Evolving Wavelets Using a Coevolutionary Genetic Algorithm and Lifting

Finding a good wavelet for a particular application and type of input data is a difficult problem. Traditional methods of wavelet design focus on abstract properties of the wavelet that can be optimized analytically but whose influence on its real-world performance are not entirely understood. In this paper, a coevolutionary genetic algorithm is developed that searches the space of biorthogonal wavelets. The lifting technique, which defines a wavelet as a sequence of digital filters, provides a compact representation and an efficient way of handling necessary constraints. The algorithm is applied to a signal compression task with good results.

[1]  Risto Miikkulainen,et al.  Solving Non-Markovian Control Tasks with Neuro-Evolution , 1999, IJCAI.

[2]  Aria Nosratinia,et al.  Wavelet-Based Image Coding: An Overview , 1999 .

[3]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[4]  Ronald R. Coifman,et al.  Entropy-based algorithms for best basis selection , 1992, IEEE Trans. Inf. Theory.

[5]  Roberto Rossi,et al.  Digital filter design through simulated evolution , 2001 .

[6]  Majid Ahmadi,et al.  Design of 1-D FIR filters with genetic algorithms , 1999, ISSPA '99. Proceedings of the Fifth International Symposium on Signal Processing and its Applications (IEEE Cat. No.99EX359).

[7]  Benjamin Belzer,et al.  Wavelet filter evaluation for image compression , 1995, IEEE Trans. Image Process..

[8]  Wim Sweldens,et al.  The lifting scheme: a construction of second generation wavelets , 1998 .

[9]  Wim Sweldens,et al.  An Overview of Wavelet Based Multiresolution Analyses , 1994, SIAM Rev..

[10]  Barry G. Sherlock,et al.  Space-frequency balance in biorthogonal wavelets , 1997, Proceedings of International Conference on Image Processing.

[11]  I. Daubechies,et al.  Factoring wavelet transforms into lifting steps , 1998 .

[12]  W. Sweldens.  The Lifting Scheme: A Custom - Design Construction of Biorthogonal Wavelets "Industrial Mathematics , 1996 .

[13]  Steven Gregory O'keefe,et al.  An Investigation of Wavelet Design using Genetic Algorithms , 2001 .

[14]  Michel Barlaud,et al.  Image coding using wavelet transform , 1992, IEEE Trans. Image Process..

[15]  M. Victor Wickerhauser,et al.  Adapted wavelet analysis from theory to software , 1994 .

[16]  Chengjun Liu,et al.  Face Recognition Using Evolutionary Pursuit , 1998, ECCV.

[17]  Marc M. Lankhorst,et al.  Wavelet-Based Signal Approximation with Genetic Algorithms , 2003, Evolutionary Programming.

[18]  Robert D. Nowak,et al.  Adaptive wavelet transforms via lifting , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).