小波系数扩散的多步图像去噪方法

More Steps De-noising Method of Wavelet Coefficients Diffusion

为了研究小波和偏微分方程在图像去噪方面的相关性,对小波阈值去噪过程进行了分析,得到了基于小波变换的偏微分方程关系式.利用小波变换的模代替梯度算子的模检测边缘,能较好地实现对图像特征的平滑.在此基础上进一步研究了该关系式的解法,提出了小波系数扩散的多步图像去噪方法.该方法通过对小波系数归一化,把得到的状态权通过各向异性扩散后作用在原小波系数上,采用多步方法实现了图像去噪,达到了既保护边缘又去除噪声的目的.数值实验结果表明:该方法使峰值信噪比平均提高约1.9dB,视觉效果也有较大提高.

For the sake of researching the relations between wavelet and PDE, the process is researched that image noise is removed by making use of discrete wavelet threshold transform. The expression form of PDE that based on wavelet transform is then obtained. The magnitude of wavelet transform is substituted for the module of the gradient operator, which realizes image smooth according to the characteristics of the image. The solution is researched for the expression form of PDE, a new more steps de-noising method of wavelet coefficients diffusion is proposed. The wavelet coefficients are normalized which can gain the corresponding state weights. The new state weights are obtained that the corresponding state weights are denoised by anisotropic diffusion. The new wavelet coeffi- cients are gained when the new state weights act on the original wavelet coefficients. The process of de-noising is achieved through the method of more steps for the solution of PDE in the end. It can achieve the purpose of keeping the detailed edges and resisting image noises at the same time. Experiments show there is an increase of about 1.9 dB on average in the peak signal to noise ratio and a re- markable improvement on the visual effects.