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3 Stolarek J.

3 2011

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On properties of a lattice structure for a wavelet filter bank implementation. Part II

Stolarek J.

Journal of Applied Computer Science

2011

Vol. 19, nr 2

125-139

This paper continues discussion of a lattice structure for parametrization and implementation of a Discrete Wavelet Transform. Based on an algorithm for converting the lattice structure to a wavelet filter bank coefficients, developed in the first part of this paper, second part of the proof demonstrating that filters implemented by the lattice structure fulfil conditions imposed on an orthogonal wavelet filter bank is carried out.

On properties of a lattice structure for a wavelet filter bank implementation. Part. 1

Stolarek J.

Journal of Applied Computer Science

2011

Vol. 19, nr 1

85-116

This paper presents concept of a lattice structure for parametrization and implementation of a Discrete Wavelet Transform. Theoretical properties of the lattice structure are discussed in detail. An algorithm for converting the lattice structure to a wavelet filter bank coeffcients is constructed. A theoretical proof demonstrating that filters implemented by the lattice structure fulfil conditions imposed on an orthogonal wavelet filter bank is conducted.

Adaptive synthesis of a wavelet transform using fast neural network

Stolarek J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2011

Vol. 59, nr 1

9-13

This paper introduces a new method for an adaptive synthesis of a wavelet transform using a fast neural network with a topology based on the lattice structure. The lattice structure and the orthogonal lattice structure are presented and their properties are discussed. A novel method for unsupervised training of the neural network is introduced. The proposed approach is tested by synthesizing new wavelets with an expected energy distribution between low- and high-pass filters. Energy compaction of the proposed method and Daubechies wavelets is compared. Tests are performed using sound and image signals.