Design of Wavelets and Filter Banks

In this book, the new approaches to design the critically sampled one-dimensional (1-D) two-channel bi-orthogonal finite impulse response (FIR) wavelet filter banks (FBs) are illustrated. These FBs are designed based on the lifting schemes. The following new FBs design techniques have been proposed : 1) Design of two-channel biorthogonal FBs using generalized and hybrid lifting structures, 2) Design of new class of triplet halfband filter banks (THFB) based on Euler-Frobenius polynomial, 3) New approach to design THFB based on balanced-uncertainty optimization. These new methods provide more degrees of freedom that result in flexible design of FBs. The proposed FBs give better wavelet properties measures as compared to existing FBs. Then, this work can be easily extended to the separable two-dimensional (2-D) FBs for the multi-channel chromosome image compression application. The popular SPIHT and JPEG-2000 image coding algorithms are incorporated to compress the chromosome image data-sets. This book provides the performance analysis and comparison of the chromosome image compression results using new wavelet FBs in terms of PSNR for different bit-rates.