Matching wavelet packets to Gaussian random processes
| Autor: | Jose M. F. Moura, Nirmal Keshava |
|---|---|
| Rok vydání: | 1999 |
| Předmět: |
Mathematical optimization
MathematicsofComputing_NUMERICALANALYSIS Wavelet transform Unitary matrix Wavelet packet decomposition symbols.namesake Wavelet Signal Processing Diagonal matrix symbols Bhattacharyya distance Electrical and Electronic Engineering Gaussian process Algorithm Eigenvalues and eigenvectors Mathematics |
| Zdroj: | IEEE Transactions on Signal Processing. 47:1604-1614 |
| ISSN: | 1053-587X |
| DOI: | 10.1109/78.765130 |
| Popis: | We consider the problem of approximating a set of arbitrary, discrete-time, Gaussian random processes by a single, representative wavelet-based, Gaussian process. We measure the similarity between the original processes and the wavelet-based process with the Bhattacharyya (1943) coefficient. By manipulating the Bhattacharyya coefficient, we reduce the task of defining the representative process to finding an optimal unitary matrix of wavelet-based eigenvectors, an associated diagonal matrix of eigenvalues, and a mean vector. The matching algorithm we derive maximizes the nonadditive Bhattacharyya coefficient in three steps: a migration algorithm that determines the best basis by searching through a wavelet packet tree for the optimal unitary matrix of wavelet-based eigenvectors; and two separate fixed-point algorithms that derive an appropriate set of eigenvalues and a mean vector. We illustrate the method with two different classes of processes: first-order Markov and bandlimited. The technique is also applied to the problem of robust terrain classification in polarimetric SAR images. |
| Databáze: | OpenAIRE |
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