Optimal Design of FIR Triplet Halfband Filter Bank and Application in Image Coding

• Published in: IEEE transactions on image processing Vol. 20; no. 2; pp. 586 - 591
• Main Authors: Kha, H H, Tuan, H D, Nguyen, T Q
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Design methodology; Detection, estimation, filtering, equalization, prediction; Errors; Exact sciences and technology; Filter bank; Filter banks; Finite impulse response filter; Frequency; Image coding; Image processing; Image reconstruction; Impulse response; Information, signal and communications theory; Least squares method; Least squares methods; Linear programming; Mathematical analysis; Nonlinear filters; Optimization; perfect reconstruction; Polynomials; Regularity; semi definite programming (SDP); Signal and communications theory; Signal processing; Signal, noise; Telecommunications and information theory; triplet halfband filter bank; Performance evaluation; Image processing; perfect reconstruction; Linear phase; Programming; regularity; Optimal design; semi-definite programming (SDP); Image coding; Digital filter; Frequency selection; Least squares method; Linear matrix inequality; Finite impulse response filter; Filter bank; triplet halfband filter bank
• ISSN: 1057-7149; 1941-0042; 1941-0042
• DOI: 10.1109/TIP.2010.2059450

This correspondence proposes an efficient semidefinite programming (SDP) method for the design of a class of linear phase finite impulse response triplet halfband filter banks whose filters have optimal frequency selectivity for a prescribed regularity order. The design problem is formulated as the minimization of the least square error subject to peak error constraints and regularity constraints. By using the linear matrix inequality characterization of the trigonometric semi-infinite constraints, it can then be exactly cast as a SDP problem with a small number of variables and, hence, can be solved efficiently. Several design examples of the triplet halfband filter bank are provided for illustration and comparison with previous works. Finally, the image coding performance of the filter bank is presented.