I think Candes (and/or the journalist) is contrasting sampling in an incoherent basis with the conventional route of compression (sample the full signal/image/w

I think Candes (and/or the journalist) is contrasting sampling in an incoherent basis with the conventional route of compression (sample the full signal/image/whatever, then try to reduce its size). The former is a form of compression, just not the kind we usually do.