结合非下采样剪切波变换的BM3D去除图像噪声方法研究

BM3D Method Combined with Non-subsampled Shearlet Transform for Removing Image Noise

强噪声图像去噪一直是图像处理技术应用领域研究的热点,为进一步提高强噪声图像的去噪质量和对图像边缘的保护,针对三维块匹配(Block Matching 3D,BM3D)方法对强噪声图像去噪效果不佳及图像线状奇异性(如边缘)缺乏最优表示的问题,提出了基于二维非下采样剪切波变换(Non-subsampled Shearlet Transform,NSST)和BM3D的组合去噪方法。该方法首先对含噪图像进行NSST正变换,得到不同尺度和不同方向高频子带的剪切波系数;然后对每个尺度不同方向的高频子带求取贝叶斯阈值,并利用渐进半软阈值函数对各高频子带进行去噪;最后对低频子带和各去噪高频子带进行NSST逆变换,得到去噪结果。将去噪图像作为BM3D中基础估计阶段的预滤波,能够进一步提高基础估计阶段分组的正确性,为BM3D去噪奠定良好基础。组合去噪方法结合了NSST与BM3D的各自优势,仿真试验结果表明,对于低噪声图像,本方法和BM3D方法去噪效果相同,略优于非局部平均法;对于强噪声卫星影像,本方法去噪效果优于BM3D和非局部平均法。

Image denoising with strong noise(noise standard deviationσ≥40)is always a hot topic in the application field of image processing technology.In order to further improve the denoising quality and edge protection of images with strong noise,a combined denoising method based on 2D non-subsampled shearlet transform and BM3D was proposed to solve the problems of poor denoising effect of block-matching 3D(BM3D)on strong noise images and the lack of optimal representation of linear singularity(such as edge).Shearlet transform provides a local,multi-scale and multi-direction analysis method that can optimally represent the linear singularity of image.BM3D method has the best effect on image noise reduction(σ<40)among traditional noise reduction methods.The denoising steps of the combined method are as follows:Firstly,NSST forward transform is performed on the image with noise,and the shear wave coefficients of high-frequency subbands with different scales and directions are obtained.Then the Bayesian threshold values of the high-frequency subbands in different directions of each scale are obtained and the asymptotic semi-soft threshold function is used to denoise the high-frequency subbands.Finally,NSST inverse transform is performed on the low frequency subband and all the denoised high frequency subbands to obtain the denoising results.The denoised image is used as the pre-filter in the basic estimation stage of BM3D,which can further improve the correctness of the grouping in the basic estimation stage and lay a good foundation for the denoising of BM3D.The method of this paper combined the advantages of NSST and BM3D.Simulation results show that for low noise images,the method has the same denoising effect as BM3D,slightly better than that of NLmeans method.The method is superior to BM3D and NLmeans method for the denoising effect of satellite images with strong noise.