Algorithms and Programming Paradigms for 2-D Wavelet Packet Decomposition on Multicomputers and Multiprocessors

Wavelet Packet Image Decomposition on MIMD Architectures

“…In preliminary experiments, we found the redundant data calculation approach to be not competitive at all which is true for a wide range of different architectures [34], so we carried on our developments using the dataswapping method. However, all the following algorithms are easily adapted to the second border treatment method if the target architecture should require it.…”

“…Therefore, algorithms tailored to both types of applications exist and we distinguish between algorithms generating the entire WP subband structure (WP-E) and algorithms generating the lowest level subbands (WP-L). For the first type, we base our developments on algorithms described in [30,34,42] and focus on the generalization of these algorithms with regard to the number of processor elements (PEs) used. Due to the subband structure inherent in 2-D WP decomposition (leading to 4 j frequency subbands at decomposition level j) former subband-based algorithms are restricted to a number of PEs equal to a power of 4.…”

Parallel adaptive wavelet analysis

“…But at a certain decomposition depth, subbands get too small to be processed efficiently in parallel since single subbands are spread across all PE. This stage is of course dependent on the number of PE employed and is denoted "redistribution level" [8,22]. At this stage, data has to be redistributed so that entire subbands are located on single PE which enables to perform the remaining computations without any additional communication.…”

“…approaches for performing the best basis algorithm and the irregular decomposition into such a basis on parallel MIMD [8,10,21,22] and SIMD [2,7] architectures, application of parallel wavelet packet decomposition in numerics [6,16]). …”

Real-Time Image Analysis Using MIMD Parallel à trous Wavelet Algorithms

“…There have been papers devoted to parallel *Corresponding author: Research Institute for Softwaretechnology Hellbrunnerstr.34 A-5020 Salzburg Austria. phone: ++43/662/8044/6303 fax: ++43/662/8044/138 E-mail: uhl@cosy.sbg.ac.at Gabor transform [10,11], continuous wavelet transform [12][13][14], wavelet packet decomposition [15][16][17][18][19][20][21] and of course to the fast wavelet transform [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. However, no (systematic) research has been conducted with respect to parallel algorithms for the a`trous decomposition (apart from the paper already mentioned above, [4], in which although experimental results for a SIMD algorithm are given the aspects concerning parallelism are not discussed at all).…”