Inverse Problems in Medical Imaging

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This research program explores the broad area of medical image processing and provides solutions to various associated inverse problems such as medical image registration. In general, many real-world inverse problems are ill-posed, mainly because of the lack of existence of a unique solution. The procedure of providing acceptable unique solutions to such problems is known as regularization. Indeed, much of the recent progress in imaging has been due to advances in the formulation and practice of regularization. This, coupled with progress in optimization and numerical analysis, has yielded much improvement in computational methods of solving inverse imaging problems. Image registration, the process of aligning different sets of data into one coordinate system, is a key challenge in many medical imaging applications, e.g., tumour detection and surgery planning, that can be modelled as an inverse problem. Given a template (or moving) image and a reference (or fixed) image, the goal is to find a reasonable transformation that maximizes a predetermined similarity measure between the reference and the transformed template image. Solving this inverse problem is specifically challenging when images of highly deformable tissue, e.g., breast, is considered. Some of the short- and medium-term research objectives of this proposal in this direction are outlined below. 1-Breast Magnetic Resonance Imaging (MRI) is frequently performed prior to breast conserving surgery in order to assess the location and extent of the lesion. Ideally, the surgeon should be able to use the pre-surgery image information during surgery to guide the excision. This requires the prone pre-surgical MR image to be aligned or co-registered to conform to the patient's supine position on the operating table. The future breast Computer Assisted Surgery (CAS) technology will demand novel efficient alignment algorithms that employ the surface information of the breast in the operating room along with the intensity information of the pre-surgical images. 2-Recently, Dynamic Contrast-Enhanced (DCE) imaging has emerged as a powerful screening tool. Accurate registration of DCE images is valuable for proper identification of the lesions. This requires defining regularization expressions that directly incorporate the underlying physical process of this inverse problem. In addition, developing relevant efficient computational schemes is necessary to address the problem. 3-In image registration, researchers generally rely on transformations to describe the alignment process relating two images. However, in the clinical setting, there are many situations where the deformation may have discontinuities. Given the limitations of current approaches to image registration, an open problem is to develop a method that would enable deformable registration in the presence of various types of large-scale discontinuities. The proposed multidisciplinary research program will not only foster scientific advances valuable to the academic community, but also directly benefit the society. The developed computational methods are of significant importance that can shape the future of computer assisted surgery, diagnosis, and treatment planning technologies of highly deformable tissue. Revision surgeries due to misplacement or misdiagnosis impose a huge financial burden on the Canadian healthcare system. This research program is directed towards affordable alternatives using multidisciplinary techniques in collaboration with leading Canadian research institutions. In addition, the proposed program will prepare students in this demanding research field and place them in a more competitive position in academia or industry.