带总观测误差约束的模糊图像恢复

Blurred Image Restoration with Total Observation Error Bound

  • 摘要: 模糊图像恢复是数字图像处理领域的研究热点之一,总变差(Total Variation, TV)规整化可以很好的保持图像的细节,然而,传统的TV图像恢复模型需要考虑最优的正则化参数,由此,提出了一族包含不同规整化因子,带总观测误差约束的模糊图像恢复模型,并分为去模糊和去噪两步求解此模型。在去模糊过程中,利用共轭梯度法求出一个满足总观测误差约束的初始恢复图像;在去噪过程中,首先,以去模糊的结果作为初始估计;其次,针对 范数最小化问题,利用优化—最小化(Majoriziation-Minimization, MM)算法的思想,将原问题转化为一系列容易求解的优化子问题;最后,极小化优化子问题,得到最终的恢复图像。实验结果表明,该算法对模糊图像的恢复效果是显著地。

     

    Abstract: Blurred image restoration is a research focus in the field of digital image processing, Total Variation (TV) regularization can well preserve the details of image, however, the optimal regularization parameter must be taken into consideration in the traditional TV image restoration model during image restoration. As a result, a kind of blurred image restoration model is presented, which consists of a family of different regularization factors and a total observation error bound. The de-blurring and de-noising processes are involved to solve this model. In the de-blurring process, the conjugate gradient method is used to obtain an initial restored image which satisfies the total observation error bound constraint. And in the de-noising process, firstly, the restored image of the de-blurring process is set as an initial estimation, secondly, according to Majoriziation-Minimization algorithm, the minimization problem is divided into a series of simple sub-problems, finally, by minimizing these sub-problems, the eventual restored image is attained. Experimental results show that the algorithm is significant for blurred image restoration.

     

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