Upper bounds of wavelet spectra on the class of discrete Lipschitzian signals

Arthur Ashot Petrosian

doi:10.1117/12.255232

23 October 1996 Upper bounds of wavelet spectra on the class of discrete Lipschitzian signals

Arthur Ashot Petrosian

Proceedings Volume 2825, Wavelet Applications in Signal and Image Processing IV; (1996) https://doi.org/10.1117/12.255232
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

Application of fast discrete orthogonal transforms with various basis functions for data compression and efficient signal coding occupies a special place in the evolution of spectral representations. This has become more apparent with the development of different wavelet and wavelet-packet transforms. Two basic compression procedures, known as zonal and threshold coding, are commonly being applied to the spectral vector. The optimal zonal coding method provides a minimum error of reconstruction for certain compression ratio. In order to determine optimal zonal coding method for the chosen transform one has to obtain the estimates of its spectra on a given class of signals. This task was considered on a general class of input vectors for classical discrete orthogonal transforms, including Fourier, Hartley, cosine, sine, as well as Walsh and Haar transforms. In this paper, we expand those results on various wavelet transforms by evaluating the upper bounds of their spectra. These estimates allow not only to a priori select the wavelet coefficient packets that have minimum input in signal reconstruction, but also to compute the maximum mean-square errors of reconstruction for a particular compression ratio and to analyze efficacy of different wavelets based on that criterion.

Citation Download Citation

Arthur Ashot Petrosian "Upper bounds of wavelet spectra on the class of discrete Lipschitzian signals", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); https://doi.org/10.1117/12.255232

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