【作者】 苗晴；

【导师】 周海银；

【作者基本信息】 国防科学技术大学 ， 应用数学， 2005， 硕士

【摘要】 图像复原是图像处理中的一个重要问题,对于改善图像质量具有重要的意义。解决该问题的关键是对图像的退化过程建立相应的数学模型,然后通过求解该逆问题获得图像的复原模型并对原始图像进行合理估计。正则化方法是在求该逆过程中解决病态性问题的有效方法。本文针对图像复原中正则化方法的研究及应用进行了广泛深入的探讨与分析,主要工作和创新点如下:第一,在正则化技术解决病态问题的基础上,从正则化方法数学理论入手,分析了图像的退化模型和图像复原的病态特征,重点讨论了正则化参数和正则项的选取,并总结了其求解算法及快速实现方法,完善了正则化方法图像复原的基本理论。第二,在现有复原模型的完善上,重新构建正则化参数与正则化项,构造了新的具有空间自适应性质的正则化图像复原模型。运算中合理地设计算法,自适应的正则化参数可以自动修正到最优值,同时自适应加权的正则项使算法的性能更加完善。仿真计算表明,该方法可有效抑制图像边界的振铃效应并保护了图像的重要信息,并且比现有的方法具有更高的峰值信噪比。第三,从传统的线性代数方法着手,提出了两种新的基于正则化思想的图像复原方法。一是从约束最小二乘出发,在加性噪声能量有界的前提下,采用正则化方法来克服病态问题,通过解一个单变量方程,并利用空域迭代运算实现了一种有效的图像复原;二是针对模糊图像的复原问题,从最小二乘算法出发,采用增量迭代的方法改善算法的收敛性,同时结合正则化技术克服问题的病态性质,并引入自适应的正则化参数,使其与图像复原的迭代运算同步进行并自动修正到最优值。计算结果表明,该方法可有效复原图像,在客观标准评价和主观视觉效果方面都有明显的改善。更多还原

【Abstract】 Image restoration is one of the essential topics in image processing, which can greatly improve image quality. The key for this issue is to model the degradation processing in mathematical form, then solve this inverse problem to get a restoring model and an estimation of original image. Effective methods that can tackle the ill-posed problems are the so-called regularization methods during the inverse process. This thesis introduces and analyses in detail the research and application of regularization in image restoration, the main contributions and creativities are listed as follows:Firstly, on the basis of the regularization technique for dealing with ill-posed problems, starting from the mathematical theories about regularization, analyzing the degraded model and the ill-posed character of image restoration, this paper mainly discusses the regularized parameter and regularized item, and the solution approaches and fast algorithms are also summarized, therefore perfects the essential theories about regularization in image restoration.Secondly, to perfect the known restoring models, a new space-adaptive regularization model of image restoration is constructed by redesigning regularized parameter and regularized item. By contriving appropriate algorithms in the computations, the regularized parameter can automatically correct to the appropriate value due to its adaptive character, meanwhile, the adaptive effect is developed with a weight matrix included in the regularized item. Simulation results show that the ringing artifacts around the image are reduced, the main information is preserved, and the Peak Signal to Noise Ratio (PSNR) is higher than the known methods.Thirdly, two new image restoration methods are proposed based on regularization idea from traditional linear algebra approach. On one hand, from the technique of constrained least squares and limited energy of additive noise, an effective restored approach by adopting regularization method to overcoming ill-posed problem, solving an equation with a single variable, and using space iterative algorithm is proposed; On the other hand, aiming at the restoration of blurred image, another effective restoration approach based on least-square algorithm is also proposed in this paper. This method firstly adopts increment iterative algorithm to improve convergence and meanwhile applies regularization technique to overcome ill-posed problem. In the computations, the regularized parameter has its adaptive character, which can be determined in terms of the restored image at each iteration step therefore automatically correct to the appropriate value. Numerical results show that these methods can effectively restore original image, and the objective standard evaluation and subjective visual effect are improved significantly.更多还原