摘要
我们生活在数字的时代,数据已经成为了我们生活中不可或缺的一部分,而图像无疑是最重要的数据类型之一.图像反问题,包括图像降噪,去模糊,修复,生物医学成像等,是图像科学中的重要领域.计算机技术的飞速发展使得我们可以用精细的数学和机器学习工具来为图像反问题设计有效的解决方案.本文主要回顾图像反问题中的三大类方法,即以小波(框架)为代表的计算调和分析法、偏微分方程(PDE)方法和深度学习方法.我们将回顾这些方法的建模思想和一些具体数学形式,探讨它们之间的联系与区别,优点与缺点,探讨将这些方法有机融合的可行性与优势.
We live in the digital age,and data has become an essential part of our lives.Images are undoubtedly one of the most important types of data.Image inverse problems,including image denoising,deblurring,restoration,biomedical imaging,etc.,are important areas in imaging science.The rapid development of computer technology has enabled us to use sophisticated mathematics and machine learning tools to design effective algorithms for image inverse problems.This paper mainly reviews three types of methods in image inverse problem,namely,applied and computational harmonic analysis method(represented by wavelets and wavelet frames),partial differential equation(PDE) method and deep learning method.We will review the modeling philosophies of these methods,explore the connections and differences among them,their advantages and disadvantages,and further discuss the feasibility and benefit of the integration of these methods.
作者
董彬
Dong Bing(Beijing International Center for Mathematical Research,Peking University,Beijing 100871,China)
出处
《计算数学》
CSCD
北大核心
2019年第4期343-366,共24页
Mathematica Numerica Sinica
关键词
图像反问题
图像重建
医疗影像
图像识别
变分模型
偏微分方程
小波变换
卷积神经网络
深度学习
Image inverse problem
image reconstruction
medical imaging
image recognition
variational model
partial differential equations
wavelet transform
convolutional neural network
deep learning
