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We present a computational approach which is tailored for reducing the complexity of the description of extended systems at the density functional theory level. We define a recipe for generating a set of localized basis functions which are…
Conventional MRI reconstruction methods treat images and coil sensitivities as discrete objects, leading to high memory demands and limited structural awareness that hamper effective regularization. These limitations hinder accurate…
Magnetic resonance imaging (MRI) is a potent diagnostic tool, but suffers from long examination times. To accelerate the process, modern MRI machines typically utilize multiple coils that acquire sub-sampled data in parallel. Data-driven…
The purpose of this research is to estimate sensitivity maps when imaging X-nuclei that may not have a significant presence throughout the field of view. We propose to estimate the coil's sensitivities by solving a least-squares problem…
LiDAR point clouds are fundamental to various applications, yet the extreme sparsity of high-precision geometric details hinders efficient context modeling, thereby limiting the compression speed and performance of existing methods. To…
We introduce an accurate and efficient method for a class of nonlocal potential evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipolar potentials. Our method is based on a Gaussian-sum approximation…
Accurate phase extraction from sinusoidal signals is a crucial task in various signal processing applications. While prior research predominantly addresses the case of asynchronous sampling with unknown signal frequency, this study focuses…
We propose a novel calibration method for computer simulators, dealing with the problem of covariate shift. Covariate shift is the situation where input distributions for training and test are different, and ubiquitous in applications of…
This note gives a summary of ideas concerning Applied Fourier Analysis, mostly formulated for those who have to give such courses to engineers or mathematicians interested in real life applications. It tries to answer recurrent questions…
Shielding sensitive scientific and medical devices from the magnetic field environment is one of the promising applications of superconductors. Magnetic field concentration by superconducting magnetic lenses is the opposite phenomenon…
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…
Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…
The availability of large spatial data geocoded at accurate locations has fueled a growing interest in spatial modeling and analysis of point processes. The proposed research is motivated by the intensity estimation problem for large…
This work presents a Fourier analysis framework for the non-interactive source simulation (NISS) problem. Two distributed agents observe a pair of sequences $X^d$ and $Y^d$ drawn according to a joint distribution $P_{X^dY^d}$. The agents…
Many problems in science and engineering require making predictions based on few observations. To build a robust predictive model, these sparse data may need to be augmented with simulated data, especially when the design space is…
Spatial orientation is a fundamental cognitive skill that relies on sensory information to update perceived direction. Understanding how sensory conditions influence directional accuracy is important for both cognitive science and the…
Estimating the first-order intensity function in point pattern analysis is an important problem, and it has been approached so far from different perspectives: parametrically, semiparametrically or nonparametrically. Our approach is close…
We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of $1$-bit…
We address three key challenges in learning continuous kernel representations: computational efficiency, parameter efficiency, and spectral bias. Continuous kernels have shown significant potential, but their practical adoption is often…
A sensitivity profile of a planar spiral coil sensor (PSCS) is proposed and is used to generate the relation of 3-D position of object observed using three PSCSs, one in each x, y, and z axis to the sensors response. A numerical procedure…