Numerical evaluation of sampling bounds for near-optimal reconstruction in compressed sensing

In this paper, we propose an empirical review of the conditions under which the compressed sensing framework allows to achieve exact image reconstruction. After a short presentation of the theoretical results related to this subject, we investigate the relevance and the limits of these theoretical results through several numerical reconstructions of some benchmark images. In particular, we discuss quantitative and qualitative artifacts that affect the reconstructed image when reducing the number of measurements in the Fourier domain. Finally, we conclude our study by extending our results to some real microscopic images.