A method for estimating an optical, electromagnetic or acoustic image having at least the successive steps of: scattering an incident optical, electromagnetic or acoustic signal using a multiple scattering medium corresponding to a known transmission matrix stored into a memory of an imaging system; measuring the scattered signal using a detector array and storing the measurements into the memory of the imaging system; and determining an estimated image having a number of image elements that is greater than the number of measurements, at full spatial bandwidth. The estimated image is determined from the measurements and the transmission matrix using a sparsity-promoting algorithm.