Title :
Theory and factorization for a class of structurally regular biorthogonal filter banks
Author :
Chen, Ying-Jui ; Oraintara, Soontorn ; Amaratunga, Kevin S.
Author_Institution :
Intelligent Eng. Syst. Lab., Massachusetts Inst. of Technol., Cambridge, MA, USA
Abstract :
Regularity is a fundamental and desirable property of wavelets and perfect reconstruction filter banks (PRFBs). Among others, it dictates the smoothness of the wavelet basis and the rate of decay of the wavelet coefficients. This paper considers how regularity of a desired degree can be structurally imposed onto biorthogonal filter banks (BOFBs) so that they can be designed with exact regularity and fast convergence via unconstrained optimization. The considered design space is a useful class of M-channel causal finite-impulse response (FIR) BOFBs (having anticausal FIR inverses) that are characterized by the dyadic-based structure W(z)=I-UV†+z-1UV† for which U and V are M×γ parameter matrices satisfying V†U=Iγ, 1≤γ≤M, for any M≥2. Structural conditions for regularity are derived, where the Householder transform is found convenient. As a special case, a class of regular linear-phase BOFBs is considered by further imposing linear phase (LP) on the dyadic-based structure. In this way, an alternative and simplified parameterization of the biorthogonal linear-phase filter banks (GLBTs) is obtained, and the general theory of structural regularity is shown to simplify significantly. Regular BOFBs are designed according to the proposed theory and are evaluated using a transform-based image codec. They are found to provide better objective performance and improved perceptual quality of the decompressed images. Specifically, the blocking artifacts are reduced, and texture details are better preserved. For fingerprint images, the proposed biorthogonal transform codec outperforms the FBI scheme by 1-1.6 dB in PSNR.
Keywords :
FIR filters; channel bank filters; convergence; data compression; filtering theory; image coding; wavelet transforms; convergence; dyadic-based structure; finite-impulse response; householder transform; image coding; linear phase filter banks; regularity; structurally regular biorthogonal filter bank factorization; unconstrained optimization; wavelet transforms; Codecs; Convergence; Design optimization; Filter bank; Fingerprint recognition; Finite impulse response filter; Image matching; Image reconstruction; PSNR; Wavelet coefficients; Biorthogonal filter bank (BOFB); Householder reflection; dyadic-based structure; fingerprint; polyphase representation; structural regularity; vanishing moment;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2005.861071