Reconstruction of signals from multiscale edges (Q1914576)

The paper presents a reconstruction procedure for univariate signals based upon the location of its singularities which are identified by a wavelet transform technique. The reconstructed signal is an inf-convolution spline approximant. Note that inf-convolution spline approximants were introduced by J. P. Laurent for the approximation of functions which are known to be smooth except for local singularities based on a variational approach. The author presents error bounds for the spline approximant and convergence results. Moreover, the paper compares the present method with the compression method based on multiresolution analysis.