基于多幅图像恢复单幅图像的快速算法实现

为解决传统的单幅图像恢复算法效果不理想的情况，现有理论利用多幅图像之间的信息互补这一条件，在图像配准的基础上，通过多幅退化图像对单幅图像进行恢复，比较流行的是使用M估计(M-estimation)对图像进行配准，然后利用L1范数进行图像融合，进而提升图像恢复的鲁棒性，但其收敛速度并不理想。为了实现算法的快速收敛，通过对下降算法的搜索梯度方向改善的探究，出了基于共轭梯度下降法(conjugate gradient descent, CGD)的图像恢复算法。在此基础上对CGD图像恢复算法进行改进，利用前后估计的值之间的差信息来优化迭代时的搜索方向，也就是在后面这次搜索梯度上面加前1次和前2次估计值的差，以此增大搜索梯度值，进一步缩短迭代到最小值的时间。仿真结果表明，所提出的改进算法比基于最速梯度下降法(batch gradient descent, BGD)的图像恢复算法的收敛速度更快。

Realization of fast algorithm of recovering single image from multiple corrupted images

In order to solve the problem that the traditional single image restoration algorithm is not ideal, the existing theory uses the condition of information complementarity between multiple images to recover a single image through multiple degraded images on the basis of image registration. It is more popular to use M-estimation to register images, and then use L1 norm for image fusion, which improves the robustness of image restoration, but its convergence speed is not ideal. In order to realize the fast convergence of the algorithm, an image restoration algorithm based on conjugate gradient descent (CGD) is proposed by exploring the improvement of the search gradient direction of the descent algorithm. On this basis, the CGD image restoration algorithm is improved. The difference information between the pre-estimated and post-estimated values is used to optimize the search direction during iteration, that is, the difference between the first and second estimation values is added to the later search gradient, so as to increase the search gradient value and further shorten the iteration time to the minimum value. The simulation results show that the convergence speed of the improved algorithm is faster than that of the image restoration algorithm based on the fastest gradient descent (BGD).