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Super-resolution (SR) is a severely ill-posed problem with inherent ambiguity, as widely recognized in both empirical and theoretical studies. Although recent semantic-guided and multi-modal SR methods exploit large models or external…
There is currently a paradigm shift in several power system monitoring applications, such as incipient fault detection and monitoring inverter-based resources, to transition from traditional phasor analytics to more informative waveform…
We present some relaxation and integral representation results for energy functionals in the setting of structured deformations, with special emphasis given to the case of multi-level structured deformations. In particular, we present an…
Recent years have seen growing interest in learning disentangled representations, in which distinct features, such as size or shape, are represented by distinct neurons. Quantifying the extent to which a given representation is disentangled…
Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…
We show how fundamental ideas from signal processing, multiscale theory and wavelets may be applied to non-linear dynamics. The problems from dynamics include iterated function systems (IFS), dynamical systems based on substitution such as…
The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…
Multi-contrast super-resolution (MCSR) is crucial for enhancing MRI but current deep learning methods are limited. They typically require large, paired low- and high-resolution (LR/HR) training datasets, which are scarce, and are trained…
Optical metasurfaces composed of precisely engineered nanostructures have gained significant attention for their ability to manipulate light and implement distinct functionalities based on the properties of the incident field. Computational…
This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…
In the framework of large deformation diffeomorphic metric mapping (LDDMM), we develop a multi-scale theory for the diffeomorphism group based on previous works. The purpose of the paper is (1) to develop in details a variational approach…
Guided depth map super-resolution (GDSR), which aims to reconstruct a high-resolution (HR) depth map from a low-resolution (LR) observation with the help of a paired HR color image, is a longstanding and fundamental problem, it has…
Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a…
The rise of generalist large-scale models in natural language and vision has made us expect that a massive data-driven approach could achieve broader generalization in other domains such as continuous control. In this work, we explore a…
We discuss how generalized multiresolution analyses (GMRAs), both classical and those defined on abstract Hilbert spaces, can be classified by their multiplicity functions $m$ and matrix-valued filter functions $H$. Given a natural number…
Since higher-order tensors are naturally suitable for representing multi-dimensional data in real-world, e.g., color images and videos, low-rank tensor representation has become one of the emerging areas in machine learning and computer…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…
This paper studies a general class of Iterated Function Systems (IFS). No contractivity assumptions are made, other than the existence of some compact attractor. The possibility of escape to infinity is considered. Our present approach is…
Representation learning is a widely adopted framework for learning in data-scarce environments, aiming to extract common features from related tasks. While centralized approaches have been extensively studied, decentralized methods remain…
To directly image Earth-like planets, contrast levels of 10^-8 - 10^-10 are required. The next generation of instruments will need wavefront control below the nanometer level to achieve these goals. The Zernike wavefront sensor (ZWFS) is a…