CASIA OpenIR  > 模式识别国家重点实验室  > 图像与视频分析
自适应拓展图像反卷积算法研究
马斌斌
Subtype硕士
Thesis Advisor彭思龙
2019-06-03
Degree Grantor中国科学院自动化研究所
Place of Conferral智能化大厦第五会议室
Degree Name工学硕士
Degree Discipline计算机应用技术
Keyword图像反卷积 全变分 归整化参数估计 Lp范数约束 P范数估计
Abstract

由于图像成像系统、自然环境及人为环境等的影响,我们获取的图像经常是降质甚至是模糊的。图像反卷积问题是图像处理的一个重要部分,它主要解决如何在给定模糊图像的基础上估计出真实的图像。由于大多数模糊核都表现出低通特性,真实图像的高频细节经过模糊后会被“丢失”,从而使图像反卷积问题成为一个病态问题。从线性方程组的角度上来看,图像反卷积需要求解的是一个欠定方程组,这样就使得真实图像有很多解。

由于真实图像是多解的,在图像反卷积过程中我们需要添加合适的图像先验项,以确保复原出来的图像有较高的图像质量。图像的先验最初主要是光滑性假设,后来改进为半二次、全变分、稀疏性约束等。其共同特点是无法有效区分图像中的平滑区域、纹理区域及边缘区域,这样容易造成纹理和边缘的模糊。

为了解决上述问题,本文研究了自适应的基于L1和Lp范数全变分的图像反卷积问题。

在基于L1范数的全变分正则项算法研究当中,本文利用了迭代重加权的方法求解L1范数;本文结合矩阵特征值计算理论给出了归整化参数的优化更新策略,使得模型参数适应于更广泛场景的图像;本文利用共轭梯度法求解复原图像,降低了算法的空间复杂度。

针对正则项无法区分平滑区域、纹理区域及边缘区域的问题,本文提出了LP范数的全变分正则项;针对全变分在P小于1的条件下不可导的问题,本文引入了Huber凸函数,并且借助Huber函数的优化形式,使得图像复原的求解结果在P大于1和P小于1两个范围上公式形式一致;本文利用图像梯度符合广义高斯分布的先验,逐像素估计出各个像素点的范数P值;

在无噪声的情况下,与一些算法相比,本文提出的两个算法复原出的图像的PSNR和MSSIM值都更大。通过在不同模糊核上的实验,本文所提出的两个算法有比较好的表现,因此本文所提出的算法对于不同的模糊核具有广泛的适应性。

Other Abstract

Due to the influence of image imaging systems, natural environments and human environments, the images we acquire are often degraded or even blurred. The image deconvolution problem is an important part of image processing. It mainly solves how to estimate the real image based on a given blurred image. Since most blur kernels act as low-pass filtering, the high-frequency details of original images are “lost” after being blurred, making the image deconvolution problem a ill-posed problem. From the point of view of the linear equations, the image deconvolution problem is to solve an underdetermined system of equations, which makes the true image have many solutions.

Since the true image has many solutions, we need to add appropriate image priors in the image deconvolution process to ensure that the restored image has higher image quality. Traditionaly, images are assumed to have smoothness of different order. The improved image models include the introduction of half-quadratic, total variation, sparsity constraints, etc. Unfortunately all these prior models can not effectively distinguish between smooth areas, texture areas and edge areas in the image. The reconstructed images are always blurred, especially in the texture and edge areas.

In order to solve the above problems, this paper studies the adaptive image deconvolution problem based on total variation of L1 and Lp norm.

In the research of the algorithm based on total variation regular term of L1 norm, the iterative reweighting method is used to solve the L1 norm. In this paper, from the matrix eigenvalue calculation theory, the optimization update strategy of the regular parameter is given, so that the model parameters are adapted to the images of the wider scene. In this paper, the conjugate gradient method is used to solve the restored image, which reduces the spatial complexity of the algorithm.

In order to solve the problem that the regular term can't distinguish between smooth region, texture region and edge region, this paper proposes the total variation regular term of LP norm. For the problem that the total variation is not derivable under the condition that P is less than 1, the Huber convex function is introduced in this paper. The optimization form of the Huber function makes sure that the solution formula form of the image restoration in the range of P greater than 1 and P less than 1 are the same. In this paper, due to the priori that the image gradient accords with the generalized Gaussian distribution, and the norm p value of each pixel is estimated pixel by pixel.

Without blur noise, compared with some algorithms, the two algorithms proposed in this paper recover images with larger PSNR and MSSIM values. Through the experiments on different blur kernels, the two algorithms proposed in this paper have better performance, so the proposed algorithm has wide adaptability to different blur kernels.

Pages89
Language中文
Document Type学位论文
Identifierhttp://ir.ia.ac.cn/handle/173211/23852
Collection模式识别国家重点实验室_图像与视频分析
Corresponding Author马斌斌
Recommended Citation
GB/T 7714
马斌斌. 自适应拓展图像反卷积算法研究[D]. 智能化大厦第五会议室. 中国科学院自动化研究所,2019.
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