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In this paper, to break the limit of the traditional linear models for synthetic aperture radar (SAR) image despeckling, we propose a novel deep learning approach by learning a non-linear end-to-end mapping between the noisy and clean SAR…

Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…

Disentangled representation learning has seen a surge in interest over recent times, generally focusing on new models which optimise one of many disparate disentanglement metrics. Symmetry Based Disentangled Representation learning…

Contraction analysis offers, through elegant mathematical developments, a unified way of designing observers for a general class of nonlinear systems, where the observer correction term is obtained by solving an infinite dimensional…

We present three variants of a lightweight, fully connected artificial neural network, suited for interactive estimation of three-dimensional, spatially resolved volumes of scattered radiation fields and a corresponding training pipeline…

Image deblurring aims to restore high-quality images by removing undesired degradation. Although existing methods have yielded promising results, they either overlook the varying degrees of degradation across different regions of the…

The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…

Recognizing symmetries in data allows for significant boosts in neural network training. In many cases, however, the underlying symmetry is present only in an idealized dataset, and is broken in the training data, due to effects such as…

The line spectral estimation problem consists in recovering the frequencies of a complex valued time signal that is assumed to be sparse in the spectral domain from its discrete observations. Unlike the gridding required by the classical…

Dimension Estimation (DE) and Dimension Reduction (DR) are two closely related topics, but with quite different goals. In DE, one attempts to estimate the intrinsic dimensionality or number of latent variables in a set of measurements of a…

How to effectively explore multi-scale representations of rain streaks is important for image deraining. In contrast to existing Transformer-based methods that depend mostly on single-scale rain appearance, we develop an end-to-end…

Discovering governing equations that describe complex chaotic systems remains a fundamental challenge in physics and neuroscience. Here, we introduce the PEM-UDE method, which combines the prediction-error method with universal differential…

We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is $O(d\log d)$ for $d$-th…

Binary representation is desirable for its memory efficiency, computation speed and robustness. In this paper, we propose adjustable bounded rectifiers to learn binary representations for deep neural networks. While hard constraining…

In this work, we study distance metric learning (DML) for high dimensional data. A typical approach for DML with high dimensional data is to perform the dimensionality reduction first before learning the distance metric. The main…

Algorithm extraction aims to synthesize executable programs directly from models trained on algorithmic tasks, enabling de novo algorithm discovery without relying on human-written code. However, applying this paradigm to Transformer is…

Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…

Dimensionality reduction (DR) on the manifold includes effective methods which project the data from an implicit relational space onto a vectorial space. Regardless of the achievements in this area, these algorithms suffer from the lack of…

We present the first experimental validation of the Deep Lie Map Network (DLMN) approach for recovering both linear and non-linear optics in a synchrotron. The DLMN facilitates the construction of a detailed accelerator model by integrating…

Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One…