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• An image denoising algorithm based on an image-dependent basis inspired by the quantum many-body theory. • The local structural similarity of images is formalized through a term akin to interaction in quantum physics. • The versatility of the adaptive basis extends its scope of applications regardless of the image characteristics and noise statistics. [Display omitted] Sparse representation of real-life images is a very effective approach in imaging applications, such as denoising. In recent years, with the growth of computing power, data-driven strategies exploiting the redundancy within patches extracted from one or several images to increase sparsity have become more prominent. This paper presents a novel image denoising algorithm exploiting such an image-dependent basis inspired by the quantum many-body theory. Based on patch analysis, the similarity measures in a local image neighborhood are formalized through a term akin to interaction in quantum mechanics that can efficiently preserve the local structures of real images. The versatile nature of this adaptive basis extends the scope of its application to image-independent or image-dependent noise scenarios without any adjustment. We carry out a rigorous comparison with contemporary methods to demonstrate the denoising capability of the proposed algorithm regardless of the image characteristics, noise statistics and intensity. We illustrate the properties of the hyperparameters and their respective effects on the denoising performance, together with automated rules of selecting their values close to the optimal one in experimental setups with ground truth not available. Finally, we show the ability of our approach to deal with practical images denoising problems such as medical ultrasound image despeckling applications. [ABSTRACT FROM AUTHOR]

• This article proposes a novel nonconvex TGV model for adaptive image restoration. • We develop in detail a highly efficient alternating direction method of multipliers. • The regularization parameter λ can be automatically estimated during the iteration. • Based on convex analysis, a novel convergence proof of our algorithm is presented. • Our scheme provide promising performance in restoration accuracy and visual quality. Overcoming the staircase effect and simultaneously preserving edge details is an important and challenging issue in image processing. To this aim, this paper investigates the nonconvex total generalized variation regularization model for image restoration. Numerically, a highly efficient alternating direction method of multipliers is constructed to deal with the optimization problem in detail, which closely incorporates the superiorities of iteratively reweighted ℓ 1 algorithm and variable splitting technique. The proposed strategy can efficiently achieve image restoration and adaptive parameter estimation by applying Morozov's discrepancy principle. Furthermore, the convergence property of our novel algorithm with the variable regularization parameter is presented. Finally, numerical simulations concertedly illustrate that our approach outperforms several state-of-the-art regularization models, in terms of reconstruction accuracy and edge-preserving ability. [ABSTRACT FROM AUTHOR]