A novel method of splitting the 3D discrete Hartley transform

@article{Grigoryan2003ANM,
  title={A novel method of splitting the 3D discrete Hartley transform},
  author={Artyom M. Grigoryan and Sos S. Agaian and Arthur R. Manukyan},
  journal={Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429)},
  year={2003},
  volume={1},
  pages={I-1009}
}
A method of the vectorial representation for splitting the calculation of the nonseparable three-dimensional discrete Hartley transform (3D DHT) into a set of one-dimensional (1D) DHTs is presented. The method is based on the vectorial, or tensor form of representation of a 3D image and can be applied to any orders of the transform. The case of the N/spl times/N&N-point DHT, for N=2/sup r/ (r>1), is considered in detail. The number of multiplications required for calculating the 3D DHT by the… 

Tables from this paper

References

SHOWING 1-10 OF 54 REFERENCES
Split manageable efficient algorithm for Fourier and Hadamard transforms
In this paper, a general, efficient, manageable split algorithm to compute one-dimensional (1-D) unitary transforms, by using the special partitioning in the frequency domain, is introduced. The
Radix-2 × 2 × 2 algorithm for the 3-D discrete Hartley transform
TLDR
The proposed algorithm is based on the principles of the divide-and-conquer approach applied directly in 3-D and has been found to offer significant savings in arithmetic operations compared with the row-column approach based on similar algorithms.
2-D and 1-D multipaired transforms: frequency-time type wavelets
TLDR
Considering paired transforms, this work analyzes simultaneously the splitting of the multidimensional Fourier transform as well as the presentation of the processed multiddimensional signal in the form of the short one-dimensional "signals", that determine such splitting.
Three algorithms for computing the 2-D discrete Hartley transform
  • A. Grigoryan, S. Agaian
  • Computer Science, Engineering
    Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101)
  • 2000
In this paper, three algorithms based on the method of vector and paired transforms for dividing the computation of the nonseparable two-dimensional discrete Hartley transform (2-D DHT) into the
Tensor form of image representation: enhancement by image-signals
TLDR
A quantitative measure of image enhancement that is related to the Weber's law of the human visual system is considered and the best parameters for image enhancement can be found for each image-signal to be processed separately.
Method of image enhancement by splitting-signals
  • Fatma Arslan, A. Grigoryan
  • Computer Science
    Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.
  • 2005
TLDR
It is proposed to enhance the image by processing only one or a few splitting-signals, to achieve image enhancement which, in many cases, can exceed enhancement by the /spl alpha/-rooting method.
Image enhancement by the tensor transform
  • A. Grigoryan, Fatma Arslan
  • Computer Science
    2004 2nd IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE Cat No. 04EX821)
  • 2004
TLDR
A new method of image enhancement based on the tensor transform of images with respect to the Fourier transform is described, which shows that the enhancement can be achieved by processing only one or a few signals.
On computing the discrete Hartley transform
TLDR
A complete set of fast algorithms for computing the discrete Hartley transform is developed, including decimation-in-frequency, radix-4, split radix, prime factor, and Winograd transform algorithms.
Split vector radix algorithm for two-dimensional Hartley transform
TLDR
A fast algorithm is presented which computes the two-dimensional Hartley transform using the decimation in frequency decomposition and, due to its in-place property, it does not require midmemory devices or matrix transposition.
New method of calculation of reversible integer 1D DCTs
TLDR
A new concept of the kernel integer discrete cosine transform is introduced, that allows the calculation of the eight-point IDCT of type II to the kernel IDCT with a fewer operations of multiplication and floor function.
...
...