Related papers: A Fast Algorithm for Multiresolution Mode Decompos…
The Dynamic Mode Decomposition (DMD) extracted dynamic modes are the non-orthogonal eigenvectors of the matrix that best approximates the one-step temporal evolution of the multivariate samples. In the context of dynamical system analysis,…
The Multiscale Hierarchical Decomposition Method (MHDM) was introduced as an iterative method for total variation regularization, with the aim of recovering details at various scales from images corrupted by additive or multiplicative…
A number of deep learning based algorithms have been proposed to recover high-quality videos from low-quality compressed ones. Among them, some restore the missing details of each frame via exploring the spatiotemporal information of…
Complex object wave recovery from single-shot interference pattern is an important practical problem in interferometry and digital holography. The most popular single-shot interferogram analysis method involves Fourier filtering of…
Multi-modality image fusion (MMIF) aims to integrate complementary information from different modalities into a single fused image to represent the imaging scene and facilitate downstream visual tasks comprehensively. In recent years,…
Neural time-series analysis has traditionally focused on modeling data in the time domain, often with some approaches incorporating equivalent Fourier domain representations as auxiliary spectral features. In this work, we shift the main…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
This paper describes a versatile method that accelerates multichannel source separation methods based on full-rank spatial modeling. A popular approach to multichannel source separation is to integrate a spatial model with a source model…
Multimodal MRIs play a crucial role in clinical diagnosis and treatment. Feature disentanglement (FD)-based methods, aiming at learning superior feature representations for multimodal data analysis, have achieved significant success in…
Hyperspectral unmixing (HU) is a critical yet challenging task in remote sensing. However, existing nonnegative matrix factorization (NMF) methods with graph learning mostly focus on first-order or second-order nearest neighbor…
Sparse random mode decomposition (SRMD) is a novel algorithm that constructs a random time-frequency feature space to sparsely approximate spectrograms, effectively separating modes. However, it fails to distinguish adjacent or overlapped…
Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article,…
Perception of the full state is an essential technology to support the monitoring, analysis, and design of physical systems, one of whose challenges is to recover global field from sparse observations. Well-known for brilliant approximation…
Multimode fibers (MMFs) can transmit multiple guided modes simultaneously, making them a promising platform for high-resolution biomedical imaging, endoscopy and high-bandwidth optical communication. However, their complex modal behavior,…
In this paper, a generic extension of variational mode decomposition (VMD) algorithm for multivariate or multichannel data sets is presented. We first define a model for multivariate modulated oscillations that is based on the presence of a…
Perhaps surprisingly, the total electron microscopy (EM) data collected to date is less than a cubic millimeter. Consequently, there is an enormous demand in the materials and biological sciences to image at greater speed and lower dosage,…
Multidimensional fitting (MDF) method is a multivariate data analysis method recently developed and based on the fitting of distances. Two matrices are available: one contains the coordinates of the points and the second contains the…
We present a high-order radial basis function finite difference (RBF-FD) framework for the solution of advection-diffusion equations on time-varying domains. Our framework is based on a generalization of the recently developed Overlapped…
In this work, we present a new technique for the decomposition of multivariate data, which we call Multivariate Fast Iterative Filtering (MvFIF) algorithm. We study its properties, proving rigorously that it converges in finite time when…
Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors.…