Fixing basis mismatch in compressively sampled photonic link

The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of vectors. In practice, however, even small deviations from an exact signal model can result in dramatic increases in estimation error; this is the so-called basis mismatch" problem. This work provides one possible solution to this problem in the form of an iterative, biconvex search algorithm. The approach uses standard ℓ1-minimization to find the signal model coefficients followed by a maximum likelihood estimate of the signal model. The process is repeated until a convergence criteria is met. The algorithm is illustrated on harmonic signals of varying sparsity and outperforms the current state-of-the-art.