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- W1887691106 abstract "AbstractIn [4,5] an algorithm was proposed for isometric mapping between smooth n-variate m-dimensional vector fields and fractal curves and surfaces, by using orthonormal wavelet bases. This algorithm matched only the orthonormal bases of scaling functions (the “V-spaces” of multiresolution analyses). In the present communication we shall consider a new algorithm which matches the orthonormal bases of wavelets (the “W-spaces” of multiresolution analyses). Being of Cantor diagonal type, it was applicable for both bounded and unbounded domains, but the complexity of its implementation was rather high. In [3] we proposed a simpler algorithm for the case of boundary-corrected wavelet basis on a bounded hyper-rectangle. In combination with the algorithm for the “V-spaces” from [4,5], the new algorithm provides the opportunity to compute multidimensional orthogonal discrete wavelet transform (DWT) in two ways – via the “classical” way for computing multidimensional wavelet transforms, and by using a commutative diagram of mappings of the bases, resulting in an equivalent computation on graphics processing units (GPUs). The orthonormality of the wavelet bases ensures that the direct and inverse transformations of the bases are mutually adjoint (transposed in the case of real entries) orthogonal matrices, which eases the computations of matrix inverses in the algorithm. 1D and 2D orthogonal wavelet transforms have been first implemented for parallel computing on GPUs using C++ and OpenGL shading language around the year 2000; our new algorithm allows to extend general-purpose computing on GPUs (GPGPU) also to higher-dimensional wavelet transforms. If used in combination with the Cantor diagonal type algorithm of [4,5] (the “V-space” basis matching) this algorithm can in principle be applied for computing DWT of n-variate vector fields defined on the whole ℝn. However, if boundary-corrected wavelets are considered for vector-fields defined on a bounded hyper-rectangle in ℝn, then the present algorithm for GPU-based computation of n-variate orthogonal DWT can be enhanced with the new simple “V-space”-basis matching algorithm of [3]. It is this version that we consider in detail in the present study.KeywordsGraphic Processing UnitDiscrete Wavelet TransformCommutative DiagramMultiresolution AnalysisIsometric MappingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W1887691106 created "2016-06-24" @default.
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- W1887691106 date "2010-01-01" @default.
- W1887691106 modified "2023-09-27" @default.
- W1887691106 title "Computing n-Variate Orthogonal Discrete Wavelet Transforms on Graphics Processing Units" @default.
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- W1887691106 doi "https://doi.org/10.1007/978-3-642-12535-5_87" @default.
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