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Abstract: This paper studies multiscale difference equation models for 1-D and M-D signals. In this modeling technique, the signal of interest is viewed as a solution to a multiscale difference equation (MSDE). The model completely characterizes the signal as well as a number of its higher derivatives. It provides a recursive signal interpolation scheme as a function of scale. It also leads naturally to multigrid signal filtering, detection and estimation algorithms. An MSDE model must be uniquely... (Update)
Context of citations to this paper: More
...data using multiscale difference equation (MSDE) models and of reconstructing the original data from the MSDE modeling parameters. In [1], the general theory of MSDEs has been developed. Specifically, the conditions for existence of unique L 1 and L 2 solutions to MSDEs have...
...of a local one, and such a solution is usually sparse. Further, there exists fast methods for solving linear programming problems. Our method [2] relies on finding a description of the solution space of eqn. 10) Any solution of (10) may be written as a = a 1 Q z; 11)...
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BibTeX entry: (Update)
M. Ali and A. H. Tewfik, "Multiscale Difference Equation Signal Models: Part I Theory," Accepted for publication in IEEE Trans. on Signal Processing, Nov. 1994. http://citeseer.ist.psu.edu/ali94multiscale.html More
@misc{ ali94multiscale,
author = "M. Ali and A. Tewfik",
title = "Multiscale Difference Equation Signal Models: Part I Theory",
text = "M. Ali and A. H. Tewfik, Multiscale Difference Equation Signal Models:
Part I Theory, Accepted for publication in IEEE Trans. on Signal Processing,
Nov. 1994.",
year = "1994",
url = "citeseer.ist.psu.edu/ali94multiscale.html" }
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32 Nonseparable Multidimensional Perfect Reconstruction Filter .. (context) - Kovacevic, Vetterli - 1992
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24 Multidimensional Iterative Interpolation (context) - Deslauriers, Dubois et al. - 1991
18 The Analysis and Design of Multidimensional FIR Perfect Reco.. (context) - Viscito, Allebach - 1991
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3 Multiscale Difference Equation Signal Models: Part II Coding.. - Ali, Tewfik
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1 On Properties of the Solutions of Linear q- Difference Equat.. (context) - Mason - 1915
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Documents on the same site (http://www.ee.umn.edu/groups/msp/subject/msde.html):
Multiscale Difference Equation Signal Modeling And Analysis.. - Ali, Tewfik (1994) (Correct)
Coding and Decoding Techniques for Multiscale Difference.. - Ali, Tewfik (1995) (Correct)
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