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High-resolution imaging in the terahertz (THz) spectral range remains fundamentally constrained by the limited numerical apertures of currently existing state-of-the-art imagers, which restricts its applicability across many fields, such as…
We study approximation properties generated by highly regular scaling functions and orthonormal wavelets. These properties are conveniently described in the framework of Gelfand-Shilov spaces. Important examples of multiresolution analyses…
The investigation of the static and dynamic structural properties of colloidal systems relies on techniques capable of atomic resolution in real space and femtosecond resolution in time. Recently, the cross-correlation function (CCF)…
Intensity correlation microscopy (ICM), which is prominently known through antibunching microscopy or super-resolution optical fluctuation imaging (SOFI), provides superresolution through a correlation analysis of antibunching of…
Imaging with a layered superlens is a spatial filtering operation characterized by the point spread function (PSF). We show that in the same optical system the image of a narrow sub-wavelength Gaussian incident field may be surprisingly…
Multiphysics simulations frequently require transferring solution fields between subproblems with non-matching spatial discretizations, typically using interpolation techniques. Standard methods are usually based on measuring the closeness…
Geospatial object detection of remote sensing imagery has been attracting an increasing interest in recent years, due to the rapid development in spaceborne imaging. Most of previously proposed object detectors are very sensitive to object…
This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the third paper, the analytical analysis of multiscale phenomena inherent in the…
We present MRPARCv2, Multi-resolution Physics-Aware Recurrent Convolutional Neural Network, designed to model complex flows by embedding the structure of advection-diffusion-reaction equations and leveraging a multi-resolution architecture.…
Multimodal object detection improves robustness in chal- lenging conditions by leveraging complementary cues from multiple sensor modalities. We introduce Filtered Multi- Modal Cross Attention Fusion (FMCAF), a preprocess- ing architecture…
Vision language models (VLMs) have achieved impressive performance across a variety of computer vision tasks. However, the multimodal reasoning capability has not been fully explored in existing models. In this paper, we propose a…
Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space $\H$ that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis…
There are many research available on the study of real-valued fractal interpolation function and fractal dimension of its graph. In this paper, our main focus is to study the dimensional results for vector-valued fractal interpolation…
Interferometers play an increasingly important role for spatially resolved observations. If employed at full potential, interferometry can probe an enormous dynamic range in spatial scale. Interpretation of the observed visibilities…
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…
Meshless solution to differential equations using radial basis functions (RBF) is an alternative to grid based methods commonly used. Since the meshless method does not need an underlying connectivity in the form of control volumes or…
Spectral imaging is a fundamental diagnostic technique with widespread application. Conventional spectral imaging approaches have intrinsic limitations on spatial and spectral resolutions due to the physical components they rely on. To…
This study considers the Block-Toeplitz structural properties inherent in traditional multichannel forward model matrices, using Full Matrix Capture (FMC) in ultrasonic testing as a case study. We propose an analytical convolutional forward…
In this paper we present a general approach to multivariate periodic wavelets generated by scaling functions of de la Vall\'ee Poussin type. These scaling functions and their corresponding wavelets are determined by their Fourier…