Quaternion Nuclear Norms Over Frobenius Norms Minimization for Robust Matrix Completion

Recovering hidden structures from incomplete or noisy data remains a pervasive challenge across many fields, particularly where multi-dimensional data representation is essential. Quaternion matrices, with their ability to naturally model multi-dimensional data, offer a promising framework for this problem. This paper introduces the quaternion nuclear norm over the Frobenius norm (QNOF) as a novel nonconvex approximation for the rank of quaternion matrices. QNOF is parameter-free and scale-invariant. Utilizing quaternion singular value decomposition, we prove that solving the QNOF can be simplified to solving the singular value $L_1/L_2$ problem. Additionally, we extend the QNOF to robust quaternion matrix completion, employing the alternating direction multiplier method to derive solutions that guarantee weak convergence under mild conditions. Extensive numerical experiments validate the proposed model's superiority, consistently outperforming state-of-the-art quaternion methods.

Quaternion Nuclear Norm minus Frobenius Norm Minimization for color image reconstruction

Color image restoration methods typically represent images as vectors in Euclidean space or combinations of three monochrome channels. However, they often overlook the correlation between these channels, leading to color distortion and artifacts in the reconstructed image. To address this, we present Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF), a novel approach for color image reconstruction. QNMF utilizes quaternion algebra to capture the relationships among RGB channels comprehensively. By employing a regularization technique that involves nuclear norm minus Frobenius norm, QNMF approximates the underlying low-rank structure of quaternion-encoded color images. Theoretical proofs are provided to ensure the method's mathematical integrity. Demonstrating versatility and efficacy, the QNMF regularizer excels in various color low-level vision tasks, including denoising, deblurring, inpainting, and random impulse noise removal, achieving state-of-the-art results.

Multi-modal Mood Reader: Pre-trained Model Empowers Cross-Subject Emotion Recognition

Emotion recognition based on Electroencephalography (EEG) has gained significant attention and diversified development in fields such as neural signal processing and affective computing. However, the unique brain anatomy of individuals leads to non-negligible natural differences in EEG signals across subjects, posing challenges for cross-subject emotion recognition. While recent studies have attempted to address these issues, they still face limitations in practical effectiveness and model framework unity. Current methods often struggle to capture the complex spatial-temporal dynamics of EEG signals and fail to effectively integrate multimodal information, resulting in suboptimal performance and limited generalizability across subjects. To overcome these limitations, we develop a Pre-trained model based Multimodal Mood Reader for cross-subject emotion recognition that utilizes masked brain signal modeling and interlinked spatial-temporal attention mechanism. The model learns universal latent representations of EEG signals through pre-training on large scale dataset, and employs Interlinked spatial-temporal attention mechanism to process Differential Entropy(DE) features extracted from EEG data. Subsequently, a multi-level fusion layer is proposed to integrate the discriminative features, maximizing the advantages of features across different dimensions and modalities. Extensive experiments on public datasets demonstrate Mood Reader's superior performance in cross-subject emotion recognition tasks, outperforming state-of-the-art methods. Additionally, the model is dissected from attention perspective, providing qualitative analysis of emotion-related brain areas, offering valuable insights for affective research in neural signal processing.

Image Denoising by Gaussian Patch Mixture Model and Low Rank Patches

Non-local self-similarity based low rank algorithms are the state-of-the-art methods for image denoising. In this paper, a new method is proposed by solving two issues: how to improve similar patches matching accuracy and build an appropriate low rank matrix approximation model for Gaussian noise. For the first issue, similar patches can be found locally or globally. Local patch matching is to find similar patches in a large neighborhood which can alleviate noise effect, but the number of patches may be insufficient. Global patch matching is to determine enough similar patches but the error rate of patch matching may be higher. Based on this, we first use local patch matching method to reduce noise and then use Gaussian patch mixture model to achieve global patch matching. The second issue is that there is no low rank matrix approximation model to adapt to Gaussian noise. We build a new model according to the characteristics of Gaussian noise, then prove that there is a globally optimal solution of the model. By solving the two issues, experimental results are reported to show that the proposed approach outperforms the state-of-the-art denoising methods includes several deep learning ones in both PSNR / SSIM values and visual quality.

Constrained low-tubal-rank tensor recovery for hyperspectral images mixed noise removal by bilateral random projections

In this paper, we propose a novel low-tubal-rank tensor recovery model, which directly constrains the tubal rank prior for effectively removing the mixed Gaussian and sparse noise in hyperspectral images. The constraints of tubal-rank and sparsity can govern the solution of the denoised tensor in the recovery procedure. To solve the constrained low-tubal-rank model, we develop an iterative algorithm based on bilateral random projections to efficiently solve the proposed model. The advantage of random projections is that the approximation of the low-tubal-rank tensor can be obtained quite accurately in an inexpensive manner. Experimental examples for hyperspectral image denoising are presented to demonstrate the effectiveness and efficiency of the proposed method.