A study of convex regularization involving discontinuities

Abstract

Regularization has been widely used to form well-posed inverse problems in computer vision, especially in low level vision. Through the detailed study on the disadvantages of nonconvex models in regularization, a general definition of influence functions has been given for convex discontinuity preserving regularization. Based on this definition, the convex discontinuity adaptive (CDA) model has been constructed. The new model satisfies several desirable analytical and computational properties for regularization of ill-posed problems, such as the stability to input data and the resulting convex minimization.