Compressed Sensing for Ill-Posed Inverse Problems: Sampling Complexity of the Sparse Radon Transform

Sparse signals can be recovered from a limited number of measurements, proportional to the signal sparsity, by leveraging compressed sensing techniques in the context of ill-posed inverse problems. This is demonstrated for the sparse Radon transform, which models computed tomography, where stable recovery is achieved under the condition that the number of angles is proportional to the signal sparsity.