Tensor ring (TR) decomposition has demonstrated remarkable capability in capturing low-rank tensor structures, achieving significant success in color image completion tasks. However, relying solely on the tensor low-rank prior cannot fully capture the details of a color image. Thus, traditional model-driven TR decomposition models often fail to recover satisfactory local detail. A natural idea is to introduce a deep neural network with end-to-end training to improve the detail quality of image reconstruction. Thus, we proposed a novel hybrid model that integrates model-driven TR decomposition with data-driven deep learning regularization. The proposed framework introduces an energy functional regularization term based on the FFDNET architecture, which enhances the robustness of rank selection while preserving global low-rank and local details. In particular, we assumed that the unfolding matrices of the TR factors exhibited low-rank properties. Thus, nuclear-norm regularization constraints were incorporated on the TR factors to enhance their global low-rank characteristics. Additionally, a deep prior regularization term derived from the FFDNET network was introduced to preserve the local details of the target tensor. We further developed an efficient alternating direction method for the multiplier algorithm to address the associated optimization problem. Extensive experiments on color images have demonstrated that the proposed method outperforms denoising approaches, yielding satisfactory results. The code for implementing the proposed method is available at https://github.com/110500617/TRDD.

The rapid development of image deraining technology has made it possible to effectively restore images captured even in severe rainy weather, thereby alleviating the decline in image quality. However, existing image deraining solutions typically use overly deep neural networks, which are prone to gradient vanishing and explosion. This often results in the restored image losing essential background details. To address this important issue, this paper proposed an enhanced dual-encoder vision transformer UNet for single-image rain removal. First, a dual-branch heterogeneous encoding structure was formed by integrating two encoders with different architectures. These encoders extract rain streaks by leveraging their distinct characteristics. Specifically, the first encoder was based on a convolutional neural network, termed the residual encoder network, which utilizes the local receptive field capabilities of convolutional kernels to capture both rain streaks and corresponding background details. Concurrently, the second encoder, the parallel vision transformer encoder network, employs self-attention mechanisms to model long-range dependencies and establish global contextual relationships between rain streaks and background details. Subsequently, the rain streak information extracted by the two encoders was fused. The decoder then performs the rain removal task. To preserve spatial consistency and overall image integrity, high-frequency detail refinement was facilitated through residual connections between the encoders and the decoder. Evaluations on synthetic and real-world datasets confirm the algorithm's robustness in processing rain streaks of varied density. The restored images exhibit enhanced visual clarity, improving visibility for computer vision applications.