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

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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.