基于曲波变换与拟合优度检验的遥感图像去噪方法

doi:10.13229/j.cnki.jdxbgxb.20211455

摘要/Abstract

摘要：

针对可见光遥感图像噪声去除问题，设计了一种基于曲波变换与拟合优度检验的遥感图像去噪方法。首先，对遥感图像进行曲波分解，得到曲波分解系数，并对曲波系数进行归一化；然后，利用拟合优度检验对归一化的曲波系数进行局部检验。经过局部检验后，得到真实信号系数，并对其进行逆归一化，得到逆归一化的曲波系数；最后，对曲波系数进行曲波逆变换，得到去噪后的遥感图像。将本文去噪算法与小波阈值去噪算法、曲波阈值去噪算法、小波变换与拟合优度检验去噪算法、曲波循环平移去噪算法进行实验对比。实验结果表明：在峰值信噪比和结构相似性的指标上，本文算法均优于以上几种算法。

关键词: 计算数学, 可见光遥感图像, 曲波变换, 拟合优度检验, 图像去噪

Abstract:

To solve the denoising problem from visible light remote sensing image， a denoising method for remote sensing image based on Curvelet transformation and Goodness of Fit test is proposed. The method first decomposes the remote sensing image by Curvelet theory to get the decomposition coefficients. Then the method normalizes Curvelet coefficients， and tests the normalized Curvelet coefficients locally by using the goodness of fit test. The real signal coefficients are obtained after the goodness of fit test， and the coefficients are inversely normalized to obtain the inversely normalized Curvelet coefficients. Finally， Curvelet coefficients are inversely transformed to obtain the denoised remote sensing image. The denoising algorithm is compared with Wavelet threshold denoising algorithm， Curvelet threshold denoising algorithm， Discrete wavelet transform and Goodness of Fit test denoising algorithm and Curvelet cyclic translation denoising algorithm. Experimental results show that this algorithm is better than the above algorithms in the indexes of peak signal-to-noise ratio and structural similarity.

Key words: computational mathematics, visible light remote sensing image, Curvelet transform, Goodness of Fit test, image denoising

中图分类号:

TP751

成丽波,李新月,李喆,贾小宁. 基于曲波变换与拟合优度检验的遥感图像去噪方法[J]. 吉林大学学报(工学版), 2023, 53(11): 3207-3213.

Li-bo CHENG,Xin-yue LI,Zhe LI,Xiao-ning JIA. Remote sensing image denoising method based on curvelet transform and goodness-of-fit test[J]. Journal of Jilin University(Engineering and Technology Edition), 2023, 53(11): 3207-3213.

图/表 7

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表1

遥感图像加噪后使用不同算法去噪的评价指标结果"

图像	算法	$σ = 10$		$σ = 15$		$σ = 20$		$σ = 25$
图像	算法	PSNR/dB	SSIM	PSNR/dB	SSIM	PSNR/dB	SSIM	PSNR/dB	SSIM
ImageA	小波阈值去噪	28.51	0.751	26.02	0.645	24.20	0.554	22.78	0.478
	曲波阈值去噪	29.08	0.806	26.72	0.755	25.24	0.717	24.35	0.688
	GOF-DWT去噪	28.99	0.816	27.02	0.773	25.66	0.739	24.56	0.685
	曲波循环平移去噪	29.80	0.827	27.70	0.781	26.37	0.748	25.48	0.722
	GOF-Curvelet去噪	31.12	0.835	28.73	0.785	27.15	0.733	25.95	0.685
ImageB	小波阈值去噪	28.27	0.750	25.94	0.651	24.21	0.564	22.84	0.491
	曲波阈值去噪	29.03	0.804	26.86	0.755	25.42	0.716	24.52	0.687
	GOF-DWT去噪	28.53	0.789	26.75	0.746	25.47	0.710	24.45	0.678
	曲波循环平移去噪	29.79	0.821	27.80	0.774	26.52	0.741	25.66	0.713
	GOF-Curvelet去噪	30.67	0.835	28.64	0.783	27.19	0.734	25.89	0.682
ImageC	小波阈值去噪	26.27	0.740	24.69	0.662	23.51	0.593	22.48	0.530
	曲波阈值去噪	27.31	0.774	25.43	0.693	24.32	0.631	23.61	0.583
	GOF-DWT去噪	26.86	0.744	25.42	0.672	24.30	0.607	23.61	0.562
	曲波循环平移去噪	27.98	0.803	26.04	0.718	24.90	0.652	24.10	0.601
	GOF-Curvelet去噪	28.49	0.806	26.90	0.750	25.64	0.695	24.70	0.648
ImageD	小波阈值去噪	26.72	0.773	24.54	0.679	22.99	0.597	21.75	0.524
	曲波阈值去噪	27.63	0.804	24.95	0.735	23.31	0.678	22.24	0.631
	GOF-DWT去噪	28.20	0.820	26.15	0.771	24.83	0.731	23.66	0.690
	曲波循环平移去噪	28.46	0.821	26.05	0.764	24.55	0.719	23.56	0.683
	GOF-Curvelet去噪	29.40	0.833	27.24	0.784	25.74	0.738	24.54	0.690

表1

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