Thomas Humphries, Faculty Mentor

Dr. Humphries’ area of research is in image reconstruction. The research project this summer will consider sparsity-exploiting reconstruction in computed tomography. Here is a little background and specific questions for this line of research:

Tomography refers to the reconstruction of three-dimensional volumetric images of an object based on planar measurements (such as X-rays) taken from different angles around the object. Medical imaging modalities such as Single Photon Emission Computed Tomography (SPECT) and Computed Tomography (CT) allow us to visualize function and structure within a patient’s body, and to make diagnosis based on this information. The reconstruction of these images is an example of an *inverse problem* whose solution requires sophisticated mathematical approaches. Dr. Humphries has been main author or co-author on four peer-reviewed articles in this area, along with a number of conference presentations. The focus of his recent research has been on iterative methods for CT reconstruction.

Research in CT is primarily driven by the desire to improve the diagnostic potential of images used in the clinic. Concurrently, because CT imaging involves taking X-rays of a patient, there is a need to keep the radiation dose to the patient as low as possible. These two objectives conflict with one another, as reducing dose typically results in diminished information about the object being imaged. One is often forced to incorporate some type of *regularization* into the reconstruction approach; i.e., introducing some additional information based on an expectation of how the image “should” look.

Over the last ten years, a number of powerful ideas and results have emerged from the mathematical field of *compressive sensing*, which refers to a specific family of regularization techniques. Compressive sensing tells us that if the object being imaged is *sparse* in some sense, it can be reconstructed from much less information than is required for an arbitrary object. A sparse image is one whose representation in some basis consists of a relatively small number of nonzero elements. Ideas from compressive sensing have been applied in a number of CT imaging studies to recover images from undersampled or poor quality data.

Dr. Humphries’ primary research interest is in finding novel applications of compressive sensing to CT image reconstruction. These include:

- Developing compressive sensing based reconstruction algorithms that incorporate realistic modeling of imaging physics, such as a polyenergetic X-rays spectrum,
- Investigating different reconstruction algorithms and regularization approaches, and assessing their performance with respect to image quality and speed of convergence, and
- Applying compressive sensing to new areas in CT imaging, such as material decomposition and spectral CT.

Students can expect to work in at least some of these directions as part of the REU. Primary responsibilities will include reviewing some current literature, modifying and implementing Matlab code for different reconstruction approaches, and assessing the performance of these approaches with simulation experiments.