A development of symmetric extension method for subband image coding

Kiya, Hitoshi; Nishikawa, Kiyoshi; Iwahashi, Masahiro

doi:10.1109/83.265982

Cited by 58 publications

(23 citation statements)

References 11 publications

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“…The second approach is symmetric extension of the data. Symmetric extension preserves signal continuity, but can be implemented only with linear-phase (symmetric and/or antisymmetric) filter banks [34,3,23,4]. We now develop symmetric extension for linear-phase multiwavelet filters, such as the Geronimo-Hardin-Massopust and Chui-Lian multifilters.…”

Section: Symmetric Extension Of Finite-length Signalsmentioning

confidence: 99%

The application of multiwavelet filterbanks to image processing

Strela

Heller

Strang

et al. 1999

IEEE Trans. on Image Process.

376

213

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Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filter banks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and short support, which is not possible with scalar 2-channel wavelet systems. After reviewing this recently developed theory, we examine the use of multiwavelets in a filter bank setting for discrete-time signal and image processing. Multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filter bank. We describe two methods (repeated row and approximation/deapproximation) for obtaining such a vector input stream from a one-dimensional signal. Algorithms for symmetric extension of signals at boundaries are then developed, and naturally integrated with approximation-based preprocessing. We describe an additional algorithm for multiwavelet processing of two-dimensional signals, two rows at a time, and develop a new family of multiwavelets (the constrained pairs) that is well-suited to this approach. This suite of novel techniques is then applied to two basic signal processing problems, denoising via wavelet-shrinkage, and data compression. After developing the approach via model problems in one dimension, we applied multiwavelet processing to images, frequently obtaining performance superior to the comparable scalar wavelet transform.

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Section: Symmetric Extension Of Finite-length Signalsmentioning

confidence: 99%

The application of multiwavelet filterbanks to image processing

Strela

Heller

Strang

et al. 1999

IEEE Trans. on Image Process.

376

213

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show abstract

“…The topic of M-channel SET's has subsequently been treated in more detail in [21,3,49,4,8,13,14,47,36]. Bamberger et al [3,49,4] also considered M-channel nonuniformly downsampled filter banks.…”

Section: Historical Developmentmentioning

confidence: 98%

Classification of Nonexpansive Symmetric Extension Transforms for Multirate Filter Banks

Brislawn

1996

Applied and Computational Harmonic Analysis

109

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“…In order to prevent the increase of the prediction error at the end of an image, the symmetric extended convolution is used in the filtering process [9]. The filter coefficients in the proposed method are determined by the NelderMead simplex method [18] with the subband mean entropy [Eq.…”

Section: Effect On the Imagementioning

confidence: 99%