Introduction

Sampling and reconstruction has been an area of great research in medical imaging. The research community has already proven that the BCC lattice is the optimal regular sampling pattern in 3D. However, medical image acquisition has been traditionally carried out on the Cartesian grid. For 3D medical images, the BCC lattice can save roughly 30% samples over the Cartesian lattice. For time-varying 3D medical sequences, the savings reach nearly 50%. In other words, for time-varying 3D scans, we can either achieve twice the frame rate at the same visual quality, or double the amount of details. Further, higher dimensional lattices analogous to the BCC lattice may exist, and could potentially offer savings of over 50%. Thus, optimality research on BCC sampling may be extensible to higher dimensions. That could in turn help the many researchers in the medical imaging community who are working on techniques involving higher dimensions.

For those reasons, the BCC grid seems well-positioned to take over the Cartesian grid in medical imaging. However, due to a lack of tools operating on the BCC lattice, this has not yet happened. On the other hand, due to the lack of tools, interest in the research community on BCC sampling has not been high. One way to break out of this cycle is to generate more tools for the BCC lattice; that is the chief motivation behind this project.

Whether in the area of medical image segmentation or registration, two types of basic tools seem necessary: one for analyzing the error due to reconstruction, and one for analyzing the error due to noise. I have investigated the first type of error for the BCC grid in a previous course project. For this course project, I intend to investigate the second type of error for the BCC grid.