Data Adaptive Linear Decomposition Transform

• Published in: Digital signal processing 2002-10, Vol.12 (4), p.494-523
• Main Authors: Cadzow, James A., Yammen, Suchart
• Format: Article
• Language: English
• Subjects: adaptive filter; compression; linear decomposition; noise reduction
• ISSN: 1051-2004; 1095-4333
• DOI: 10.1006/dspr.2001.0408

Cadzow, J. A., and Yammen, S., Data Adaptive Linear Decomposition Transform, Digital Signal Processing 12 (2002) 494–523 In this paper a novel method for decomposing one-dimensional data sequences is developed. It is of the wavelet variety with important distinctions. A standard wavelet transform entails down-sampling the responses of two fixed structured filters to the sequence being decomposed to produce the half length detail sequence and a coarse sequence. The new transform entails processing down-sampled data by an optimum interpolation filter which seeks to approximate the odd indexed sequence elements by a linear combination of neighboring even indexed elements. The resulting interpolation error sequence of half length plays the role of the wavelet detail sequence. Unlike a traditional wavelet transform, the interpolation filter employed is adapted to the data being analyzed. This data dependency typically produces improved performance relative to traditional wavelet transforms. This enhanced performance is demonstrated on a number of standard test signals. Furthermore, this new transform is computationally efficient due to the inherent parallel structure of the data decomposition method.