Easley Glenn R, Labate Demetrio, Colonna Flavia
System Planning Corporation, Arlington, VA 22209,
IEEE Trans Image Process. 2009 Feb;18(2):260-8. doi: 10.1109/TIP.2008.2008070. Epub 2008 Dec 16.
We propose a shearlet formulation of the total variation (TV) method for denoising images. Shearlets have been mathematically proven to represent distributed discontinuities such as edges better than traditional wavelets and are a suitable tool for edge characterization. Common approaches in combining wavelet-like representations such as curvelets with TV or diffusion methods aim at reducing Gibbs-type artifacts after obtaining a nearly optimal estimate. We show that it is possible to obtain much better estimates from a shearlet representation by constraining the residual coefficients using a projected adaptive total variation scheme in the shearlet domain. We also analyze the performance of a shearlet-based diffusion method. Numerical examples demonstrate that these schemes are highly effective at denoising complex images and outperform a related method based on the use of the curvelet transform. Furthermore, the shearlet-TV scheme requires far fewer iterations than similar competitors.
我们提出了一种用于图像去噪的全变差（TV）方法的剪切波公式。数学上已证明，与传统小波相比，剪切波能更好地表示诸如边缘等分布式不连续性，是一种用于边缘表征的合适工具。将类似小波的表示（如曲波）与TV或扩散方法相结合的常见方法，旨在在获得近乎最优估计后减少吉布斯型伪影。我们表明，通过在剪切波域中使用投影自适应全变差方案来约束残差系数，可以从剪切波表示中获得更好的估计。我们还分析了基于剪切波的扩散方法的性能。数值示例表明，这些方案在对复杂图像去噪方面非常有效，并且优于基于曲波变换的相关方法。此外，与类似的竞争方法相比，剪切波 - TV方案所需的迭代次数要少得多。
