Bregman inverse filter

An inverse problem in which the observed signal is produced by passing the original signal through a filter that is derived from a convex minimisation problem is dealt. The filter is available as a black box. It is shown that the Bregman iteration, which is a tool for convex optimisation, can be used to solve this inverse problem. This novel application of the Bregman iteration is demonstrated through successful restoration of the original image from images filtered by a low-pass filter. Theoretical analysis is conducted to explain the inversion process.