基于具结构性噪声去除的图像重建的研究

Image reconstruction is everywhere – in cell phones, digital cameras and movie production. It is used routinely in science, engineering and medicine for diagnostics, inspection, control, etc. It allows great scientific breakthroughs such as pictures of Pluto from space probes, mapping of mental processes in the brain, and internal structures of the Earth, Moon and Sun...No matter the application or instrumentation, noise is present in the data. The only way to produce high-quality images is to use methods that remove the noise without deteriorating the image. This is not easy: different imaging systems involve different types of noise, and often the noise has structure that resembles components in the image...Consider X-ray body scanners that replace physical search in airports, prisons, etc. The X-ray dose must be kept low, and this increases the signal-to-noise ratio resulting in reconstruction artifacts. Here it is necessary to use noise-removal methods tailored to the Poisson noise of such systems...This project deals with a much broader type of noise: structured noise – unwanted image components such as ring artifacts in computed tomography, stripe effects in microscopy, and compression artifacts in digital images. The time is ripe to define and formulate structured noise in a unified mathematical framework and to use this insight to design algorithms that can handle structured-noise removal...The project will establish the first fundamental and unified framework for structured-noise removal, which incorporates a new system that automatically learns the structure. This framework will provide a new view of working with noise removal, and it will have a broad impact on many applications. The core elements of the project are 1) design a unified formulation of structured noise based on the underlying imaging systems, 2) develop mathematical analysis and algorithms to learn the structure of the noise automatically, 3) develop mathematical noise-removal models and corresponding theory, 4) design efficient computational algorithms.

图像重建广泛的应用于一切与图像相关的领域，而用于重建的数据中噪声是无法避免的，因此如何有效的去噪重建高质量图像一直都是图像科学中一个重要的研究课题。由于噪声的多变性和随机性，有效去噪并不容易。特别是当噪声具有一定的结构，我们很难将噪声与图像本身的信息区分开。..这个项目聚焦于一类更广泛意义的噪声——具结构性的噪声，如计算机断层扫描中的环状伪影，显微镜学中的条纹效应和数字图像中的压缩伪像。经过多年对各种噪声的研究，基于一个更加广义的数学框架来定义和去除具结构性噪声的时机已经成熟。在该项目中，我们将建立第一个针对具结构性噪声去除的统一框架，以期打破不同领域中一些本质相似或相关的噪声被反复研究的现状，构造一个可以涵盖并被应用于更多领域的平台。该项目的核心要素是：1）基于成像系统的具结构性噪声的模型; 2）对噪声结构的分析和算法; 3）去噪的数学模型和理论; 4）高效的算法。

图像重建广泛的应用于一切与图像相关的领域，而用于重建的数据中噪声是无法避免的，因此如何有效的去噪重建高质量图像一直都是图像科学中一个重要的研究课题。由于噪声的多变性和随机性，有效去噪并不容易。特别是当噪声具有一定的结构，我们很难将噪声与图像本身的信息区分开。..在这个项目中，我们围绕含有具结构性的噪声的图像重建问题进行了一系列深入的研究。我们主要考虑的问题有：1）对具有方向性的结构如何进行有效的重建；2）对于具有更复杂结构的问题如何构建数学模型，并进行图像分割和重建；3）对结构性噪声的另一来源，模型误差，的研究。针对这三个问题我们提出了一系列新的重建模型与算法，并在模拟数据和实际数据中进行了充分的验证。

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