Related papers: Tensor Denoising via Amplification and Stable Rank…

Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression…

Image denoising is a fundamental operation in image processing and holds considerable practical importance for various real-world applications. Arguably several thousands of papers are dedicated to image denoising. In the past decade,…

Hyperspectral image super-resolution addresses the problem of fusing a low-resolution hyperspectral image (LR-HSI) and a high-resolution multispectral image (HR-MSI) to produce a high-resolution hyperspectral image (HR-HSI). Tensor analysis…

To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…

Denoisers trained with synthetic data often fail to cope with the diversity of unknown noises, giving way to methods that can adapt to existing noise without knowing its ground truth. Previous image-based method leads to noise overfitting…

Seismic data denoising is an important part of seismic data processing, which directly relate to the follow-up processing of seismic data. In terms of this issue, many authors proposed many methods based on rank reduction, sparse…

Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…

Tensor decomposition on big data has attracted significant attention recently. Among the most popular methods is a class of algorithms that leverages compression in order to reduce the size of the tensor and potentially parallelize…

Noisy images are a challenge to image compression algorithms due to the inherent difficulty of compressing noise. As noise cannot easily be discerned from image details, such as high-frequency signals, its presence leads to extra bits…

Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…

Modern digital cameras rely on the sequential execution of separate image processing steps to produce realistic images. The first two steps are usually related to denoising and demosaicking where the former aims to reduce noise from the…

Denoising, the process of reducing random fluctuations in a signal to emphasize essential patterns, has been a fundamental problem of interest since the dawn of modern scientific inquiry. Recent denoising techniques, particularly in…

Removal or cancellation of noise has wide-spread applications for imaging and acoustics. In every-day-life applications, denoising may even include generative aspects, which are unfaithful to the ground truth. For scientific use, however,…

Recurrent neural networks (RNNs) are powerful models of sequential data. They have been successfully used in domains such as text and speech. However, RNNs are susceptible to overfitting; regularization is important. In this paper we…

The current methods for learning representations with auto-encoders almost exclusively employ vectors as the latent representations. In this work, we propose to employ a tensor product structure for this purpose. This way, the obtained…

Tensors naturally model many real world processes which generate multi-aspect data. Such processes appear in many different research disciplines, e.g, chemometrics, computer vision, psychometrics and neuroimaging analysis. Tensor…

Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…

In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…

The orthogonal decomposition factorizes a tensor into a sum of an orthogonal list of rankone tensors. We present several properties of orthogonal rank. We find that a subtensor may have a larger orthogonal rank than the whole tensor and…

We develop a framework to analyse invariant decompositions of elements of tensor product spaces. Namely, we define an invariant decomposition with indices arranged on a simplicial complex, and which is explicitly invariant under a group…