Completing multidimensional color images is a fundamental challenge in image processing and computer vision. However, some tensor-based methods often treat RGB channels as independent modes, thereby neglecting their intrinsic correlations. To address this limitation, we represent RGB values as pure quaternions and organize them into a quaternion tensor for holistic modeling that preserves chromatic relationships. To better capture the nonlinear characteristics inherent in visual data and to improve the compactness of low-rank representations, we propose a nonlinear transformation within the quaternion domain. This design enables more expressive modeling compared to conventional linear approaches. In addition, we introduce two novel regularization terms that jointly encode global low-rankness and local smoothness, with the nonlinear transformation further enhancing the exploitation of structural priors. The overall model is optimized via a nonlinear alternating direction method of multipliers (ADMM), with theoretical guarantees of convergence. Extensive experiments on several datasets demonstrate that the proposed method significantly outperforms state-of-the-art low-rank tensor and quaternion tensor recovery techniques in multidimensional color image completion tasks.

Deep learning has been widely applied to various aspects of computer vision, but the emergence of adversarial attacks raises concerns about its reliability. Adversarial training (AT) is one of the most effective defense methods, which incorporates adversarial examples into the training data. However, AT is typically employed in a discriminative learning manner, i.e., learning the mapping (conditional probability) from samples to labels, it essentially reinforces this mapping without considering the underlying data distribution. It is notable that adversarial examples often deviate from the distribution of normal (clean) samples. Therefore, building upon existing adversarial defense schemes, we propose to further exploit the distribution of normal samples, partly from the generative learning perspective, resulting in a novel robustness enhancement paradigm. We train a simple autoencoder (AE) autoregressively on normal samples to learn their prior distribution, effectively serving as an image manifold. This AE is then used as a manifold projection operator to incorporate the distribution information of normal samples. Specifically, we organically integrate the pretrained AE into the training process of both AT and adversarial distillation (AD), a method aiming at improving the robustness of small models with low capacity. Since the AE captures the distribution of normal samples, it can adaptively pull adversarial examples closer to the normal sample manifold, weakening the attack strength of adversarial samples and easing the learning of mappings from adversarial samples to correct labels. From the Pearson correlation coefficient (PCC) between the statistics on normal and adversarial examples, it’s validated that the AE indeed pulls adversarial samples closer to normal samples. Extensive experiments illustrate that our proposed adversarial defense paradigm significantly improves the robustness compared with previous state-of-the-art AT and AD methods.

Spectral super-resolution (SSR) from RGB images, which involves reconstructing hyperspectral images (HSIs) from color images, has recently received great attention. While convolutional neural network (CNN)-based methods have demonstrated strong performance, they often overlook the self-similarity across the spectral dimension of HSIs. Transformer-based approaches have addressed this limitation by leveraging self-attention mechanisms to capture spectral correlations. However, these methods encounter computational and memory overheads that scale quadratically with the size of the HSIs. To overcome these challenges, we introduce a novel Spectral-wise Low-Rank Attention (SLORA) mechanism that captures inter-spectral consistency in a low-dimensional space, thereby reducing both computational costs and model complexity. Additionally, we propose a flow-based refinement module to enhance generalization and performance on unseen HSIs. Experimental results from the NTIRE 2022 spectral reconstruction challenge and the spectral snapshot compression imaging task datasets validate the superiority of our method over state-of-the-art approaches.

Tensor completion aims at estimating missing values from an incomplete observation, playing a fundamental role for many applications. This work proposes a novel low-rank tensor completion model, in which the inherent low-rank prior and external degradation accordant data-driven prior are simultaneously utilized. Specifically, the tensor nuclear norm (TNN) is adopted to characterize the overall low-dimensionality of the tensor data. Meanwhile, an implicit regularizer is formulated and its related subproblem is solved via a deep convolutional neural network (CNN) under the plug-and-play framework. This CNN, pretrained for the inpainting task on a mass of natural images, is expected to express the external data-driven prior and this plugged inpainter is consistent with the original degradation process. Then, an efficient alternating direction method of multipliers (ADMM) is designed to solve the proposed optimization model. Extensive experiments are conducted on different types of tensor imaging data with the comparison with state-of-the-art methods, illustrating the effectiveness and the remarkable generalization ability of our method.