Methods for Few-View CT Image Reconstruction

Abstract

Computed Tomography (CT) is an essential non-destructive three dimensional imaging modality used in medicine, security screening, and inspection of manufactured components. Typical CT data acquisition entails the collection of a thousand or more projections through the object under investigation through a range of angles covering one hundred eighty degrees or more. It may be desirable or required that the number of projections angles be reduced by one or two orders of magnitude for reasons such as acquisition time or dose. Unless specialized reconstruction algorithms are applied, reconstructing with fewer views will result in streak artifacts and failure to resolve object boundaries at certain orientations. These artifacts may substantially diminish the usefulness of the reconstructed CT volumes. Here we develop constrained and regularized numerical optimization methods to reconstruct CT volumes from 4-28 projections. These methods entail utilization of novel data fidelity and convex and non-convex regularization terms. In addition, the methods outlined here are usually carried out by a sequence of two or three numerical optimization methods in sequence. The efficacy of our methods is demonstrated on four measured and three simulated few-view CT data sets. We show that these methods outperform other state of the art few-view numerical optimization methods.

Figures (8)

• Figure 1: Sampling the fan-beam X-ray Transform. (left) Essential support of the 2D Fourier Transform of the fan-beam X-ray Transform. The vertical direction is the frequency variable for $u$ (detector column) and the horizontal direction is the frequency variable for $\beta$ (projection angle). Aliased copies of the essential support of the 2D Fourier Transform of the fan-beam X-ray Transform for the cases when the angles are (center) sufficiently sampled and (right) under-sampled.
• Figure 2: An example of a histogram sparsity loss function with target values $\mu = (0.0, 0.02, 0.069)$.
• Figure 3: Reconstructed slices of 19 measured CT projection of a 180 um diameter glass fiber. Notice that the Simple Function RLS image is the only image where the germanium-doped core at the center of the image is visible.
• Figure 4: Reconstruction of flash x-ray CT data at DEVCOM ARL using the RDLS algorithm. (top left) 3D rendering of a bullet passing through an aluminum plate, where it is possible to observe the bullet jacket has been stripped from its core. (top right) 3D rendering of an explosive charged detonator at an early time when the detonation front is still in the booster. (bottom left) Same as top right, but showing a reconstructed slice. (bottom right) Same as bottom left, but here the imaging was taken at a later time when the detonation front was in the main charge.
• Figure 5: Reconstructed slices from 28 simulated projections.