Abstract: In order to research the image restoration technology, this paper proposes a kind of approach by using cartoon texture image decomposition and a generalized accelerated proximal gradient algorithm to realize image restoration. To decompose the original fuzzy image into cartoon part and texture part, cartoon part is the low frequency component of the image, noise interference is small, the texture of the image is the high frequency component of the image, noise interference is sharp, and it deblurs and denoises by using the generalized accelerated proximal gradient algorithm, selects small regularization parameters for the cartoon parts, selects big regularization parameters for the texture parts, composes the restoration of the cartoon part and the restoration of the texture part to achieve restoration image. Through simulation of two standard test images by MATLAB, it shows that this method not only converges faster but also is better than the effect of generalized accelerated proximal gradient algorithm, especially is suitable for recovering the image of small fuzzy degrees.

Key words: cartoon texture image decomposition, total variation, generalized accelerated proximal gradient algorithm, image restoration, regularization, MATLAB

摘要： 为了研究图像恢复技术，提出采用卡通纹理分解和基于全变分的广义加速临近梯度算法实现图像恢复。将原始模糊图像分解成卡通部分和纹理部分，卡通部分主要是图像的低频成分受噪声干扰小，纹理部分主要是图像的高频成分受噪声干扰大，采用基于全变分的广义加速临近梯度算法进行图像去模糊和去噪，卡通部分选择较小的正则化参数，纹理部分选择较大的正则化参数，将恢复的卡通部分和纹理部分进行合成得到恢复图像。通过对两张标准测试图像的MATLAB实验仿真，证明了该方法不仅收敛速度快而且效果比一般的临近梯度算法要好，尤其适合于恢复模糊度不是很高的图像。

关键词: 卡通纹理分解, 全变分, 广义加速临近梯度算法, 图像恢复, 正则化, MATLAB