A novel method of filtration by the discrete heap transforms

Artyom M. Grigoryan; Mehdi Hajinoroozi

doi:10.1117/12.2039982

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25 February 2014 A novel method of filtration by the discrete heap transforms

Proceedings Volume 9019, Image Processing: Algorithms and Systems XII; 901903 (2014) https://doi.org/10.1117/12.2039982
Event: IS&T/SPIE Electronic Imaging, 2014, San Francisco, California, United States

Abstract

In this paper, we describe the method of filtering the frequency components of the signals and images, by using the discrete signal-induced heap transforms (DsiHT), which are composed by elementary rotations or Givens transformations. The transforms are fast, because of a simple form of decomposition of their matrices, and they can be applied for signals of any length. Fast algorithms of calculation of the direct and inverse heap transforms do not depend on the length of the processed signals. Due to construction of the heap transform, if the input signal contains an additive component which is similar to the generator, this component is eliminated in the transform of this signal, while preserving the remaining components of the signal. The energy of this component is preserved in the first point, only. In particular case, when such component is the wave of a given frequency, this wave is eliminated in the heap transform. Different examples of the filtration over signals and images by the DsiHT are described and compared with the known method of the Fourier transform.

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Artyom M. Grigoryan and Mehdi Hajinoroozi "A novel method of filtration by the discrete heap transforms", Proc. SPIE 9019, Image Processing: Algorithms and Systems XII, 901903 (25 February 2014); https://doi.org/10.1117/12.2039982

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