The article focuses on "missing pixels" which doesn't have much to do with the original Candes paper. The usual setup for compressed sensing is that you're samp

The article focuses on "missing pixels" which doesn't have much to do with the original Candes paper. The usual setup for compressed sensing is that you're sampling the entire image one coefficient at a time in some "incoherent" basis (ie, noiselets). Thus, every little spot of Obama's acne may very well be reconstructed-- though more generally you're right, if the image is too sharp then something gets lost.