algorithms for Non-linear Sparse Recovery

In this work we address the problem of recovering sparse solutions to non-linear inverse problems. We look at two variants of the basic problem - the synthesis prior problem when the solution is sparse and the analysis prior problem where the solution is co-sparse in some linear basis. For the first problem, we propose non-linear variants of the Orthogonal Matching Pursuit (OMP) and CoSamp algorithms, for the second problem we propose a non-linear variant of the Greedy Analysis Pursuit (GAP) algorithm. We empirically test the success rates of our algorithms on exponential and logarithmic functions.