"Mathematical imaging, image multifunctions, diagnostically lossless image compression, fractal-based methods of analysis and approximation"

“数学成像、图像多功能、诊断无损图像压缩、基于分形的分析和近似方法”

• 批准号: 106270-2012
• 负责人: Vrscay, Edward
• 金额: $ 1.82万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=569136
• 关键词: Mathematical; imaging; image; multifunctions; diagnostically

Much of my research can be called "mathematical imaging,'' the use of mathematics to develop new methods of image processing or image analysis. One such image processing method, which still receives a great deal of attention, is ''denoising'', the removal of troublesome noise from images (e.g., instrument noise from an MRI). I have also returned to the research area of image compression -- reducing the amount of computer memory needed to store a digital image. (The standard "JPEG" method used to compress images in digital cameras is based on a well-known mathematical principle.) The efficient storage, transmission, retrieval and display of images - in particular medical images - in large-scale databases has become a major challenge. The question that remains unanswered is "To what degree can a medical image be compressed before diagnostic information is lost?'' Currently, most assessments of such distortions are done by radiologists, making them subjective, extremely expensive and time-consuming. In collaboration with a radiologist at McMaster University and a software designer at Agfa HealthCare, we are working on the problem of automating this assessment, i.e., predicting when diagnostically critical distortions will occur. This leads to another problem in image processing - assessing the "visual quality" of images. There is a standard, mathematically-based method of computing the "distance" between two images. However, two images that are close in this distance may not be close visually. One of my collaborators at UW is a co-author of the "structural similarity measure," (SSIM) recognized as one of the best measures of visual closeness to date. We have been working on the use of SSIM to denoise images and now plan to use it in the medical image compression problem outlined above. I am also interested in the mathematical properties of SSIM. My research in mathematical imaging evolved from an earlier research programme centered around "fractal analysis.'' In fractal analysis, one tries to express an "object'' as a union of smaller, possibly distorted copies of itself. I continue to pursue this area of research which has interesting applications, particularly in imaging.

我的大部分研究可以被称为“数学成像”，即利用数学来开发图像处理或图像分析的新方法。一种这样的图像处理方法，仍然受到大量的关注，是“去噪”，即从图像中去除令人讨厌的噪声（例如，来自MRI的仪器噪声）。 我还回到了图像压缩的研究领域--减少存储数字图像所需的计算机内存量。 (The用于在数码相机中压缩图像的标准“JPEG”方法基于众所周知的数学原理。 在大规模数据库中有效地存储、传输、检索和显示图像（特别是医学图像）已经成为一个主要挑战。 仍然没有答案的问题是“在诊断信息丢失之前，医学图像可以压缩到什么程度？目前，大多数对这种扭曲的评估都是由放射科医生完成的，这使得他们主观，非常昂贵和耗时。我们与麦克马斯特大学的一位放射科医生和爱克发医疗保健公司的一位软件设计师合作，正在研究自动化评估的问题，即，预测何时将发生诊断上的严重失真。 这导致了图像处理中的另一个问题-评估图像的“视觉质量”。 有一个标准的，基于几何的方法来计算两个图像之间的“距离”。 然而，在该距离上接近的两个图像可能在视觉上不接近。 我在华盛顿大学的一位合作者是“结构相似性度量”（SSIM）的合著者，该度量被认为是迄今为止最好的视觉接近度度量之一。我们一直致力于使用SSIM去噪图像，现在计划将其用于上述医学图像压缩问题。 我对SSIM的数学性质也很感兴趣。 我在数学成像方面的研究是从早期的以“分形分析”为中心的研究项目发展而来的。在分形分析中，人们试图将一个“对象”表示为一个更小的，可能是其自身扭曲的副本的联合体。我继续追求这个有有趣应用的研究领域，特别是在成像方面。