全变差数字滤波器与Ridgelet变换相结合的图像去噪方法

Image Denoising Method with Combination of Digital TV Filter and Ridgelet Transform

针对Gurvelet变换采用的金字塔分解对图像细节表现的不足,我们提出利用全变差数字滤波器提取图像细节,然后对其采用基于分数阶傅立叶变换和投影-切片定理的Ridgelet变换,在变换域中由极小化极大误差准则进行阈值估计并对变换域系数进行阈值处理,以实现图像去噪.与金字塔分解相比,全变差数字滤波器能够简化图像分解并得到包含几乎所有细节的单幅图像,从而更有利于在Ridgelet域中进行降噪处理.实验结果表明,相对于Ridgelet和Curvelet变换的去噪方法,本文方法在抑制噪声的同时具有更有效的边缘保护能力,同时消除了边缘处的振荡,并且相对于Curvelet变换节省了计算.

Since inefficient representation for details with Pyramid decomposition in Curvelet transform, we propose a new image denoising method, which extracts details by Digital TV filter and then applies Ridgelet transform to it, The Ridgelet transform here is based on Fractional Fourier transform and Projection-Slice theorem, and its coefficients are thresholded according to Minimax error criterion of wavelet. The Digital TV filter,compared with Pyramid decomposition,facilitates denoising in Ridgelet domain because it simplifies image decomposition and obtains a single image containing all edge information. Experiments show that our approach performs better than Ridgelet and Curvelet transform in protecting edges and reducing noise, and it eliminates oscillating patterns near edges. Furthermore, its computation is less fairly than Curvelet transform.