带限剪切波变换与全变差结合的图像去噪

Total Variation Based Band-limited Sheralets Transform for Image Denoising

基于带限剪切波变换理论,提出了一种带限剪切波与全变差相结合的去噪算法.根据剪切波变换在不同分解尺度的噪音标准差设置不同的阈值对噪音图像进行重构,以此重构图像作为全变差去噪的初始图像进行全变差最小化去噪,经过迭代后得到最终去噪结果.实验结果表明,与基于多尺度几何分析的其他去噪算法(曲波变换、非下采样轮廓波变换、剪切波变换直接硬阈值去噪)相比,视觉效果与峰值信噪比数值有明显的提高,且保留了更多的纹理、边缘等图像细节信息.

Noise reduction is an important image pre-processing for improving the quality of image. Shearlet transform, as a method of multiscale geometric analysis, is more suitable for image processing because of better approximation precision and sparsity description. A novel approach based on the band-limited shearlet transform and total variation for image denoising was proposed. Unlike traditional hard threshold method, different thresholdings were used at each scale to obtain good estimate. The reconstruction image was used as initial image of total variation minimum method. Numerical examples demonstrated that the approach is highly effective at denoising complex images. Compared with other methods in multiscale geometric analysis domain, such as nonsubsampled contourlet transform, curvelet transform and hard- threshod method of shearlet transform, the denoised image in this paper removed the noise while retaining as much as possible the important signal features and details such as edges and texture information.