A Fast Algorithm of Regularization of the Total Variation for the Class of Radially Symmetrical Functions

The total variation regularization for 2D radially symmetrical piecewise constant functions is considered in this paper. The system of equations that solves the direct problem of the total variation regularization with the use of subgradients is obtained. On the basis of the obtained system of equations, the algorithm of calculation of the extremal function is formulated and the geometrical interpretation of the extremal function is given with the use of the modified approach to constructing the taut string. The proposed algorithm of the total variation regularization is used in the 2D case for realizing the adaptive algorithm of the total variation regularization with the variable regularization parameter. The algorithmic complexity of the proposed algorithm of the 1D total variation regularization is equal to the complexity of the known Condat algorithm. The efficiency of the developed algorithm of the total variation regularization is illustrated with the help of computer modeling.