考虑尺度相关性及几何约束的小波扩散平滑滤波

Wavelet diffusion filter considering scale correlation and geometry constraint

在系统分析各向异性扩散与小波平滑去噪的特点与不足的基础上,研究提取重要小波系数的8邻域几何约束方法;考虑到小波系数间存在一定的局部相关性,提出利用窗口内信号的方差与噪声方差的比值估计扩散系数函数;为了加快扩散速度并提高平滑效果,提出一个考虑小波尺度间相关性及几何约束的扩散平滑模型。研究结果表明:与P&M函数相比,利用扩散系数函数扩散图像具有更高的峰值信噪比(PSNR),且受扩散时间尺度的影响较小;对受噪声污染的指纹图像(σ=25),利用所提出的方法扩散平衡时信噪比为28.809dB,当扩散时间尺度为50时,信噪比为28.724dB,而利用P&M函数的信噪比分别为27.127dB和25.623dB;新扩散模型性能比其他方法的性能优。对于Lena图像,当σ=25时,维纳滤波法小波滤波方法、BayesShrink法、LAWMAP法及本文方法处理后的信噪比分别为24.866,26.613,26.854,27.245和27.831dB。

Based on the systemic analysis of character and shortcoming of anisotropic diffusion and wavelet de-noise, 8 neighborhoods geometry constraint method as extracting significant wavelet coefficient was analyzed. Considering scale correlation between wavelet coefficient, the estimation method of diffusion coefficient function was proposed by the ratio of signal variance to noise variance in local window. For improving diffusion velocity and diffusion effect, a new diffusion filter model considering scale correlation and geometry constraint was proposed. The results show that the proposed diffusion coefficient function takes on higher peak signal to noise ratio （PSNR） and lower influence by diffusion time scale compared with P＆M function, for example, as noise variance σ-=25, the PSNR of diffusion balance of the finger image is 28.809 dB and 28.724 dB after 50 iterations by proposed method, 27.127 dB and 25.623 dB by P＆M function respectively. The proposed model preserves image feature better and not sensitive to diffusion time scale compared with other method, PSNR of the Lena image contaminated by noise σ=25 are 24.866, 26.613, 26.854, 27.245 and 27.831 dB by Wiener, wavelet, BayesShrink, LAWMAP and proposed filter method respectively.