Edge-preserving piecewise-constant image restoration via method of minimum of extension

Problem of edge-preserving piecewise-constant image restoration is considered in the paper. Algorithm based on solution of nonlinear nonquadratic regularization problem is developed and discussed in the paper. Nonenergy measure of signal in the form of time duration of signal or spatial extension of image is introduced and used afterwards as a nonquadratic regularization term. Proposed approach is investigated through numerical simulations for one-dimensional signals and images, and compared to results given by standard Tikhonov regularization scheme. Results of application of developed algorithm for filtration of noisy aerospace images are given.