Aug 2026· Neural Networks· Vol 205 Pt B, pp.
109489
· 0 citations· 52 references
Medicine
TL;DR
A robust non-parametric Bayesian method known as the Bayesian adaptive tensor ring decomposition (BATR) method, which accomplishes an adaptive low tensor ring (TR) rank model by incorporating a more advanced generalized hyperbolic (GH) prior into the probabilistic framework, thereby facilitating automatic TR rank determination.
Abstract
Robust tensor decomposition (RTD) is designed to distinguish low-rank and sparse tensors from noisy high-dimensional data, which holds fundamental significance in the fields of machine learning and computer vision. Nevertheless, current RTD-based methods fall short in addressing the issues of automatic noise adaptation and determination of model capacity. In response to these challenges, this paper introduces a robust non-parametric Bayesian method known as the Bayesian adaptive tensor ring decomposition (BATR) method. More precisely, BATR models unknown noise using a Dirichlet process Gaussian mixture model (DP-GMM), with automatic determination of the noise components. Besides, BATR accomplishes an adaptive low tensor ring (TR) rank model by incorporating a more advanced generalized hyperbolic (GH) prior into the probabilistic framework, thereby facilitating automatic TR rank determination. Furthermore, a variational Bayesian inference algorithm is employed to update the posteriors of the model. Extensive experiments on synthetic data, color images, face images, multispectral images, and hyperspectral images demonstrate the improved performance of BATR compared to other state-of-the-art methods.
A robust tensor recovery model based on second-order difference-induced adaptive tensor nuclear norm regularization that consistently improves PSNR and ERGAS under all tested noise settings while achieving competitive SSIM values is proposed.
The sampling process of Denoising Diffusion Probabilistic Models (DDPMs) can be accelerated by leveraging second-order information in the form of approximations to the denoising posterior covariance -- allowing samples of acceptable quality to be produced in fewer but larger sampling steps. Previous attempts at using such information have used drastic (e.g.\ diagonal) simplifications of the covariance. These do not do justice to the peculiar statistical structure of natural images, which exhibit strong non-diagonal correlations between pixels and color channels, and a slow-decaying power-law frequency spectrum. Here, we develop a novel covariance model that captures these features. Our Kronecker-DCT (K-DCT) model uses a Kronecker-factored decomposition of inter-color covariances and spatial covariances modeled in the frequency domain using the Discrete Cosine Transform (DCT). The use of the DCT reduces the computational complexity from quadratic to log-linear, resulting in negligible computational and memory overhead in each denoising step. By learning K-DCT-structured amortizations of the denoising posterior covariance using pre-trained score models on CIFAR-10, Celeb-A, ImageNet and LSUN datasets, we show improved performance compared to previous SOTA denoising samplers, both in terms of FID and likelihoods, especially in the regime of few denoising steps.
Rui Xia, Ayan Das, A. Artemev et al.· Trans. Mach. Learn. Res.· 0 citations
Image Sparse Noise Removal constitutes a core issue within the domain of image processing. The tensor nuclear norm (TNN) has achieved great success in color image sparse denoising, but it suffers from the problem of direction sensitivity. In order to address this problem, a color image sparse noise removal scheme via the rotational tensor nuclear norm (RTNN) is proposed. First, to characterize the correlation across each dimension of the image, the RTNN is introduced. Then, on the basis of the RTNN, a model for image sparse noise removal is established. Next, an effective algorithm for the image sparse noise removal model is designed by adopting the ADMM. Finally, numerical experiments demonstrate that our scheme surpasses other compared methods with respect to evaluation metrics.
Li Guo, Pei-Yu Qin· Journal of Physics, Conferen...· 0 citations
High-dimensional multi-way (tensor) data pose significant challenges for covariance estimation due to the curse of dimensionality. We introduce a unified framework for scalable estimation of tensor covariances based on a Kronecker-structured sparse inverse Cholesky (KSIC) projection. Our approach is grounded in the geometry of information projection, defining the estimator as the moment-matching projection of a target distribution onto a manifold characterized by sparse, Kronecker-factored inverse Cholesky factors. By leveraging physical or data-driven nearest-neighbor sparsity, KSIC provides a geometry-aware representation that is both statistically interpretable and computationally efficient. Our framework integrates two estimation regimes: a nonparametric estimator that projects the empirical covariance directly onto the manifold, utilizing the KSIC structure to implicitly regularize rank-deficient data; and a parametric estimator that fits generative covariance models (e.g., Mat\'ern) by maximizing the likelihood of their KSIC projections, formulated as a nested double forward Kullback-Leibler minimization. Theoretically, we establish the conditions for the existence of the KSIC projection and finite-sample concentration rates for the nonparametric regime, proving that the KSIC estimator gainfully exploits cross-mode information and is robust to data scarcity. Numerical experiments demonstrate that the proposed KSIC estimators achieve state-of-the-art accuracy and scalability, particularly in settings with high dimensionality and limited sample sizes. We apply KSIC to spatiotemporal temperature anomalies and functional MRI data, demonstrating its broad applicability across diverse multi-way data domains.
This work provides a theoretical analysis which establishes a non-asymptotic reconstruction error bound that characterizes the effects of sampling complexity, optimization convergence, and model mismatch in a structured tensor approximation problem.
Jeongmin Chae, Usama Saleem, Selin Bac et al.· 0 citations
An efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format and observing that the proposed NTT fitting procedure exhibits drastically faster convergence than an alternative multiplicative update method that has been previously proposed is observed.
Xun Tang, Rajat Vadiraj Dwaraknath, Le-Xing Ying· SIAM Journal on Scientific C...· 0 citations
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