摘要: A general method is proposed to factor a discrete W transform (DWT) into lifting steps and additions. Then, based on the relationships among various types of sinusoidal transforms, other transforms such as Fourier (DFT) cosine (DCT) are factored After approximating matrices, we get new integer IntDWT, IntDFT IntDCT which floating-point multiplication free. Transforms map also proposed. Fast algorithms given for their computational complexities analyzed. Based polynomial an index mapping, multi-dimensional presented with especially low complexity.
sci-hub.se 参考文章(12)
Henrique S. Malvar, Signal processing with lapped transforms ,(1992)
A.R. Calderbank, Ingrid Daubechies, Wim Sweldens, Boon-Lock Yeo, Wavelet Transforms That Map Integers to Integers Applied and Computational Harmonic Analysis. ,vol. 5, pp. 332- 369 ,(1998) , 10.1006/ACHA.1997.0238
S. Venkataraman, V.R. Kanchan, K.R. Rao, M. Mohanty, Discrete transforms via the Walsh-Hadamard transform Signal Processing. ,vol. 14, pp. 371- 382 ,(1988) , 10.1016/0165-1684(88)90095-3
WAI-KUEN CHAM, PERCY PUI-CHIU YIP, Integer sinusoidal transforms for image processing International Journal of Electronics. ,vol. 70, pp. 1015- 1030 ,(1991) , 10.1080/00207219108921345
Wim Sweldens, The Lifting Scheme: A Construction of Second Generation Wavelets SIAM Journal on Mathematical Analysis. ,vol. 29, pp. 511- 546 ,(1998) , 10.1137/S0036141095289051
Vladimir Britanak, K.R. Rao, The fast generalized discrete Fourier transforms: a unified approach to the discrete sinusoidal transforms computation Signal Processing. ,vol. 79, pp. 135- 150 ,(1999) , 10.1016/S0165-1684(99)00088-2
Yui-Lam Chan, Wan-Chi Siu, Variable temporal-length 3-D discrete cosine transform coding IEEE Transactions on Image Processing. ,vol. 6, pp. 758- 763 ,(1997) , 10.1109/83.568933
N. Memon, X. Wu, B.L. Yeo, Improved techniques for lossless image compression with reversible integer wavelet transforms international conference on image processing. pp. 891- 895 ,(1998) , 10.1109/ICIP.1998.727395
G.P. Abousleman, M.W. Marcellin, B.R. Hunt, Compression of hyperspectral imagery using the 3-D DCT and hybrid DPCM/DCT IEEE Transactions on Geoscience and Remote Sensing. ,vol. 33, pp. 26- 34 ,(1995) , 10.1109/36.368225
Yonghong Zeng, Xiaomei Li, Multidimensional polynomial transform algorithm for multidimensional discrete W transform IEEE Transactions on Signal Processing. ,vol. 47, pp. 2050- 2053 ,(1999) , 10.1109/78.771054