1. A method comprising: receiving, at a processor, an observation vector comprising a set of observation of a signal; generating, by the processor, a signal vector estimate based on the observation vector and an observation matrix using compressed sensing optimization; determining, by the processor, an index set of most dominant elements of the signal vector estimate according to a sparsifying norm, wherein a number of the most dominant elements is at most the number of elements of the observation vector; and generating, by the processor, an index set of nonzero elements of a signal vector by performing a non-underdetermined estimation method based on the observation matrix, the observation vector, and the index set of the most dominant elements of the signal vector estimate.