兰州大学机构库 >萃英学院
基于可学习正则化的图像重建方法研究
Alternative TitleReserch on Learnable Regularization Method for Image Reconstruction
周星
Subtype学士
Thesis Advisor焦桂梅
2023-05-19
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name理学学士
Degree Discipline数学与应用数学
Keyword图像重建 image reconstruction 正则化 regularization 去噪器 denoising device 深度学习 deep learning 数据模型双驱动 data model dual drive
Abstract

       图像重建是基于物体外部测量数据获得其形状信息的技术,已经在许多领域获得广泛应用,具有很强的现实意义。图像重建的本质是求解图像成像的反问题,即从观察到的损坏或压缩版本数据中恢复高质量图像,面临的主要挑战是不适定性。在求解反问题的过程中,模型驱动方法基于物理机制构建并求解一个变分正则化模型,虽可解释较强但面临着精确建模困难,尤其是对于先验信息正则化项选择困难的问题;数据驱动的深度学习方法则是基于数据及通用的深度神经网络模型学习观测数据到高质量图像之间的非线性映射。虽然算法精度高且运算速度快,但其可解释性差且对数据质量有很强的依赖性。基于数据模型双驱动的思想,在传统最大后验概率框架中使用深度神经网络学习正则化函数项,从而结合模型驱动方法和数据驱动方法的优点来解决上述问题。

       在本文中,我们主要对近年来提出的两种具有代表性的可学习正则化方法进行了分析推导及实验验证。首先,我们介绍了势函数驱动去噪正则化方法,详细说明了其使用的去噪器的网络架构、算法步骤以及收敛性,并分析了其缺陷。作为其改进,我们介绍了另外一种可学习正则化方法——具有收敛性保障的即插即用近端去噪器法,具体地阐述了近端算子的表征问题、算法流程和收敛性分析。最后我们以图像去模糊和超分辨率两种任务为例,使用具有收敛性保障的即插即用近端去噪器法在 DRUNET 和 CBSD68 数据集上进行了数值实验,并和传统去噪器的结果进行对比。由实验结果可以看出:此方法取得了良好的图像重建效果,并且相比于现阶段流行的基于深度学习的方法有较强的竞争力且具有收敛性保障。

Other Abstract

      Image reconstruction is a technique to obtain information about the shape of an object based on its external measurement data, which has been widely used in many fifields and has a strong relevance. The essence of image reconstruction is to solve the inverse problem of image imaging, i.e., to recover high-quality images from the observed corrupted or compressed versions of data, and the main challenge is discomfort. In the process of solving the inverse problem, model-driven methods construct and solve a variational regularization model based on physical mechanisms, which is more interpretable but faces diffificulties in accurate modeling, especially for the selection of prior information regularization terms; Data-driven deep learning methods are based on data and generalized deep neural network models to learn the nonlinear mapping between observed data and high-quality images, although the algorithms are highly accurate and fast, they are poorly interpretable and have a strong dependence on data quality. Based on the idea of dual-driven data model, the above problem is solved by using deep neural networks to learn regularized function terms in the traditional maximum a posteriori probability framework, thus combining the advantages of model-driven and data-driven methods.

       In this paper, we mainly analyze, deduce and verify two representative learnable regularization methods proposed in recent years. Firstly, we introduce the regularization method of potential function-driven denoising, explain in detail the network architecture, algorithm steps and convergence of the denoiser used by it, and analyze its defects. As an improvement, we introduce another learnable regularization method, the plug-and-play near-end noise reducer method with convergence guarantee, and specififically expound the characterization problem, algorithm flflow and convergence analysis of the near-end operator. Finally, we take image deblurring and super-resolution tasks as examples, and use the plug-and-play near-end denoising method with convergence guarantee to carry out numerical experiments on DRUNET and CBSD68 data sets, and compare the results with those of traditional denoisers. From the experimental results, it can be seen that this method has achieved good image reconstruction effect, and it is more competitive and has convergence guarantee compared with the popular deep learning-based methods at this stage.

Subject Area图像重建
MOST Discipline Catalogue理学 - 数学类 - 数学与应用数学
URL查看原文
Language中文
Other Code262010_320190928141
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/537367
Collection萃英学院
Affiliation
兰州大学萃英学院
Recommended Citation
GB/T 7714
周星. 基于可学习正则化的图像重建方法研究[D]. 兰州. 兰州大学,2023.
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