Local smoothness maps: a new method for solving inverse problems with the accurate recovery of sharp gradients

We describe a novel Bayesian approach to solving inverse problems by simultaneously estimating the reconstructed signal and the local smoothness map (LSM), which is a generalization of the global smoothness parameter that is often used to stabilize inverse problems. The greater flexibility afforded by the introduction of the local smoothness map makes the new method very effective on inverse problems that involve discontinuities or other regions with sharp gradients. We demonstrate the LSM method on the problem of reducing noise in one-dimensional (1-D) signals.