Schedule for Short course

Saturday, September 5, 2009

This short course on image reconstruction will be divided in eight sessions of 45 minutes each. The first session, given by Dr. Defrise, will discuss fundamental aspects of image reconstruction. These aspects include on one hand the problem of data modeling, with the option of using either discrete or continuous models, and, on the other hand, the issue of ill-posed problems and the regularization concept.

The second, the third and the fourth sessions, given by Dr. Noo, will focus on analytical reconstruction methods. The first of these three sessions will be on two-dimensional tomography in parallel-beam geometry. Two algorithms will be reviewed: the classical filtered-backprojection method, and the two-step Hilbert method. In each case, the review will address the problem of implementation, emphasizing difficulties and remedies.

The third session will be on cone-beam tomography. The 3D Radon transform and its use for reconstruction from cone-beam projections will be first presented. Then, the problem of developing efficient filtered-backprojection methods in cone-beam geometry will be discussed and illustrated with examples.

The fourth session will first present the fundamental formula of Katsevich for helical cone-beam tomography. This presentation will be based on the general filtered-backprojection theory discussed in the previous session, and will emphasize the aspects of efficiency and good data utilization. Afterwards, a generalization of the two-step Hilbert method to cone-beam tomography will be presented along with a discussion of its pro and cons over filtered-backprojection techniques.

The fifth, sixth, and seventh sessions, given by Dr. Qi, will focus on iterative reconstruction methods. The first of these three sessions will discuss the basics of statistical image reconstruction, with a detailed review of two fundamental approaches: the maximum-likelihood method and the Maximum A Posteriori formulation.

The sixth and the seventh session will discuss the challenging problem of performing the iterative reconstruction in a computationally-efficient way. Several approaches have been devised over time, and the most successful techniques will be reviewed. These include expectation maximization, pre-conditioned conjugate gradient, optimization transfer, and ordered-subset techniques. Time permitting, further advanced topics such as the problem of characterizing the image properties for iterative reconstructions will be discussed.

Developing improved reconstruction algorithms require a careful analysis of image quality. The last session, given by Dr. Defrise, will discuss the problem of image quality assessment. Various figures of merit will be discussed along with their strengths and limitations. These figures include noise-versus-resolution curves and task-based metrics.