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This paper discusses different approaches used for millimeter wave imaging of two-dimensional objects. Imaging of a two dimensional object requires reflected wave data to be collected across two distinct dimensions. In this paper, we…
In this paper we show that the discrete Fourier transform can be performed by scattering a coherent particle or laser beam off a two-dimensional potential that has the shape of rings or peaks. After encoding the initial vector into the…
The effects of particle discreteness in N-body simulations of Lambda Cold Dark Matter (LambdaCDM) are still an intensively debated issue. In this paper we explore such effects, taking into account the scatter caused by the randomness of the…
In the future, optical stellar interferometers will provide true images thanks to larger number of telescopes and to advanced cophasing subsystems. These conditions are required to have sufficient resolution elements (resel) in the image…
The present chapter [submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011] is concerned with the introduction and study of a quadratic discrete Fourier…
The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which…
Recent developments in machine learning and signal processing have resulted in many new techniques that are able to effectively capture the intrinsic yet complex properties of hyperspectral imagery. Tasks ranging from anomaly detection to…
The efficient multiangle centered discrete fractional Fourier transform (MA-CDFRFT) [1] has proven to be a useful tool for time-frequency analysis; in this paper, we generalize the MA-CDFRFT to general M -periodic transforms, which, among…
Knowledge of the diffuse-field coherence between array sensors is a basic assumption for a wide range of array processing applications. Explicit relations previously existed only for omnidirectional and first-order directional sensors, or a…
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…
First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made---for the continuous-time case---in Mallat, 2012, and Wiatowski and B\"olcskei, 2015. This paper considers the discrete case,…
We calculate the frequency-dispersed nonlinear transmission signal of a phase-shaped visible pulse to fourth order in the field. Two phase profiles, a phase-step and phase-pulse, are considered. Two dimensional signals obtained by varying…
Finite field transforms have many applications and, in many cases, can be implemented with a low computational complexity. In this paper, the Z Transform over a finite field is introduced and some of its properties are presented.
Room Impulse Responses estimation is a fundamental problem in spatial audio processing and speech enhancement. In this paper, we build upon our previously introduced diffusion-based inpainting framework for Room Impulse Response…
We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…
In a follow-up effort to our prior report on the optical transmission of a moving Fabry-Perot interferometer \cite{Pyvovar}, this work seeks to establish a general framework that describes the transmission and reflection properties of a…
We show how spatial dispersion can be used as a mechanism to customize the longitudinal profiles of electric fields inside modulated wire media, using a fast and remarkably accurate 1D inhomogeneous model. This customization gives fine…
Surface wave dispersion curve inversion is crucial for estimating subsurface shear-wave velocity (vs), yet traditional methods often face challenges related to computational cost, non-uniqueness, and sensitivity to initial models. While…
Transfer learning is a machine learning technique designed to improve generalization performance by using pre-trained parameters obtained from other learning tasks. For image recognition tasks, many previous studies have reported that, when…
The discrete cosine transform is a valuable tool in analysis of data on undirected rectangular grids, like images. In this paper it is shown how one can define an analogue of the discrete cosine transform on triangles. This is done by…