Mathematical Sciences: Use of Enhancement Techniques and A Priori Information in Electrical Impedance Tomography

9503114桑托萨我们的方法是将成像问题归结为一个带有约束和惩罚项的最优化问题。约束将表示先验信息，而添加惩罚项是为了在图像中达到一定的质量。这种方法的主要困难之一是开发专门的优化方法。优化方法必须能够(1)解决大问题，(2)处理约束，(3)处理代价函数的不可微性。为此，我们将探索使用内点方法。虽然这种成像技术具有一些吸引人的特点，如低成本和便携，但它的缺点是无法分辨图像中的细微特征。我们建议通过结合已知的边信息以及在重建过程中应用增强技术来克服这一困难。这项研究涉及使用图像增强和计算机视觉中的最新技术来克服被称为电阻抗断层成像的成像方法的模糊效果。电阻抗断层成像是一种使用在样品边界收集的直流电测量对样品内部进行成像的技术。它已在临床应用、地球物理勘探和无损评估中得到应用。预计我们将能够开发软件，当与电阻抗断层成像设备一起使用时，将提供高分辨率的图像。

DMS-9503114 Santosa Our approach is to pose the imaging problem as an optimization problem with constraints and penalty terms. The constraints would represent a priori information, while the penalty terms are added to achieve certain quality in the image. One of the main difficulties in this approach is development of specialized optimization methods. The optimization methods must be capable of (1) solving large problems, (2) dealing with constraints, (3) dealing with nondifferentiability of the cost function. To this end, we will explore the use of interior point methods. While this imaging technique has several attractive features such as low-cost and portability, it suffers from the ability to resolve fine features in the image. We propose to overcome this difficulty by incorporating known side information as well as applying enhancement techniques in the reconstruction process. This research concerns the use of recent techniques in image enhancement and computer vision in overcoming the blurring effects of an imaging method known as electrical impedance tomography. Electrical impedance tomography is a technique for imaging the interior of a specimen using DC electrical measurements collected on the boundary of the specimen. It has found use in clinical applications, geophysical prospecting, and nondestructive evaluations. It is anticipated that we will be able to develop software, that when used with electrical impedance tomographic devices, would deliver images with high resolution.