Dynamic Cone-beam Reconstruction for Perfusion Computed Tomography
Perfusion CT (Computed Tomography) is a dynamic imaging technique whose aim is to assess the blood supply to tissue. The limited field of view of current CT detectors restricts its use to perfusion studies of a small volume. The introduction of large area detectors in CT, however, will allow perfusion studies of entire organs, increasing the clinical relevance of perfusion CT. On the other hand, this will also increase patient exposure and requirements for the reconstruction hardware as a consequence of the huge amount of acquired data. This thesis deals with dynamic reconstruction algorithms for scanners with large area detectors within the framework of perfusion CT. Its main focus lies on the development of methods efficient in terms of both the X-ray exposure and the computational cost. The first part of the thesis is devoted to the problem of dynamic reconstruction of objects with time dependent attenuation. Theoretical analysis reveals that the reconstruction from projections in a limited angular interval over several rotations can be interpreted as a non-ideal sampling on a regular grid. Dynamic reconstruction can then be performed by estimating a continuous signal from the samples using an efficient interpolation scheme. A temporal interpolation approach based on polynomial spline interpolation is proposed. This approach increases the temporal resolution for a given sampling rate and thus enables the use of slow rotating scanners for dynamic imaging purposes. Assuming that the maximum frequency of the dynamic process is known, the sampling rate can be adapted according to this frequency in order to acquire only the necessary data to estimate the continuous signal accurately. This leads to a reduction of the acquired data and therefore of the computational complexity. The temporal interpolation approach does not consider noise. The noise level in the images is inversely proportional to the applied dose. According to the sampling interpretation, noise can be reduced by limiting the bandwidth of the estimated continuous signal to the bandwidth of the fastest perfusion signal in the volume of interest. This is denoted as optimal-SNR estimation. Optimal-SNR reconstruction can be carried out independently of the number of scans performed during acquisition as long as the sampling condition is fulfilled. Based on this principle, the temporal interpolation is extended to a temporal smoothing approach with polynomial splines. This approach allows adapting the temporal bandwidth of the reconstructed sequence, yielding an optimal SNR reconstruction for a given total applied dose. This can be used either to reduce dose while preserving image quality as in standard reconstruction, or alternatively to increase image quality while using the same dose as in the standard procedure. Finally, the results obtained in this thesis represent the first step towards the use of C-arm systems for perfusion imaging purposes.
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