the idea is that one can use randomness as a sensing mechanism; that is, as a way of extracting information about an object of interest from a small number of randomly selected observations. for example, we have seen that if an object has a sparse gradient then we can "image" this object by measuring a few Fourier samples at random locations rather than by acquiring a large number of pixels.
this point of view is very broad. suppose we wish to reconstruct a signal f assumed to be
sparse in a fixed basis, e.g. a wavelet basis. then by applying random sensing (taking a
small number of random measurements) the number of measurement we need depends far
more upon the structural content of the signal (the number of significant terms in the wavelet expansion) than the resolution N.
candes romberg & tao
candes romberg & tao
