Optimal triplet halfband filter banks with k-regularity and image coding application

The triplet halfband filter bank structure is well known to be efficient for the design and implementation of a class of biorthogonal wavelet filter banks. Previously, two extreme cases in filter characteristics including equiripple filters with no regularity and maximally flat filters with poor frequency selectivity have mainly been treated. This paper proposes an efficient semi-definite programming (SDP) method for the design of linear phase finite impulse response (FIR) triplet halfband filter banks whose filters have optimal frequency selectivity for a prescribed regularity order. By using the linear matrix inequality (LMI) characterization of the trigonometric semi-infinite constraints, the design problem can be exactly cast as an SDP problem with a small number of variables and, hence, can be solved efficiently. A design example of the triplet halfband filter bank with different regularity orders is provided to validate the proposed method. Finally, the image coding performance of the filter bank is presented.