Restoration of optical objects using regularization

Using the regularization theory for improperly posed problems, we discuss object restoration beyond the diffraction limit in the presence of noise. Only the case of one-dimensional coherent objects is considered. We focus attention n the estimation of the error on the restored objects, and we show that, in most realistic cases, it is at best proportional to an inverse power of |In epsilon|, where epsilon is the error on the data (logarithmic continuity). Finally we suggest the extension of this result to other inverse problems.