Design and Application of a New Multiscale Multidirectional Non-subsampled Filter Bank

We propose a new method for design of computationally efficient nonsubsampled multiscale multidirectional filter bank with perfect reconstruction (PR). This filter bank is composed of two nonsubsampled filter banks, for multiscale decomposition and for directional expansion. For multiscale decomposition, we transform the 1-D equivalent sub band filters directly into 2-D equivalent sub band filters. The computational cost is considerably reduced by avoiding the computation of 2-D convolutions. The multidirectional decomposition utilizes fan filters. A new method for design of 2-D zero phase FIR fan filter transformation function is developed. This method also aids the transformation of a 1D filter bank to a 2-D multidirectional filter bank. The potential application of the proposed filter bank is illustrated by comparing the image denoising performance of the proposed filter bank with other design method that exist in available literature.

[1]  Mark J. T. Smith,et al.  A filter bank for the directional decomposition of images: theory and design , 1992, IEEE Trans. Signal Process..

[2]  Minh N. Do,et al.  The finite ridgelet transform for image representation , 2003, IEEE Trans. Image Process..

[3]  G. Beylkin.  On the representation of operators in bases of compactly supported wavelets , 1992 .

[4]  Minh N. Do,et al.  The Nonsubsampled Contourlet Transform: Theory, Design, and Applications , 2006, IEEE Transactions on Image Processing.

[5]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[6]  Emmanuel J. Candès.  Monoscale Ridgelets for the Representation of Images with Edges , 1910 .

[7]  R. Saxena,et al.  Multirate Systems and Filterbanks , 2011 .

[8]  Edward H. Adelson,et al.  Shiftable multiscale transforms , 1992, IEEE Trans. Inf. Theory.

[9]  Mark J. Shensa,et al.  The discrete wavelet transform: wedding the a trous and Mallat algorithms , 1992, IEEE Trans. Signal Process..

[10]  Russell M. Mersereau,et al.  McClellan transformations for two-dimensional digital filtering. II - Implementation , 1976 .

[11]  Ronald R. Coifman,et al.  In Wavelets and Statistics , 1995 .

[12]  Minh N. Do,et al.  Ieee Transactions on Image Processing the Contourlet Transform: an Efficient Directional Multiresolution Image Representation , 2022 .

[13]  Minh N. Do,et al.  Pyramidal directional filter banks and curvelets , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[14]  David L. Donoho,et al.  Digital curvelet transform: strategy, implementation, and experiments , 2000, SPIE Defense + Commercial Sensing.

[15]  S. Pei,et al.  Design of 2D FIR digital filters by McClellan transformation and least squares eigencontour mapping , 1993 .

[16]  M. Do.  Directional multiresolution image representations , 2002 .

[17]  D. Donoho,et al.  Translation-Invariant De-Noising , 1995 .

[18]  Soontorn Oraintara,et al.  A Class of Multiresolution Directional Filter Banks , 2007, IEEE Transactions on Signal Processing.

[19]  V. Mertzios,et al.  Design of two-dimensional zero phase FIR fan filters via the McClellan transform , 1990 .

[20]  David L. Donoho,et al.  Curvelets, multiresolution representation, and scaling laws , 2000, SPIE Optics + Photonics.

[21]  Young-Seog Song,et al.  Formulas for McClellan transform parameters in designing 2-D zero-phase FIR fan filters , 1996, IEEE Signal Process. Lett..

[22]  R. M. Mersereau,et al.  McClellan transformations for two-dimensional digital filtering-Part I: Design , 1976 .

[23]  A.K. Krishnamurthy,et al.  Multidimensional digital signal processing , 1985, Proceedings of the IEEE.