Properties of the Discrete Pulse Transform for Multi-Dimensional Arrays
Roumen Anguelov, Inger Fabris-Rotelli
TL;DR
This paper explores the properties of the Discrete Pulse Transform applied to multi-dimensional arrays, providing detailed proofs of key lemmas to deepen understanding of its mathematical foundations.
Contribution
It offers a comprehensive analysis of the Discrete Pulse Transform's properties and includes detailed proofs of important lemmas previously omitted due to complexity.
Findings
Properties of the Discrete Pulse Transform are formally established.
Key lemmas are proved with detailed technical arguments.
The results support further applications in image processing and multi-dimensional data analysis.
Abstract
This report presents properties of the Discrete Pulse Transform on multi-dimensional arrays introduced by the authors two or so years ago. The main result given here in Lemma 2.1 is also formulated in a paper to appear in IEEE Transactions on Image Processing. However, the proof, being too technical, was omitted there and hence it appears in full in this publication.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Advanced Scientific Research Methods · Advanced Control and Stabilization in Aerospace Systems