  Compressive sensing is a methodology for the reconstruction of sparse or
compressible signals using far fewer samples than required by the Nyquist
criterion. However, many of the results in compressive sensing concern random
sampling matrices such as Gaussian and Bernoulli matrices. In common physically
feasible signal acquisition and reconstruction scenarios such as
super-resolution of images, the sensing matrix has a non-random structure with
highly correlated columns. Here we present a compressive sensing type recovery
algorithm, called Partial Inversion (PartInv), that overcomes the correlations
among the columns. We provide theoretical justification as well as empirical
comparisons.
