Ten lectures on wavelets
Orthogonal Transforms for Digital Signal Processing
Orthogonal Transforms for Digital Signal Processing
ICASSP '97 Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '97)-Volume 3 - Volume 3
Theory of wavelet transform over finite fields
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 03
Realization of paraunitary filter banks over fields of characteristic two
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 01
Cyclic LTI systems in digital signal processing
IEEE Transactions on Signal Processing
Paraunitary filter banks over finite fields
IEEE Transactions on Signal Processing
Embedded image coding using zerotrees of wavelet coefficients
IEEE Transactions on Signal Processing
Wavelet transforms associated with finite cyclic groups
IEEE Transactions on Information Theory
A binary wavelet decomposition of binary images
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Image coding using wavelet transform
IEEE Transactions on Image Processing
Context-based embedded image compression using binary wavelet transform
Image and Vision Computing
Directional Binary Wavelet Patterns for Biomedical Image Indexing and Retrieval
Journal of Medical Systems
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Wavelet decomposition has recently been generalized to binary field in which the arithmetic is performed wholly in GF(2). In order to maintain an invertible binary wavelet transform with multiresolution properties, three constraints are placed on the filters, namely the bandwidth, the perfect reconstruction and the vanishing moment constraints. While these constraints guarantee the existence of the inverse filters, their form is unconstrained and could be signal length dependent. In this paper, we propose to use the perpendicular constraint to relate the forward and inverse filters. With this constraint, it is shown that the form of the inverse filters remains unchanged after the up-sampling operation associated with the wavelet transform. We also explore an efficient implementation structure in the binary filters so as to save memory space and reduce the computational complexity. A detailed comparison with the lifting implementation in the real field wavelet transform is carried out. It is found that the computational complexity of the binary filter is significantly less than that of the real field wavelet kernel.