Basis Mismatch in a Compressively Sampled Photonic Link

To accurately reproduce an incoming signal, compressive sampling requires that the signal have a sparse representation from within a finite basis or dictionary of vectors. If the incoming signal cannot be sparsely represented by vectors within the given basis or dictionary-a situation sometimes termed basis mismatch-then reconstruction error or failure is likely. In this letter, we present both simulated and experimental results showing the influence of basis mismatch on the ability of a photonic compressive sampling system to accurately reconstruct harmonic signals. Our reconstruction algorithm utilizes gradient projection for sparse reconstruction coupled with a discrete Fourier basis.