X-ray tomography with sparse data: physics, mathematics, and application

Due to advances in large-area flat-panel X-ray digital detectors, applications for X-ray tomography have diversified to a wide range of applications in medical imaging such as image-guided radiation therapy and surgery, and devices such as extremity scanners, dental CT, and digital breast tomosynthesis. An important part of all of these specialized scanners, is the development of new image reconstruction algorithms that result from the study of inverse problems in X-ray tomography. Of particular interest for this talk are sparse-data inverse problems where the number of image voxels is larger than the number of measurements in the X-ray projection data. This presentation will explain how prior information on the scanned subject can be used to arrive at accurate solution to the inverse problem associated with under-sampled image reconstruction. The presentation will mainly rely on images and examples with few equations. After explaining the theory, application will be presented in the domain of tomographic mammography imaging, exploiting under-sampled image reconstruction for novel scan configurations and X-ray dose and scan-time reduction.