| The discovery of Carbon Nanotubes and their ability to produce X-rays can usher in a new era in Computed Tomography (CT) technology. These devices will be lightweight, flexible and portable. The proposed device, currently under development, is envisioned as a flexible sheet of tiny X-ray emitters and detectors. The device is wrapped around an appendage to acquire X-ray projections and reconstruct a CT image. However, current CT reconstruction algorithms can only be used if the geometry of the CT device is regular (usually circular). We present an efficient and accurate reconstruction technique that is unconstrained by the geometry of the CT device. Indeed the geometry can be both regular and highly irregular. To evaluate the feasibility of reconstructing a CT image from such a device, a simulation test bed was built to generate simulated CT ray sums of an image. This data was then used in our reconstruction method. The reconstruction method consists of resampling the irregular X-ray projection onto a regular grid, whereupon the Filtered Backprojection method can be used. Our method depends on the ability to know the locations of the X-ray emitters and detectors; we foresee integrating a shape-tracking device into the CT-scanner. In anticipation that a real-world implementation of such a device will have to be robust to measurement errors, we have conducted tests to analyze how our reconstructions behave in the presence of errors. Observations of reconstructions, as well as quantitative results, suggest that this simple method is efficient and accurate. |
