NDLI: Reconstruction of Wideband Reflectivity Densities by Wavelet Transforms

Content Provider	Springer Nature Link
Author	Dahlke, Stephan Maass, Peter Teschke, Gerd
Copyright Year	2003
Abstract	This paper is concerned with reconstruction problems arising in the context of radar signal analysis. The goal in radar is to obtain information about objects by emitting certain signals and analyzing the reflected echoes. In this paper, we shall focus on the general wideband model for radar echoes and on the case of continuously distributed objects D (reflectivity density). In this case, the echo is given by an inverse wavelet transform of the density D where the role of the analyzing wavelet is played by the transmitted signal. However, the null space of an inverse wavelet transform is nontrivial, it is described by the corresponding reproducing kernel. Following the approach of Naparst [14] and Rebolla-Neira et al. [16], we suggest to treat this problem by transmitting not just one signal but a family of signals. Indeed, a reconstruction formula for one- and 2-dimensional reflectivity densities can be derived, provided that the set of outgoing signals forms an orthogonal basis or – more general – a frame. We also present some rigorous error estimates for these reconstruction formulas. The theoretical results are confirmed by some numerical examples.
Starting Page	189
Ending Page	209
Page Count	21
File Format	PDF
ISSN	10197168
Journal	Advances in Computational Mathematics
Volume Number	18
Issue Number	2-4
e-ISSN	15729044
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2003-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theory of Computation Numeric Computing Mathematics Algebra Calculus of Variations and Optimal Control Optimization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Discrete Wavelet Petrov–Galerkin Methods

Numerical stability of biorthogonal wavelet transforms

On the estimation of wavelet coefficients

Wavelet-based preconditioners for boundary integral equations

Localization of Dual Periodic Scaling and Wavelet Functions

Periodic wavelet frames

A note on fast Fourier transforms for nonequispaced grids

Parallel Dixon Matrices by Bracket

Adaptive Interpolation by Scaled Multiquadrics

Reconstruction of Wideband Reflectivity Densities by Wavelet Transforms

Similar Documents

Discrete Wavelet Petrov–Galerkin Methods

Numerical stability of biorthogonal wavelet transforms

On the estimation of wavelet coefficients

Wavelet-based preconditioners for boundary integral equations

Localization of Dual Periodic Scaling and Wavelet Functions

Periodic wavelet frames

A note on fast Fourier transforms for nonequispaced grids

Parallel Dixon Matrices by Bracket

Adaptive Interpolation by Scaled Multiquadrics

Reconstruction of Wideband Reflectivity Densities by Wavelet Transforms