New unitary transforms based on multiwavelets

Hsieh-Sheng Hou

doi:10.1117/12.449773

7 December 2001 New unitary transforms based on multiwavelets

Hsieh-Sheng Hou

Proceedings Volume 4472, Applications of Digital Image Processing XXIV; (2001) https://doi.org/10.1117/12.449773
Event: International Symposium on Optical Science and Technology, 2001, San Diego, CA, United States

Abstract

In this paper, we present a pair of new unitary transforms that were derived from the symmetric and antisymmetric orthonormal multiwavelet transform and the discrete cosine transform (DCT). This is motivated by the fact that the current international image compression standard, JPEG, is using DCT, whereas the proposed new standard, JPEG 2000, is using the 9/7 biorthogonal wavelet transforms as the default transform. Yet, recent research has reported that the Lapped transform which uses DCT as building blocks can obtain better performance than the 9/7 biorthogonal wavelet transform. ON the other hand, the relationship between the wavelet transform and DCT is not well known because of completely different paths of evolution. In this paper we explore the connection between the symmetric and antisymmetric orthonormal multiwavelet transform and the DCT. The known multiwavelet transforms today have been limited to the types consisting of only two scaling (dilation) functions and two wavelet functions. Based on the multiwavelet concept a pair of new block transforms, similar to the DCT, can be generated. Through extensive simulations we can show that both of the new unitary transforms perform better than the ordinary DCT. One of the new unitary transforms is preferred not only for its better performance but also fir its nice data-flow architecture. This new unitary transform also leads to a new MWT with four scaling functions and four wavelet functions.

Citation Download Citation

Hsieh-Sheng Hou "New unitary transforms based on multiwavelets", Proc. SPIE 4472, Applications of Digital Image Processing XXIV, (7 December 2001); https://doi.org/10.1117/12.449773

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KEYWORDS

Transform theory

Wavelet transforms

Wavelets

Image compression

Aerospace engineering

Image processing

Lithium

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