Discrete unitary transforms generated by moving waves

Artyom M. Grigoryan; Merughan M. Grigoryan

doi:10.1117/12.728383

20 September 2007 Discrete unitary transforms generated by moving waves

Artyom M. Grigoryan, Merughan M. Grigoryan

Proceedings Volume 6701, Wavelets XII; 670125 (2007) https://doi.org/10.1117/12.728383
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

Abstract

This paper describes a new class of discrete heap transforms which are unitary energy-preserving transforms and induced by input signals. These transforms have a simple form of composition and fast algorithms for any size of processed signals. We consider the heap transforms, defined by two-dimensional elementary rotations, as satisfying the given decision equations. The main feature of each heap transform is the corresponding system of basis functions, which represent themselves a family of interactive waves which are moving in the field generated by the input signal. Properties and examples of heap transforms, which we also call discrete signal-induced heap transforms, are described in detail.

Citation Download Citation

Artyom M. Grigoryan and Merughan M. Grigoryan "Discrete unitary transforms generated by moving waves", Proc. SPIE 6701, Wavelets XII, 670125 (20 September 2007); https://doi.org/10.1117/12.728383

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