基于小波域稀疏最优的图像修复方法

发布时间：2018-01-08 12:28

本文关键词：基于小波域稀疏最优的图像修复方法　出处：《电子学报》2016年03期 　论文类型：期刊论文

【摘要】：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.
[Abstract]:Image degradation caused by blur and noise is a nonlinear ill-conditioned inverse problem, which is difficult to repair. Because of the strong sparse representation ability of wavelet, in order to improve the repair quality, orthogonal wavelet is used as sparse basis. A convex function is constructed with the sparsity of wavelet coefficients as a priori, and the reconstructed image is obtained after minimization. The optimization problem is transformed into approximation operator and solved by fixed point theory. It is proved that the optimal solution can be obtained by iterating the analytic solution of the constructed iterative form. The convergence and complexity of the method are analyzed in detail, and the iterative solution is given. Simulation results show that the proposed method has a strong ability to repair and converge quickly, which can effectively remove blur and noise and retain the edge and detail information of the image.
【作者单位】：西安理工大学机械与精密仪器工程学院;
【基金】：陕西省自然科学基金(No.2014JM7273)
【分类号】：TP391.41
【正文快照】： 1引言图像在拍摄、传输和储存中会降低质量,图像修复很重要.图像降质的主要原因有模糊、噪声、像素丢失、有损压缩等.造成模糊的主要原因包括相机振动(运动模糊)、对焦不准(高斯模糊)、目标高速运动(运动模糊)、大气湍流(湍流模糊)、人为因素(均值模糊).目前,去模糊方法多种多

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