| Traditionally, x-ray CT images are produced by an algorithm called filtered back projection, or FBP. FBP is an analytical solution to the idealized CT image reconstruction problem, the inverse problem of turning raw x-ray measurements into a full 3-dimensional (3D) image, and is derived assuming a continuous set of noiseless measurements. However real CT data are noisy and biased, especially so if the scans are performed at low x-ray dose, and advanced statistical estimation techniques have been shown to produce higher quality images than FBP. This work presents two applications of statistical modeling in CT image reconstruction. The first application discusses the statistics of CT data noise, and compares the performance of several common models for estimation in a simplified 1D experiment. The second application concerns modeling temporal CT data, in which the measured data typically contain redundancies. It proposes an estimation method that exploits these redundancies to address two key challenges in CT image reconstruction: reducing noise and lowering computation time. We demonstrate this noise reduction analytically and through experimental simulations. In addition, a third study validates the use of the statistical models used in this work by comparing them to measured data from a clinical CT scanner. Overall, these methods contribute to the methodology of statistical CT image reconstruction to enable ultra-low dose x-ray CT imaging. |
