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A new phase-coherent technique for the calibration of polarimetric data is presented. Similar to the one-dimensional form of convolution, data are multiplied by the response function in the frequency domain. Therefore, the system response…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
In this paper, we study wavelet filters and their dependence on two numbers, the scale N and the genus g. We show that the wavelet filters, in the quadrature mirror case, have a harmonic analysis which is based on representations of the…
A brief review is provided of the use of the Square Wave Method (SWM) in the field of signal and image analysis and it is specified how results thus obtained are expressed using the Square Wave Transform (SWT), in the frequency domain. To…
A general machine learning architecture is introduced that uses wavelet scattering coefficients of an inputted three dimensional signal as features. Solid harmonic wavelet scattering transforms of three dimensional signals were previously…
A naive theory of additive perturbations on a continuous probability distribution is presented. We propose a new privatization mechanism based on a naive theory of a perturbation on a probability using wavelets, such as a noise perturbs the…
A multilayered particle is illuminated by plane acoustic or electromagnetic waves of one or several frequencies. We consider the inverse scattering problem for the identification of the layers and of the refraction coefficients of the…
Pansharpening aims to combine a high-resolution panchromatic (PAN) image with a low-resolution multispectral (LRMS) image to produce a high-resolution multispectral (HRMS) image. Although pansharpening in the frequency domain offers clear…
Surface-consistent deconvolution is a standard processing technique in land data to uniformize the wavelet across all sources and receivers. The required wavelet estimation step is generally done in the homomorphic domain since this is a…
Algorithms are proposed for the computation of set-valued quantiles and the values of the lower cone distribution function for bivariate data sets. These new objects make data analysis possible involving an order relation for the data…
We discuss statistical techniques for detecting and quantifying bimodality in astronomical datasets. We concentrate on the KMM algorithm, which estimates the statistical significance of bimodality in such datasets and objectively partitions…
With the onset of large-scale astronomical surveys capturing millions of images, there is an increasing need to develop fast and accurate deconvolution algorithms that generalize well to different images. A powerful and accessible…
We develop the idea of employing localization systems of Boolean coverings, associated with measurement situations, in order to comprehend structures of Quantum Observables. In this manner, Boolean domain observables constitute structure…
The article provides a brief survey of the mathematics of some of the newly being developed so called "hybrid" (also called "multi-physics" or "multi-wave") imaging techniques.
In this short note we discuss the interplay between finite Coxeter groups and construction of wavelet sets, generalized multiresolution analysis and sampling.
We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers of an arrangement as a byproduct of computing its…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…
Distributed surveillance systems have become popular in recent years due to security concerns. However, transmitting high dimensional data in bandwidth-limited distributed systems becomes a major challenge. In this paper, we address this…
The paper introduces the idea of non-uniform quantization in the detail components of wavelet transformed image. It argues that most of the coefficients of horizontal, vertical and diagonal components lie near to zeros and the coefficients…
This paper introduces a novel algorithmic solution for the approximation of a given multivariate function by a nomographic function that is composed of a one-dimensional continuous and monotone outer function and a sum of univariate…