On symmetric extensions orthogonal transforms of images, and paraunitary filter banks

Periodic or symmetric extensions are commonly used for processing images and other finite-length signals with a paraunitary filter bank (PUFB). Unlike infinite-length signals, PUFBs applied to finite-length signals will not necessarily lead to an orthogonal system. The authors show that for symmetric extensions, orthogonality is only possible for special PUFBs based on linear-phase filters. They also discuss implementation issues.<<ETX>>

[1]  Ricardo L. de Queiroz,et al.  Time-varying lapped transforms and wavelet packets , 1993, IEEE Trans. Signal Process..

[2]  R. H. Bamberger,et al.  Generalizing symmetric extension: multiple nonuniform channels and multidimensional nonseparable IIR filter banks , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[3]  Henrique S. Malvar.  Extended lapped transforms: fast algorithms and applications , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[4]  Mark J. T. Smith,et al.  Analysis/synthesis techniques for subband image coding , 1990, IEEE Trans. Acoust. Speech Signal Process..

[5]  Stephen A. Martucci,et al.  Signal extension and noncausal filtering for subband coding of images , 1991, Other Conferences.

[6]  Truong Q. Nguyen,et al.  Generalised lapped orthogonal transforms , 1994 .

[7]  Hitoshi Kiya,et al.  Property of circular convolution for subband image coding , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[8]  Ricardo L. de Queiroz,et al.  On Orthogonal Transforms of Images Using Paraunitary Filter Banks , 1995, J. Vis. Commun. Image Represent..

[9]  Truong Q. Nguyen,et al.  Linear phase paraunitary filter banks: theory, factorizations and designs , 1993, IEEE Trans. Signal Process..

[10]  Kannan Ramchandran,et al.  Tilings of the time-frequency plane: construction of arbitrary orthogonal bases and fast tiling algorithms , 1993, IEEE Trans. Signal Process..

[11]  P. P. Vaidyanathan,et al.  Cosine-modulated FIR filter banks satisfying perfect reconstruction , 1992, IEEE Trans. Signal Process..

[12]  Martin Vetterli,et al.  Perfect reconstruction FIR filter banks: some properties and factorizations , 1989, IEEE Trans. Acoust. Speech Signal Process..

[13]  Veyis Nuri,et al.  A theory of size-limited filter banks , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.