Title: Solving Inverse Problems in Matlab
Abstract:
We present the inverse problem for image reconstruction and regularization, along with a Matlab implementation to solve it. This type of problem is present in many areas of MR imaging where research in this field is motivated by the desire to reduce the imaging time inside the magnet which in turn reduces patient discomfort and costs incurred by health care system. As a case study, the MR velocity imaging problem is modeled and solved using the conjugate gradient implementation in Matlab. We show how the problem can be formulated to be solved by the Matlab lsqr function and how regularization terms can be added to the problem. The implementation solves the problem of missing data and noisy data that are present in real application. Results obtained from using the discrete Laplacian as a regularizer are presented and how the sampling strategy affects these results.

The paper and presentation are available at http://www.cas.mcmaster.ca/~elshawn/.