The total variation method has been widely used because it can preserve important sharp edges and target boundaries in the image, but one of its shortcomings is that the \(L_{1}\) norm would cause excessive punishment. To overcome excessive penalization, suppress step effects, and maintain a clean contour, this article introduces the \(L_{q}\) non-convex function to design a new regularization term and proposes a new non-convex variational model. For non-convex variational optimization problems, the algorithm employs the alternating direction method of multipliers to obtain optimal approximate solutions, and rigorous convergence proofs are provided based on rich mathematical theory. By comparing with advanced fractional-order and other total variation recovery algorithms, it can be observed that this algorithm achieves better visual effects and quantitative analysis results on images with complex texture structures.
