Adaptive Orthogonal Matrix-Valued Wavelets and Compression of Vector-Valued Signals

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Title: Adaptive Orthogonal Matrix-Valued Wavelets and Compression of Vector-Valued Signals
Authors: Ginzberg, P
Walden, AT
Item Type: Conference Paper
Abstract: Wavelet transforms using matrix-valued wavelets (MVWs) can process the components of vector-valued signals jointly, and thus offer potential advantages over scalar wavelets. For every matrix-valued scaling filter, there are infinitely many matrix-valued wavelet filters corresponding to rotated bases. We show how the arbitrary orthogonal factor in the choice of wavelet filter can be selected adaptively with a modified SIMPLIMAX algorithm. The 3×3 orthogonal matrix-valued scaling filters of length 6 with 3 vanishing moments have one intrinsic free scalar parameter in addition to three scalar rotation parameters. Tests suggest that even when optimising over these parameters, no significant improvement is obtained when compared to the naive scalar-based filter. We have found however in an image compression test that, for the naive scaling filter, adaptive basis rotation can decrease the RMSE by over 20%.
Issue Date: 31-Dec-2012
URI: http://hdl.handle.net/10044/1/12538
Journal / Book Title: Proceedings of the 9th IMA International Conference on Mathematics in Signal Processing
Copyright Statement: © 2012 The Authors
Conference Name: 9th IMA International Conference on Mathematics in Signal Processing
Notes: https://www.dropbox.com/s/j45zqv5896dlgqu/waveletrotation2.pdf file: Ginzberg Walden paper.pdf:C:\Users\pg05\AppData\Roaming\Mozilla\Firefox\Profiles\8qwsb261.default\zotero\storage\7R4TQKDC\Ginzberg Walden paper.pdf:application/pdf
Place of Publication: Birmingham, UK
Start Date: 2012-12-17
Finish Date: 2012-12-20
Conference Place: Birmingham, UK
Appears in Collections:Mathematics
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