Segmented computation of wavelet transform via lifting scheme

Segmented computation of wavelet transform via lifting scheme

Paper in proceedings (conference paper)

This paper presents a novel algorithm for segmented (segmentwise) computation of forward and inverse wavelet transform via a lifting scheme, applicable to any type of a lifting scheme representation of wavelets. The main idea is to process segments taken from a long one-dimensional signal so that after reconstruction, no border distortion between segments occurs.This is achieved by means of sophisticated segment overlapping. In this work, arbitrary and possibly varying segment lengths are considered. The derivation of formulas for overlap enumeration is the main concern of this work. The algorithm produces sets of coefficients for each segment. These sets from each segment ordered correctly are exactly the same coefficients the whole signal discrete wavelet transform results in. Similarly, the whole signal inverse discrete wavelet transform is equal to applying the algorithm to sets of coefficients and overlapping the results accordingly. The algorithm makes it possible to process signals in real-time, allows coarse parallelization since the computation on the particular segments is independent and also allows computation of wavelet transform on devices with a limited amount of memory.

This paper presents a novel algorithm for segmented (segmentwise) computation of forward and inverse wavelet transform via a lifting scheme, applicable to any type of a lifting scheme representation of wavelets. The main idea is to process segments taken from a long one-dimensional signal so that after reconstruction, no border distortion between segments occurs.This is achieved by means of sophisticated segment overlapping. In this work, arbitrary and possibly varying segment lengths are considered. The derivation of formulas for overlap enumeration is the main concern of this work. The algorithm produces sets of coefficients for each segment. These sets from each segment ordered correctly are exactly the same coefficients the whole signal discrete wavelet transform results in. Similarly, the whole signal inverse discrete wavelet transform is equal to applying the algorithm to sets of coefficients and overlapping the results accordingly. The algorithm makes it possible to process signals in real-time, allows coarse parallelization since the computation on the particular segments is independent and also allows computation of wavelet transform on devices with a limited amount of memory.

wavelet transform, lifting scheme, parallelization, segments, real-time

wavelet transform, lifting scheme, parallelization, segments, real-time

PRŮŠA, Z.; RAJMIC, P.

2012

18.08.2011

ASSZISZTENCIA Congress Bureau

Budapest

978-1-4577-1409-2

34rd International Conference on TELECOMMUNICATIONS AND SIGNAL PROCESSING

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