Design of Optimal Quincunx Filter Banks for Image Coding

Two new optimization-based methods are proposed for the design of high-performance quincunx filter banks for the application of image coding. These new techniques are used to build linear-phase finite-length-impulse-response (FIR) perfect-reconstruction (PR) systems with high coding gain, good frequency selectivity, and certain prescribed vanishing-moment properties. A parametrization of quincunx filter banks based on the lifting framework is employed to structurally impose the PR and linear-phase conditions. Then, the coding gain is maximized subject to a set of constraints on vanishing moments and frequency selectivity. Examples of filter banks designed using the newly proposed methods are presented and shown to be highly effective for image coding. In particular, our new optimal designs are shown to outperform three previously proposed quincunx filter banks in 72% to 95% of our experimental test cases. Moreover, in some limited cases, our optimal designs are even able to outperform the well-known (separable) 9/7 filter bank (from the JPEG-2000 standard).

[1]  Toshiyuki Yoshida,et al.  Multidimensional Two-channel Linear Phase FIR Filter Banks and Wavelet Bases with Vanishing Moments , 1998, Multidimens. Syst. Signal Process..

[2]  W. Sweldens.  The Lifting Scheme: A Custom - Design Construction of Biorthogonal Wavelets "Industrial Mathematics , 1996 .

[3]  T. Q. Nguyen,et al.  A novel and efficient design of multidimensional PR two-channel filter banks with hourglass-shaped passband support , 2004, IEEE Signal Processing Letters.

[4]  P. P. Vaidyanathan,et al.  Multidimensional multirate filters and filter banks derived from one-dimensional filters , 1993, IEEE Trans. Signal Process..

[5]  Thierry Blu,et al.  Isotropic polyharmonic B-splines: scaling functions and wavelets , 2005, IEEE Transactions on Image Processing.

[6]  Gunnar Karlsson,et al.  Theory of two-dimensional multirate filter banks , 1990, IEEE Trans. Acoust. Speech Signal Process..

[7]  Stephen P. Boyd,et al.  Applications of second-order cone programming , 1998 .

[8]  Yi Chen.  Design and application of quincunx filter banks , 2006 .

[9]  Jerome M. Shapiro,et al.  Adaptive McClellan transformations for quincunx filter banks , 1994, IEEE Trans. Signal Process..

[10]  Jan P. Allebach,et al.  The analysis and design of multidimensional FIR perfect reconstruction filter banks for arbitrary sampling lattices , 1991 .

[11]  Minh N. Do,et al.  Special paraunitary matrices, Cayley transform, and multidimensional orthogonal filter banks , 2006, IEEE Transactions on Image Processing.

[12]  Ton Kalker,et al.  A group theoretic approach to multidimensional filter banks: theory and applications , 1996, IEEE Trans. Signal Process..

[13]  Shing-Chow Chan,et al.  On the design and implementation of a class of multiplierless two-channel 1D and 2D nonseparable PR FIR filterbanks , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[14]  D H Tay,et al.  Flexible design of multidimensional perfect reconstruction FIR 2-band filters using transformations of variables , 1993, IEEE Trans. Image Process..

[15]  Dimitri Van De Ville,et al.  An orthogonal family of quincunx wavelets with continuously adjustable order , 2005, IEEE Transactions on Image Processing.

[16]  I. Daubechies,et al.  Factoring wavelet transforms into lifting steps , 1998 .

[17]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .

[18]  Jelena Kovacevic,et al.  Wavelet families of increasing order in arbitrary dimensions , 2000, IEEE Trans. Image Process..

[19]  P. P. Vaidyanathan,et al.  A new class of two-channel biorthogonal filter banks and wavelet bases , 1995, IEEE Trans. Signal Process..

[20]  Jelena Kovacevic,et al.  Perfect Reconstruction Filter Banks for Hdtv Representation and Coding* , 1989 .

[21]  Minh N. Do,et al.  Multidimensional orthogonal filter bank characterization and design using the Cayley transform , 2005, IEEE Transactions on Image Processing.

[22]  Truong T. Nguyen,et al.  Multiresolution direction filterbanks: theory, design, and applications , 2005, IEEE Transactions on Signal Processing.

[23]  Jiro Katto,et al.  Performance evaluation of subband coding and optimization of its filter coefficients , 1991, J. Vis. Commun. Image Represent..

[24]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[25]  Truong Q. Nguyen,et al.  Linear-phase perfect reconstruction filter bank: lattice structure, design, and application in image coding , 2000, IEEE Trans. Signal Process..

[26]  I. Daubechies,et al.  Wavelet Transforms That Map Integers to Integers , 1998 .

[27]  Jelena Kovacevic,et al.  Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for Rn , 1992, IEEE Trans. Inf. Theory.

[28]  Michel Barlaud,et al.  Quincunx lifting scheme for lossy image compression , 2000, Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101).