Existing image smoothing methods usually lack flexibility and cause problems,such as unclear edges,missing structures,and excessive sharpening.To tackle these problems,this paper proposes a novel regularization method involving an adaptive weighted matrix.This method is primarily applied to image smoothing and can be extended to other applications.It introduces a new regularization term by combining gradient operators ▽ and an adaptive weighted matrix T into a L0 norm regularization term,and imparting anisotropic characteristics to the model.Through assigning different weights to various gradient directions,the model characterizes the local structure of smoothed images,thus local features can be better emphasized and excessive smoothing can be prevented.Given that the proposed model is non-smooth and non-convex,solving it is relatively complex.Thus,the ADMM algorithm is employed to solve the model by decomposing the objective function into several easily solvable subproblems.Each subproblem is solved separately,and the optimal solution for the model is ultimately obtained.Both subjective and objective experiments indicate a significant improvement in both visual effects and numerical aspects by the proposed model.
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