Keywords
Wavelet adaptada
Transformada shapelet discreta
Transformada wavelet discreta
Wavelet filter design
Matched wavelet
Discrete shapelet transform
Discrete wavelet transform
How to Cite
Abstract
The use of adapted wavelets for pattern recognition is very attractive because of the multiscalarity of the wavelet transform. However, the good performance of these algorithms in pattern detection strongly depends on the construction of the filters adapted to the pattern of interest. The Discrete Shapelet Transform II [9] (DST-II) is an algorithm inspired by the wavelet transform, which allows the design of tailored filters for pattern detection in one-dimensional signals. The construction of these filters requires the solution of a system of nonlinear equations, which according to [9] can be performed by any iterative method. This research presents a novel and comprehensive numerical study that demonstrates the impact of the choice of the appropriate numerical method for the solution of the nonlinear system in DST-II. The efficiency of the estimated filters has an impact on the performance of this transform in pattern detection. The best results are obtained by combining Newton’s method with preiteration using the continuation algorithm. The convergence achieved for 55,37% of the patterns suggests that DST-II could be suitable for patterns with specific shapes, useful in biomedical signal applications.
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Copyright (c) 2024 Damian Valdés-Santiago, Ángela M. León-Mecías, Marta L. Baguer Díaz-Romañach, Manuel González-Hidalgo, Antoni Jaume-I-Capó