Wavelet Based Compression of multichannel human chromosome Images

Abstract

The wavelets and filter banks (FBs) are widely used in signal and image processing newlineapplications such as data compression, de-noising, pattern recognition, water marking, newlineetc. Conventional filter bank design consists orthogonal and biorthogonal FBs. The dif- newlineferent design techniques are exist for these two types of FBs. Although, both these types newlinehave their respective advantages, the biorthogonal FBs are preferred in image process- newlineing applications because of its linear phase characteristics. Biorthogonal wavelets can newlinehave symmetry and are associated with perfect reconstruction (PR) filter banks. The newlinecritically sampled biorthogonal FBs are designed with some desirable properties such newlineas frequency selectivity, regularity, symmetry, near-orthogonality etc. The design of FBs newlinewith these properties is a challenging task and hence received an attention over many newlineyears. newlineThe class of biorthogonal wavelets were developed by Cohen et al., Vetterli, Her- newlineley and Daubechies. Most of the biorthogonal FBs are designed by the factorization newlineof a halfband polynomial (HBP) which has maximum number of zeros at z = and#8722;1 e.g. newlineCohen-Daubechies-Feauveau (CDF-9/7) and spline family of wavelet FBs are designed newlineby the factorization of Lagrange halfband polynomial (LHBP). The CDF-9/7 filter bank newlinehas been used in the JPEG-2000 image coding standard. The LHBP has maximum newlinenumber of zeros at z = 1 to achieve the maximum regularity. However, LHBP filters newlinedo not have any degree of freedom and no direct control over frequency response of newlinethe filters. In order to have some independent parameters which can be optimized to newlineobtain some control over frequency response of the filter, Patil et al. used general half- newlineband polynomial (GHBP) factorization (not LHBP) to design two-channel biorthogonal newlinewavelet FIR FBs. However, this method of factorization is more tedious for higher order newlinepolynomials. newlineA new construction of wavelets, called the lifting scheme, has been developed by newlineDaubechies and Sweldens. Lifting structure is one of the alternative sch