A regularization method for one-dimensional edge detection and edge-preserving smoothing (Q1965973)

The authors consider the problem of detecting discontinuities and estimating unknown discontinuous functions from noisy data. This is an illposed inverse problem which needs to be regularized beyond the conventional dilemma between the fidelity to the data and the degree of global smoothness which now doesn't exist. A regularization functional with two items is introduced. The first item is a measure of piecewise-smoothness of the functions while the second is penalized by the local components. A methodology is developed for the edge-preserving smoothing and edge detection. Two algorithms are proposed and simulations were run for several one-dimensional synthetic images.