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《Acta Optica Sinica》 2008-11
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Analysis of Frequency Aliasing of Contourlet Transform Based on Laplace Pyramidal Transform

Feng Peng Wei Biao Pan Yingjun Mi DelingKey Laboratory of Opto-Electronics Technology & System,Ministry of Education,Chongqing University,Chongqing 400044,China  
A major drawback of the original contourlet transform is frequency aliasing,i.e.,its basis images are not localized in the frequency domain.We analyze the cause of this problem from the aspect of Laplace pyramidal(LP) transform to make sure that the aliasing is caused by the reason that the two lowpass filters of LP transform do not satisfy with Nyquist-Shannon sampling theorem and its stopband frequency is more than π/2.Based on this reason,we design a new low-pass filter with stopband frequency smaller than π/2 and propose an anti-aliasing contourlet transform.The anti-aliasing contourlet is superior to contourlet transform in the respects of the regularity and localization of basis function,and depresses the frequency aliasing efficiently.Numerical experiments on peppers image denoising show that the proposed anti-aliasing contourlet transform can significantly outperform the original transform both in terms of peak signal-noise-ratio(PSNR) by 2.3 dB with noise root-mean-square of 30 and in visual quality.It also depresses the scratch phenomenon after anti-aliasing contourlet transform denosing.
【Fund】: 国家自然科学基金(60172074);; 国防预研基金(JW2025056);; 重庆市自然科学基金(CSTC2007BB3174)资助项目
【CateGory Index】: TP391.41
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