Compressive Sensing is built on 2 properties: 1) the sparsity of the representation basis relative to the sampling basis and 2) the incoherence between the singular vectors from each of the 2 bases in a). On the surface this seems fine to me but he "incoherence" relationship is confusing me a little.
Some texts refer to the coherence between the bases (representation, sampling) and other refer to the coherence between each basis and the standard basis (e1, e2, e3 ...).
Is there a difference between these two statements?
"We are in the position to state our main result: if a matrix has row and column spaces that are incoherent with the standard basis, then nuclear norm minimization can recover this matrix from a random sampling of a small number of entries."
"Incoherent sampling ... The coherence between the sensing basis and and the representation basis". Page 3: http://authors.library.caltech.edu/10092/1/CANieeespm08.pdf
My question is related to this question: https://dsp.stackexchange.com/a/13017/4038