Journal ArticleDOI
Multidimensional polynomial transform algorithm for multidimensional discrete W transform
Yonghong Zeng,Xiaomei Li +1 more
TLDR
A new polynomial transform algorithm for the MDDWT is obtained that needs no operations on complex data and the number of multiplications for computing an r-dimensional DWT is only 1 times that of the commonly used row-column method.Abstract:
The multidimensional (MD) polynomial transform is used to convert the MD W transform (MDDWT) into a series of one-dimensional (1-D) W transforms (DWTs). Thus, a new polynomial transform algorithm for the MDDWT is obtained. The algorithm needs no operations on complex data. The number of multiplications for computing an r-dimensional DWT is only 1 times that of the commonly used row-column method. The number of additions is also reduced considerably.read more
Citations
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Proceedings ArticleDOI
Integer sinusoidal transforms based on lifting factorization
Yijie Zeng,Guoan Bi,Zhiping Lin +2 more
TL;DR: A general method is proposed to factor a discrete W transform (DWT) into lifting steps and additions, and various types of new integer discrete transforms which are floating-point multiplication free are proposed.
Journal ArticleDOI
New algorithms for multidimensional discrete Hartley transform
TL;DR: New fast algorithms for multidimensional discrete Hartley transform (MD-DHT) are presented, based on the index mapping and multiddimensional polynomial transform (PT), which achieves considerable savings on the number of operations.
Journal ArticleDOI
Combined polynomial transform and radix-q algorithm for MD discrete W transform
TL;DR: A radix-q algorithm and a cyclic convolution algorithm are presented for the computation of the 1-D reduced DWT-IIs by using the multidimensional polynomial transform and an index permutation.
Journal ArticleDOI
Fast Computation of MD-DCT-IV/MD-DST-IV by MD-DWT or MD-DCT-II
TL;DR: Based on the relationships, MD-DCT-IV can be efficiently computed by using the fast algorithms for MD- DCT-II orMD-DWT-III or MD-W transform, and it is shown that the proposed fast algorithms save time.
Journal ArticleDOI
Fast algorithms for the 2-D discrete W transform
TL;DR: New fast algorithms are proposed for the two-dimensional type-II, -III and -IV discrete W transform that have a regular computational structure to achieve desirable properties such as regular data indexing and in-place computation, which effectively minimizes the overall computation and implementation costs.
References
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Journal ArticleDOI
The discreteW transform
Zhongde Wang,B. R. Hunt +1 more
TL;DR: The relationship among different versions of DWT and their relation with the discrete Fourier transform (DFT) are given and Convolution theorems represented by different version of the DWT are derived.
Journal ArticleDOI
Variable temporal-length 3-D discrete cosine transform coding
Yui-Lam Chan,Wan-Chi Siu +1 more
TL;DR: The idea is to let the motion activity in each block be very low, while the efficiency of the 3-D DCT coding could be increased, and experimental results show that this technique is indeed very efficient.
Proceedings ArticleDOI
Motion detection using 3D-FFT spectrum
TL;DR: A novel motion detection technique for multiple objects from image sequences is proposed, based on directional filtering in the spatiotemporal frequency domain, using the 3-D fast Fourier transform.
Journal ArticleDOI
A three-dimensional DFT algorithm using the fast Hartley transform
Hong Hao,Ronald N. Bracewell +1 more
TL;DR: A three-dimensional (3-D) Discrete Fourier Transform (DFT) algorithm for real data using the one-dimensional Fast Hartley Transform (FHT) is introduced that is simpler and retains the speed advantage that is characteristic of the Hartley approach.
Journal ArticleDOI
Implementation of parallel FFT algorithms on distributed memory machines with a minimum overhead of communication
TL;DR: Methods for the many mono-dimensional and multi-dimensional FFT algorithms which minimize the communication overhead are presented and implementations onto mesh and torus topologies are derived by using emulation results of hypercube communications on these topologies.