Nonlinear Inverse Problems in Imaging

Chapter 6

CT, MRI and Image Processing Problems

Image processing has become one of the most important components in medical imaging modalities such as magnetic resonance imaging, computed tomography, ultrasound and other functional imaging modalities. Image processing techniques such as image restoration and sparse sensing are being used to deal with various imperfections in the data acquisition processes of the imaging modalities. Image segmentation, referring to the process of partitioning an image into multiple segments, has numerous applications, including tumor detection, quantification of tissue volume, computer-guided surgery, study of anatomical structure and so on. In this chapter, we review the basic mathematics behind X-ray computed tomography (CT) and magnetic resonance imaging (MRI), and then discuss some image processing techniques.

6.1 X-ray Computed Tomography

X-ray computed tomography (CT) is the most widely used tomographic imaging technique, which uses X-rays passing through the body at different angles. It visualizes the internal structures of the human body by assigning an X-ray attenuation coefficient to each pixel, which characterizes how easily a medium can be penetrated by an X-ray beam Hounsfield (1973). The idea is to visualize the imaging object in a slice by taking X-ray data at all angles around the object based on mathematical methods suggested by Cormack (1963). They shared the 1979 Nobel Prize. Indeed, some of the ideas of CT (reconstructing cross-sectional ...