Non linear sparse recovery algorithm

Compressed sensing addresses the problem of recovering a sparse solution to a system of linear under-determined equations. In this work we are interested in deriving algorithms when the system is non-linear. Our algorithm is based on gradient descent approach followed by subsequent soft thresholding. We have tested our algorithm for both l
₂
-norm and l
₁
-norm cost functions (data fidelity) with linear and exponential systems.