运用TGV正则化分解模型实现天文图像去噪

Decomposition Model Based on TGV Regularization for Astronomical Image Denoising

通过对天文图像进行分解达到去噪的目的,针对图像分解模型中常用的总变差(Total Variation,TV)半范假设图像由分片常数区域构成这一局限性,提出了基于2阶总广义变差(Total Generalized Variation,TGV)半范正则化的图像分解方法.假设图像的主体部分在有界总变差(Bounded Generalized Variation,BGV)空间中,振荡部分在G空间中,建立图像分解极小化模型,使得分解后的各部分之和逼近原始图像的同时,主体部分满足一定的光滑性要求.运用快速迭代压缩-阈值算法(Fast Iterative Shrinkage-Thresholding Algorithm,FIS-TA)迭代算法及Chambolle投影算法对模型求解,收敛速度快,耗时小.数值实验表明,与TV正则化方法相比,利用本文方法能更好地去除太阳射电动态频谱图中的噪声,从而更准确地将纤维精细结构提取出来.

Denoising is achieved through decomposing the original astronomical image. The common TV semi-norm has the shortcoming that an image is composed of piecewise constant areas. A new image decomposition method based on TGV semi-norm regularization is proposed in this paper. Based on the assumption that cartoon and oscillation belong to BGV space and G space respectively, the minimized model for decomposing image is established. The sum of the two decomposed parts approximates the original image, at the same time the cartoon meets a certain smooth requirement. The minimizer of the model is found out by using FISTA algorithm and Chamholle projection algorithm, which has a fast convergence speed and takes less time. Numerical experiment shows, that compared to the TV regularization method, the new method can more effectively remove the noise of the solar radio dynamic spectrum and therefor can extract the fiber fine structures more accurately.