Adaptive reference constrained regularization by denoising for image restoration

High-quality reference images can be seen as a baseline for many image reconstruction techniques. The reconstruction performance gets improved as shown in the Reference Image Constrained Regularization by Denoising. But, low-quality reference images lead to disappointing results, even underperforming methods that use no reference at all. To address this limitation, a novel framework termed Adaptive Reference Constrained Regularization by Denoising is proposed in this paper. This new method mitigates the influence of low-quality reference images by adaptively leveraging the reconstruction results obtained from the existing algorithm to form a more reliable constraint. Furthermore, an enhanced version is introduced, equipped with a self-tuning parameter that progressively diminishes the weight of a poor reference throughout the optimization iterations. Extensive experiments on single-image super-resolution and MRI reconstruction demonstrate that the proposed approach significantly outperforms state-of-the-art methods, including Regularization by Denoising and Reference Image Constrained Regularization by Denoising, in both quantitative metrics and visual fidelity.