Optimally smooth symmetric quadrature mirror filters for image coding

Peter N. Heller; Jerome M. Shapiro; Raymond O. Wells Jr.

doi:10.1117/12.205379

6 April 1995 Optimally smooth symmetric quadrature mirror filters for image coding

Peter N. Heller, Jerome M. Shapiro, Raymond O. Wells Jr.

Proceedings Volume 2491, Wavelet Applications II; (1995) https://doi.org/10.1117/12.205379
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

Symmetric quadrature mirror filters (QMFs) offer several advantages for wavelet-based image coding. Symmetry and odd-length contribute to efficient boundary handling and preservation of edge detail. Symmetric QMFs can be obtained by mildly relaxing the filter bank orthogonality conditions. We describe a computational algorithm for these filter banks which is also symmetric in the sense that the analysis and synthesis operations have identical implementations, up to a delay. The essence of a wavelet transform is its multiresolution decomposition, obtained by iterating the lowpass filter. This allows one to introduce a new design criterion, smoothness (good behavior) of the lowpass filter under iteration. This design constraint can be expressed solely in terms of the lowpass filter tap values (via the eigenvalue decomposition of a certain finite-dimensional matrix). Our innovation is to design near- orthogonal QMFs with linear-phase symmetry which are optimized for smoothness under iteration, not for stopband rejection. The new class of optimally smooth QMF filter banks yields high performance in a practical image compression system.

Citation Download Citation

Peter N. Heller, Jerome M. Shapiro, and Raymond O. Wells Jr. "Optimally smooth symmetric quadrature mirror filters for image coding", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); https://doi.org/10.1117/12.205379

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