Related papers: Discrete Scaling Based on Operator Theory
Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…
We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to…
Smoothing is omnipresent in astronomy, because almost always measurements performed at discrete positions in the sky need to be interpolated into a smooth map for subsequent analysis. Still, the statistical properties of different…
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…
The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains,…
How do the geometric properties of a domain impact the spectrum of an operator defined on it? How do we compute accurate and reliable approximations of these spectra? The former question is studied in spectral geometry, and the latter is a…
Graph signal sampling is the problem of selecting a subset of representative graph vertices whose values can be used to interpolate missing values on the remaining graph vertices. Optimizing the choice of sampling set using concepts from…
Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the desired results due to irregularities or uncertainties of…
We consider distributed sensing of non-local quantities. We introduce quantum enhanced protocols to directly measure any (scalar) field with a specific spatial dependence by placing sensors at appropriate positions and preparing a spatially…
Context: The technique of disentangling has been applied to numerous high-precision studies of spectroscopic binaries and multiple stars. Although, its possibilities have not yet been fully understood and exploited. Aims: Theoretical…
Scale is often seen as a given, disturbing factor in many vision tasks. When doing so it is one of the factors why we need more data during learning. In recent work scale equivariance was added to convolutional neural networks. It was shown…
This note shows how to align a periodic signal with its the Fourier transform by means of frequency or time scaling. This may be useful in developing new algorithms, e.g. for pitch estimation. This note also convolves the signals and the…
Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify…
Dynamic spectrum sharing approach is a paradigm shift from the conventional static and exclusive approach to spectrum allocation. The existing methodologies to define use of the spectrum and quantify its efficiency are based on the static…
Many numerical methods for multiscale differential equations require a scale separation between the larger and the smaller scales to achieve accuracy and computational efficiency. In the area of multiscale dynamical systems, so-called,…
In recent years, there is a growing interest in the studying octonions, which are 8-dimensional hypercomplex numbers forming the biggest normed division algebras over the real numbers. In particular, various tools of the classical complex…
Mobile communication channels are often modeled as linear time-varying filters or, equivalently, as time-frequency integral operators with finite support in time and frequency. Such a characterization inherently assumes the signals are…
Finite-difference simulations of fluid dynamics and magnetohydrodynamics generally require an explicit diffusion operator, either to maintain stability by attenuating grid-scale structure, or to implement physical diffusivities such as…
We initiate a systematic study of natural differential operators in Riemannian geometry whose leading symbols are not of Laplace type. In particular, we define a discrete leading symbol for such operators which may be computed pointwise, or…
In this paper we study the scale-space classification of signals via the maximal set of kernels. We use a geometric approach which arises naturally when we consider parameter variations in scale-space. We derive the Fourier transform…