A new approach to design triplet halfband filter banks based on balanced-uncertainty optimization

This paper presents a novel approach to design a class of triplet halfband filter banks (THFB) based on optimized time–frequency localization. First, an Euler–Frobenius polynomial (EFP) is introduced to design a class of halfband polynomial. The vanishing moments and perfect reconstruction conditions are imposed on EFP to obtain maximally flat halfband filter. The resultant halfband filter is optimized using a balanced-uncertainty (BU) metric in order to have balance between time and frequency spread. Next, this optimized halfband filter is used in three-step lifting scheme to obtain analysis and synthesis wavelet filters which have balance between time and frequency localization. The proposed method provides three degrees of freedom that results in flexible design of filter bank. It is observed that the proposed filter bank gives more regularity and better frequency selectivity as compared to existing filter banks. These designed filters are then used for human chromosome image compression application. The performance of the designed filter bank is compared in terms of PSNR using different bit-rates with well-known existing filter banks in order to validate the experimental results.