Reducing Basis Mismatch in Harmonic Signal Recovery via Alternating   Convex Search
  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 basis 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 $\ell_1$-minimization to find the signal model coefficients followed by a maximum likelihood estimate of the signal model. The algorithm is illustrated on harmonic signals of varying sparsity and outperforms the current state-of-the-art. 
Jonathan M. Nichols, Albert K. Oh, Rebecca M. Willett
math.OC stat.AP