Parameterization Construction of A Class of Biorthogonal Interpolating Wavelets and Their Application to Image Coding

Liu Zaide; Chang Jinyi; Shen Junyi

doi:10.11834/jig.20100403

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Parameterization Construction of A Class of Biorthogonal Interpolating Wavelets and Their Application to Image Coding
Vol. 15, Issue 4, Pages: 557(2010)
Published：2010
DOI： 10.11834/jig.20100403
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DOI：

Liu Zaide, Chang Jinyi, Shen Junyi. Parameterization Construction of A Class of Biorthogonal Interpolating Wavelets and Their Application to Image Coding[J]. Journal of Image and Graphics, 2010, 15(4): 557. DOI： 10.11834/jig.20100403.

摘要

研究采用了提升构造参数化的双正交小波类方法，构造了一类仅用一个自由参数表达的双正交插值小波，并推导出了其相关小波滤波器的参数表达式。自由参数为小波的优化设计提供了一个自由度，以编码增益为优化准则，构造出一种新的插值小波，其滤波器系数为二进制分数，可实现非乘法运算的离散小波变换（DWT）。实验结果表明，其图像压缩性能超过在小波变换编码领域中应用最为广泛的9/7小波（CDF-9/7），而且计算复杂度降低了17%以上，因此，在压缩性能和计算复杂度两者之间取得了一个较好的平衡。

Abstract

This paper depicts how to construct parametric biorthogonal wavelet family via lifting scheme

and gives the complete construction of a new class of parametric biorthogonal interpolating wavelets with one parameter. The exact parameter expressions of their associated interpolating filter banks are also derived. The free parameter provides a degree of freedom to optimize the resulting wavelets

and a previously unpublished interpolating wavelet is obtained with respect to the coding gain criteria

which has binary filter coefficients and can realize a multiplication free discrete wavelet transform（DWT）. Simulations show that the new wavelet has exhibited image compression performance superior to the most widely used 9/7 tap wavelet by Cohen et al. in the field of wavelet transform coding

yet its computational complexity has decreased by more than 17%. This indicates a better tradeoff between compression performance and computational complexity.