Related papers: Signal and Image Processing with Sinlets
We consider the applicability of phase space Wannier functions" to electronic structure calculations. These generalized Wannier functions are analogous to localized plane waves and constitute a complete, orthonormal set which is…
Periodic splines are a special kind of splines that are defined over a set of knots over a circle and are adequate for solving interpolation problems related to closed curves. This paper presents a method of implementing the objects…
Neural networks possess incredible capabilities for extracting abstract features from data. Electromagnetic computing harnesses wave propagation to execute computational operations. Metasurfaces, composed of subwavelength meta-atoms, are…
We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…
Semantic communication systems aim to transmit task-relevant information between devices capable of artificial intelligence, but their performance can degrade when heterogeneous transmitter-receiver models produce misaligned latent…
We present a detailed study of the use of localized spherical-wave basis sets, first introduced in the context of linear-scaling, in first-principles density-functional calculations. Several parameters that control the completeness of this…
Image tokenizers map images to sequences of discrete tokens, and are a crucial component of autoregressive transformer-based image generation. The tokens are typically associated with spatial locations in the input image, arranged in raster…
Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the…
Seismic processing plays a crucial role in transforming raw data into high-quality subsurface images, pivotal for various geoscience applications. Despite its importance, traditional seismic processing techniques face challenges such as…
This paper describes a very efficient algorithm for image signal extrapolation. It can be used for various applications in image and video communication, e.g. the concealment of data corrupted by transmission errors or prediction in video…
The theory of orthonormal wavelet bases is a useful tool in multifractal analysis, as it provides a characterization of the different exponents of pointwise regularities (H{\"o}lder, p-exponent, lacunarity, oscillation, etc.). However, for…
In the realm of signal processing, frequency and spectrum detection are fundamental tasks that can be computationally intensive. This project leverages the power of FPGAs to perform wavelet analysis on an input signal. The goal is to detect…
Rapid developments in synthetic aperture (SA) systems, which generate a larger aperture with greater angular resolution than is inherently possible from the physical dimensions of a single sensor alone, are leading to novel research avenues…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…
Birefringent metasurfaces are two-dimensional structures capable of independently controlling the amplitude, phase and polarization of orthogonally polarized incident waves. In this work, we propose a in-depth discussion on the mathematical…
Here we present a method of constructing steerable wavelet frames in $L_2(\mathbb{R}^d)$ that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the need…
Large foundation models, known for their strong zero-shot generalization capabilities, can be applied to a wide range of downstream tasks. However, developing foundation models for medical image segmentation poses a significant challenge…
Interferometry can measure the shape or the material density of a system that could not be measured otherwise by recording the difference between the phase change of a signal and a reference phase. This difference is always between $-\pi$…
The rapid growth of wireless communications has created a significant demand for high throughput, seamless connectivity, and extremely low latency. To meet these goals, a novel technology -- stacked intelligent metasurfaces (SIMs) -- has…
In previous work, we presented a general framework for instantaneous time-frequency analysis but did not provide any specific details of how to compute a particular instantaneous spectrum (IS). In this work, we use instantaneous…