Related papers: Tomograms and other transforms. A unified view
One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
Metamorphism is a recently introduced integral transform, which is useful in solving partial differential equations. Basic properties of metamorphism can be verified by direct calculations. In this paper we present metamorphism as a sort of…
Network tomography, a classic research problem in the realm of network monitoring, refers to the methodology of inferring unmeasured network attributes using selected end-to-end path measurements. In the research community, network…
In many tomographic imaging problems the data consist of integrals along lines or curves. Increasingly we encounter "rich tomography" problems where the quantity imaged is higher dimensional than a scalar per voxel, including vectors…
A tomographic method is considered that forms images from sets of spatially randomized source signals and receiver sensitivities. The method is designed to allow image reconstruction for an extended number of transmitters and receivers in…
Critical phase transitions have proven to be a powerful concept to capture the phenomenology of many systems, including deeply non-equilibrium ones like living systems. The study of these phase transitions has overwhelmingly relied on…
Quantum computing has emerged as a transformative paradigm, capable of tackling complex computational problems that are infeasible for classical methods within a practical timeframe. At the core of this advancement lies the concept of…
Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to…
We study the transmission of a quantum particle along a straight input--output line to which a graph $\Gamma$ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant…
A tomographic technique has been used in the past to decompose complex signals in its components. The technique is based on spectral decomposition and projection on the eigenvectors of a family of unitary operators. Here this technique is…
Recent progress in graph signal processing (GSP) has addressed a number of problems, including sampling and filtering. Proposed methods have focused on generic graphs and defined signals with certain characteristics, e.g., bandlimited…
Atom probe tomography is often introduced as providing "atomic-scale" mapping of the composition of materials and as such is often exploited to analyse atomic neighbourhoods within a material. Yet quantifying the actual spatial performance…
The new method for the simulation of nonstationary quantum processes is proposed. The method is based on the tomography representation of quantum mechanics, {\it i.e.}, the state of the system is described by the {\it nonnegative} function…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of…
Digital array orthogonal transformations that can be presented as a decomposition over basis items or basis images are considered. The orthogonal transform provides digital data scattering, a process of pixel energy redistributing, that is…
Continuous phase spaces have become a powerful tool for describing, analyzing, and tomographically reconstructing quantum states in quantum optics and beyond. A plethora of these phase-space techniques are known, however a thorough…
We establish a general principle for the tomographic approach to quantum state reconstruction, till now based on a simple rotation transformation in the phase space, which allows us to consider other types of transformations. Then, we will…
The transmission matrix (TM) is a representation to describe the light scattering process through a scattering medium. The degree of control elements in TM is correlated with the capacity of evaluating enormous equations with tremendous…