基于小波域稀疏最优的图像修复方法

由模糊和噪声引起的图像退化属于非线性病态逆问题,修复比较困难.由于小波的稀疏表示能力较强,为提高修复质量,提出利用正交小波作为稀疏基,以小波系数的稀疏性为先验构造凸函数,最小化后得到修复图像;并提出将优化问题转化为逼近算子形式,利用不动点理论求解;证明了只需对构造出来的迭代形式的解析解反复迭代就可以得到最优解.对方法的构造过程、收敛性和复杂度进行了细致的分析,给出了迭代解,并结合加速方法提高了算法速度.仿真表明,本文方法具有较强的修复能力,收敛速度较快,能够有效去除模糊和噪声,保留图像的边缘和细节信息.

Image Restoration Based on Sparse-Optimal Strategy in Wavelet Domain

Due to the nonlinear ill-posing characteristic of image degradation caused by blur and noise,image restora-tion is generally difficult.To improve image quality,orthogonal wavelet was taken as sparse basis and the sparsity of wavelet coefficients as prior.By constructing a convex function and minimizing this function,we obtained the recovered image.The minimization problem was transferred into a proximal operator which is solved by the fixed point theory.We proved that the optimal solution can be obtained through repeatedly iterating an analytical formula.The construction process, convergence rate and complexity of the method were discussed,and an accelerated algorithm was presented.Simulation results indicate that our method can remove blur and noise,and keep detail information meanwhile.