基于混合全变分模型的图像去模糊算法

Image Deblurring Algorithm Based on Hybrid TV Model

针对全变分图像去模糊模型的局限性,将各向同性全变分模型和各向异性全变分模型相结合,提出一种图像去模糊混合全变分模型.为求解该模型,利用变量分裂方法对其处理,得到一个等价的最小化问题.在交替最小化作用下,变量分裂后生成的图像去模糊问题被分解为最小化子问题组.借助快速傅里叶变换和软阈值函数等,子问题可高效获得其精确解.在迭代过程中,通过逐个求解每个子问题,可获得图像去模糊问题的解.实验对高斯型模糊噪声图像进行复原,复原结果验证本文提出算法的有效性.与基于全变分模型的图像去模糊算法相比,可获得更优的复原结果,处理速度更快.

In view of the limitations of total variation deblurring model, this paper combines the isotropic total variation model with the anisotropic total variation model and proposes a new hybrid total variation model for image deblurring.In order to solve the model, we first deal with it by using the variable splitting method to get an equivalent minimization problem.With the help of alternate minimization, the image deblurring prob- lem generated by variable splitting is decomposed into a group of minimization subproblems.With the aid of fast Fourier transforms and soft thresholding functions, the subproblems can be efficiently solved for their ex- act solutions.In the iterative process,by solving each subproblem one by one,the solution of the image deblur- ring problem can be finally obtained.The experiment recovers the Gaussian-type blurred-noise images.The re- covery results verify the effectiveness of the proposed algorithm.Compared with the image deblurring algo- rithm based on the total variation model, better recovery results can be obtained and the processing speed is faster.