基於半頻濾波器之內差型DPCM金字塔之研究和應用

Abstract

在本論文中, 吾人提出一種稱為內差型DPCM金字塔之多解析訊號表示 法,並探討其在影像壓縮及曲面重建問題上的應用。此種內差型DPCM金字 塔和傳統型金字塔之不同處在於低解析訊號的取得並未經過低通濾波器, 同時利用半頻濾波器去內差低解析訊號以求得高解析估測訊號。此種設計 可幫助建構一整數與整數間之轉換。此種表示法可等效於一濾波器組, 亦 可等效於一內差型小波轉換。在本論文中將對其間之關聯性加以深入探討 。本論文中亦將探討半頻濾波器的正則性與多項式間之關係並考慮非最平 濾波器在適應性內差中的應用。同時適應型內差DPCM金字塔在影像壓縮中 的應 In this thesis, a multiresolution representation called interpolative DPCMpyramid is proposed and its applications on image compression and fast surfaceinterpolation are also investigated.Interpolative DPCM pyramid is similar to the Laplacian pyramid except the wayof generating the low resolution signal.Instead of filtering the signal before downsampling, the low resolution signalis obtained by direct downsampling the high resolution signal withoutprefilters. The high resolution signal is estimated by interpolating the low resolution signal with the halfband filters. With this approach,an integer to integer multiresolution transform can be constructed.This pyramid can be treated as a biorthogonal perfect reconstructionfilter bank.It can also be treated as the discrete-time interpolative wavelet transform.Based on the framework of critically sampled pyramid, the relations betweeninterpolative DPCM pyramid, interpolative filter bank and interpolative wavelettransform are clarified in this thesis.The role of halfband filters in the construction of wavelet bases is discussed.Based on the time-domain Strang-Fix condition, the relation between theregularity and the polynomial interpolation is made more clear.The non-maximally flat filters are shown to provide much flexibility than themaximally flat filters in the scheme of adaptive interpolation. With thisadaptive interpolation algorithm,the adaptive interpolative DPCM pyramid is described andits applications on the lossless image compression are also investigated.Experimental results show that the adaptive interpolative DPCM pyramid arecomparable to the state-of-art lossless image compression methods.Based on the multiresolution scheme of interpolative wavelet transform, the fastcomputation algorithm is developed for the surface interpolation.In the developed fast algorithm, the interpolative wavelet transform isfirst appliedto construct the multiresolution representation of the interpolation problem, then, the multigrid algorithm is followed by the wavelet transform to solvethis problem.The wavelet transform can be treated as a precondition of the problem and theresultant signal to be solved will have an octave-band decomposition structure. This structure possesses the representation form needed for multigridcomputation and naturally inducesthe combined multiresolution/multigrid computationstructure.This combined structure is proposed in this thesis.Experimental results show that the proposed computation structure yieldssignificant improvement in the computation speed.