Identification of discontinuities in blurred noisy signals

In this paper we address the problem of estimating the locations of discontinuities in blurred and noisy signals. The discontinuity parameters (location and size) are embodied in a model describing the signal regular and singular components. First, the well-posedness of the estimation problem, i.e., uniqueness and robustness of the solution, is established. Then data are processed by a smoothing multiscale resolution technique that, besides providing some noise filtering, enhances the effect of the discontinuities. Hence, a maximum-likelihood method is used for parameter estimation. Numerical results are obtained both on simulated and real data.