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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., Comment: This paper was accepted by Pattern Recognition on September 5, 2024

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., Comment: Accepted by International Conference on Neural Computing for Advanced Applications, 2024

Effective connectivity estimation plays a crucial role in understanding the interactions and information flow between different brain regions. However, the functional time series used for estimating effective connectivity is derived from certain software, which may lead to large computing errors because of different parameter settings and degrade the ability to model complex causal relationships between brain regions. In this paper, a brain diffuser with hierarchical transformer (BDHT) is proposed to estimate effective connectivity for mild cognitive impairment (MCI) analysis. To our best knowledge, the proposed brain diffuser is the first generative model to apply diffusion models to the application of generating and analyzing multimodal brain networks. Specifically, the BDHT leverages structural connectivity to guide the reverse processes in an efficient way. It makes the denoising process more reliable and guarantees effective connectivity estimation accuracy. To improve denoising quality, the hierarchical denoising transformer is designed to learn multi-scale features in topological space. By stacking the multi-head attention and graph convolutional network, the graph convolutional transformer (GraphConformer) module is devised to enhance structure-function complementarity and improve the ability in noise estimation. Experimental evaluations of the denoising diffusion model demonstrate its effectiveness in estimating effective connectivity. The proposed model achieves superior performance in terms of accuracy and robustness compared to existing approaches. Moreover, the proposed model can identify altered directional connections and provide a comprehensive understanding of parthenogenesis for MCI treatment., Comment: 13pages, 14 figures

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.

This paper describes a new algorithm for computing Nonnegative Low Rank Matrix (NLRM) approximation for nonnegative matrices. Our approach is completely different from classical nonnegative matrix factorization (NMF) which has been studied for more than twenty five years. For a given nonnegative matrix, the usual NMF approach is to determine two nonnegative low rank matrices such that the distance between their product and the given nonnegative matrix is as small as possible. However, the proposed NLRM approach is to determine a nonnegative low rank matrix such that the distance between such matrix and the given nonnegative matrix is as small as possible. There are two advantages. (i) The minimized distance by the proposed NLRM method can be smaller than that by the NMF method, and it implies that the proposed NLRM method can obtain a better low rank matrix approximation. (ii) Our low rank matrix admits a matrix singular value decomposition automatically which provides a significant index based on singular values that can be used to identify important singular basis vectors, while this information cannot be obtained in the classical NMF. The proposed NLRM approximation algorithm was derived using the alternating projection on the low rank matrix manifold and the non-negativity property. Experimental results are presented to demonstrate the above mentioned advantages of the proposed NLRM method compared the NMF method., Comment: 25 pages 13 figures

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., Comment: Accepted by IGARSS 2019