结合波原子和全变差方法的图像去噪*

传统的硬阈值去噪会产生伪吉普斯现象,而波原子本身的周期化过程也会出现新的方向性纹理失真。采用全变差最小化方法来抑制这些失真,提出一种改进的波原子去噪算法。该算法不是直接将低于阈值的小系数置为零，而是对这些系数在全变差最小的意义上作修正迭代，得到最终的去噪图像。数值实验结果表明,波原子去噪保留边缘和纹理的效果优于小波和曲线波,改进算法去噪的视觉质量明显好于传统波原子去噪。最后还指出了进一步的研究方向。

Image denoising based on wave atoms and total variation

Traditional hard-threshold denoising can produce pseudo-Gibbs phenomena, and a new oriented texture distortion will appear in the cycle process of wave atoms itself. This paper suppressed these distortions using total variation regularization, obtaining an improved denoising algorithm based on wave atoms. These small coefficients below to the given threshold was not directly set to zero, but rather to values that minimize the total variation, so could get the reconstructed image. Numerical experiment results show that wave atoms denoising retains better edges and textures than wavelet and curvelets, and the improved algorithm has significantly better visual quality than the traditional wave atoms denoising. Finally, this paper pointed out the directions for further research.