General choice of the regularization functional in regularized image restoration

The determination of the regularization parameter is an important issue in regularized image restoration, since it controls the trade-off between fidelity to the data and smoothness of the solution. A number of approaches have been developed in determining this parameter. In this paper, a new paradigm is adopted, according to which the required prior information is extracted from the available data at the previous iteration step, i.e., the partially restored image at each step. We propose the use of a regularization functional instead of a constant regularization parameter. The properties such a regularization functional should satisfy are investigated, and two specific forms of it are proposed. An iterative algorithm is proposed for obtaining a restored image. The regularization functional is defined in terms of the restored image at each iteration step, therefore allowing for the simultaneous determination of its value and the restoration of the degraded image. Both proposed iteration adaptive regularization functionals are shown to result in a smoothing functional with a global minimum, so that its iterative optimization does not depend on the initial conditions. The convergence of the algorithm is established and experimental results are shown.