15,424 research outputs found
Radix-2 x 2 x 2 algorithm for the 3-D discrete hartley transform
The discrete Hartley transform (DHT) has proved
to be a valuable tool in digital signal/image processing and communications and has also attracted research interests in many multidimensional applications. Although many fast algorithms have been developed for the calculation of one- and two-dimensional (1-D and 2-D) DHT, the development of multidimensional algorithms in three and more dimensions is still unexplored and has not been given similar attention; hence, the multidimensional
Hartley transform is usually calculated through the row-column approach. However, proper multidimensional algorithms can be more efficient than the row-column method and need to be developed. Therefore, it is the aim of this paper to introduce the concept and derivation of the three-dimensional (3-D) radix-2 2X 2X
algorithm for fast calculation of the 3-D discrete Hartley transform. The proposed algorithm is based on the principles of the divide-and-conquer approach applied directly in 3-D. It has a simple butterfly structure and has been found to offer significant savings in arithmetic operations compared with the row-column approach based on similar algorithms
On the solutions of generalized discrete Poisson equation
The set of common numerical and analytical problems is introduced in the form
of the generalized multidimensional discrete Poisson equation. It is shown that
its solutions with square-summable discrete derivatives are unique up to a
constant. The proof uses the Fourier transform as the main tool. The necessary
condition for the existence of the solution is provided.Comment: 8 pages, LaTe
Multiple multidimensional morse wavelets
This paper defines a set of operators that localize a radial image in space and radial frequency simultaneously. The eigenfunctions of the operator are determined and a nonseparable orthogonal set of radial wavelet functions are found. The eigenfunctions are optimally concentrated over a given region of radial space and scale space, defined via a triplet of parameters. Analytic forms for the energy concentration of the functions over the region are given. The radial function localization operator can be generalised to an operator localizing any L-2(R-2) function. It is demonstrated that the latter operator, given an appropriate choice of localization region, approximately has the same radial eigenfunctions as the radial operator. Based on a given radial wavelet function a quaternionic wavelet is defined that can extract the local orientation of discontinuous signals as well as amplitude, orientation and phase structure of locally oscillatory signals. The full set of quaternionic wavelet functions are component by component orthogonal; their statistical properties are tractable, and forms for the variability of the estimators of the local phase and orientation are given, as well as the local energy of the image. By averaging estimators across wavelets, a substantial reduction in the variance is achieved
For the Jubilee of Vladimir Mikhailovich Chernov
On April 25, 2019, Vladimir Chernov celebrated his 70th birthday, Doctor of Physics and Mathematics, Chief Researcher at the Laboratory of Mathematical Methods of Image Processing of the Image Processing Systems Institute of the Russian Academy of Sciences (IPSI RAS), a branch of the Federal Science Research Center "Crystallography and Photonics RAS and part-Time Professor at the Department of Geoinformatics and Information Security of the Samara National Research University named after academician S.P. Korolev (Samara University). The article briefly describes the scientific and pedagogical achievements of the hero of the day. © Published under licence by IOP Publishing Ltd
Orthogonality within the Families of C-, S-, and E-Functions of Any Compact Semisimple Lie Group
The paper is about methods of discrete Fourier analysis in the context of
Weyl group symmetry. Three families of class functions are defined on the
maximal torus of each compact simply connected semisimple Lie group . Such
functions can always be restricted without loss of information to a fundamental
region of the affine Weyl group. The members of each family satisfy
basic orthogonality relations when integrated over (continuous
orthogonality). It is demonstrated that the functions also satisfy discrete
orthogonality relations when summed up over a finite grid in
(discrete orthogonality), arising as the set of points in
representing the conjugacy classes of elements of a finite Abelian subgroup of
the maximal torus . The characters of the centre of the Lie
group allow one to split functions on into a sum
, where is the order of , and where the component
functions decompose into the series of -, or -, or -functions
from one congruence class only.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Compact Simple Lie Groups and Their C-, S-, and E-Transforms
New continuous group transforms, together with their discretization over a
lattice of any density and admissible symmetry, are defined for a general
compact simple Lie groups of rank . Rank 1 transforms are
known. Rank 2 exposition of - and -transforms is in the literature. The
-transforms appear here for the first time.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
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