2D orthogonal symmetricwavelet filters using allpass filters

Abstract

This paper proposes a new class of 2D orthogonal symmetric wavelet filters using 2D nonseparable allpass filters. The proposed wavelet filters are based on the parallel structure of allpass filters with realvalued coefficients, which can be implemented with a low computational complexity and is robust to finite precision effects. The resulting wavelet bases are not only orthogonal, including perfect reconstruction (PR) condition, but also symmetric, whose analysis and synthesis filters have exactly linear phase response. It is also shown that the design problem of the proposed wavelet filters can be reduced to the phase approximation of the corresponding allpass filters. Therefore, it is easy to design this class of orthogonal symmetric wavelet filters by using the existing design methods of allpass filters. Finally, some examples are presented to demonstrate the effectiveness of the proposed orthogonal symmetric wavelet filters.

Wavelet Filter Banks Using Allpass Filters

“…There is no solution to all of orthogonality, symmetry and causal stablity. The wavlet filter banks using allpass filters have been extended to Hilbert transform pair of wavelets [25], 2D wavelet filter banks [26], and applied to lossy to lossless image coding [27][28][29][30] and scalable video compression [31]. It is possible also to extend them to higher dimension and irregural signal processing and to apply them to wavelet denoising, image fusion and so on.…”