About Publications

# Selected publications

For a full list, see my CV (PDF) or the list on Google Scholar.
1. Alternating dual updates algorithm for X-ray CT reconstruction on the GPU
Madison G. McGaffin, Jeffrey A. Fessler
IEEE Transactions on Computational Imaging, September 2015 (PDF)
Slides from Fully3D 2015 conference (PDF)
This paper demonstrates a way to use the proximal point algorithm with stochastic group coordinate ascent to "split" different parts of a cost function from one another (e.g., a data fidelity term and a noise-reducing regularizer). This trick also allows one to design algorithms that consider only a portion of the data at a time (as in stochastic gradient methods), but provides some convergence theory without relying on relaxation.

2. Edge-preserving image denoising via group coordinate descent on the GPU
Madison G. McGaffin, Jeffrey A. Fessler
IEEE Transactions on Image Processing, April 2015 (PDF)
Slides from SPIE Computational Imaging 2014 (PDF)
This paper presents an intuitive algorithm for doing edge-preserving image denoising using group coordinate descent. The trick is to select the groups of pixels that are uncoupled by the cost function; these pixels can be simultaneously updated on a GPU. Because group coordinate descent requires storing no additional variables besides the problem parameters and the variable being optimized, this algorithm requires very little memory and so is well-suited to the GPU.

3. Algorithmic design of majorizers for large-scale inverse problems
Madison G. McGaffin, Jeffrey A. Fessler
Preprint on arXiv (PDF)
This preprint considers finding a matrix $$D$$ such that $$K'DK \succeq H$$, where $$H$$ is a given large positive semidefinite matrix. This problem could easily be solved with semidefinite programming techniques, if not for needing to manipulate and factor enormous matrices. We present an approach to find majorizers solutions that are approximately minimum Frobenius norm. The method only requires storing vectors and computing matrix-vector products. Our hope is that this opens the door to more exotic and power matrix majorizers that would be difficult to design by hand.

## Dissertation

X-ray CT Image Reconstruction on Highly-Parallel Architectures