Continuous wavelet transform on reconfigurable meshes

Wavelet transforms have proven to be useful tools for several applications, including signal analysis, signal coding, and image compression. In this paper, faster parallel algorithms for computing the continuous wavelet transform are designed for reconfigurable meshes. An -time algorithm for computing the continuous wavelet transform with signals and an integer grid on a 3-D reconfigurable mesh is proposed, where is the number of bits used to represent the values in calculation. A constant-time algorithm 3-D reconfigurable mesh is also proposed. To the best knowledge of the author, this is the first constanttime algorithm for continuous wavelet transform on any parallel architecture.

[1]  Mounir Hamdi.  Parallel architectures for wavelet transforms , 1993, 1993 Computer Architectures for Machine Perception.

[2]  Quentin F. Stout,et al.  Reconfigurable SIMD massively parallel computers , 1991 .

[3]  Toshimitsu Masuzawa,et al.  A sub-logarithmic time sorting algorithm on a reconfigurable array , 1991 .

[4]  Michael Unser,et al.  Fast implementation of the continuous wavelet transform with integer scales , 1994, IEEE Trans. Signal Process..

[5]  Mohan Vishwanath,et al.  Time-frequency distributions: complexity, algorithms and architectures , 1993 .

[6]  Andreas Uhl,et al.  Computation of the Continuous Wavelet Transform on Massively Parallel SIMD Arrays , 1999, Parallel Process. Lett..

[7]  Viktor K. Prasanna,et al.  An O(1) Time Optimal Algorithm for Multiplying Matrices on Reconfigurable Mesh , 1993, Inf. Process. Lett..

[8]  T. Nishitani,et al.  VLSI architectures for discrete wavelet transforms , 1993, IEEE Trans. Very Large Scale Integr. Syst..

[9]  Chaitali Chakrabarti,et al.  Architectures for wavelet transforms: A survey , 1996, J. VLSI Signal Process..

[10]  Elias S. Manolakos,et al.  Distributed memory and control VLSI architectures for the 1-D Discrete Wavelet Transform , 1994, Proceedings of 1994 IEEE Workshop on VLSI Signal Processing.

[11]  Koji Nakano,et al.  A Bibliography of Published Papers on Dynamically Reconfigurable Architectures , 1995, Parallel Process. Lett..

[12]  Mats Holmström.  Parallelizing the Fast Wavelet Transform , 1995, Parallel Comput..

[13]  Koichi Wada,et al.  Integer Summing Algorithms on Reconfigurable Meshes , 1998, Theor. Comput. Sci..

[14]  Olivier Rioul,et al.  Fast algorithms for discrete and continuous wavelet transforms , 1992, IEEE Trans. Inf. Theory.