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 s imultaneously estimating the reconstructed signal and the local smooth ness map (LSM), which is a generalization of the global smoothness par ameter that is often used to stabilize inverse problems, The greater f lexibility afforded by the introduction of the local smoothness map ma kes the new method very effective on inverse problems that involve dis continuities or other regions with sharp gradients. We demonstrate the LSM method on the Problem of reducing noise in one-dimensional (1-D) signals.