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The goal of 4D computed tomography (4D CT) is to study the temporal behavior of a 3D sample with a sufficiently high temporal and spatial resolution. Conventionally, the sample is sequentially scanned, resulting in datasets of successive time frames. Each of these datasets is then independently reconstructed. This framework results in a trade-off between the temporal resolution and the signal to noise ratio (SNR) of the reconstructed images. The proposed registration based simultaneous iterative reconstruction technique (RB SIRT) allows shortening the acquisition time per time frame, thereby improving the temporal resolution, without decreasing the SNR. To this end, the algorithm estimates the deformation field between different time frames, which allows adding projections of other time frames into the reconstruction of a particular time frame. The technique was validated on a real dynamic experiment of a polyurethane foam sample. The reconstructions obtained with RB SIRT have a significantly higher SNR with respect to conventional reconstructions.

In computed tomography (CT), X-ray projections are acquired from different angles, which are then used to reconstruct a 3D image. Prior to reconstruction, the projections have to be normalised with respect to a white field, which is generally referred to as Flat Field Correction (FFC). The white field is computed from projections acquired without object between the x-ray source and detector. Conventional FFC assumes the flat fields to be stationary. However, due to beam intensity changes, temperature fluctuations or detector efficiency fluctuations, dynamic changes are observed resulting in projections that are not properly FFC corrected. We propose an efficient procedure to model and correct for flat field dynamics. The dynamics of the flat fields are described by eigen flat fields, derived from a series of prior and/or post flat fields using Principal Components Analysis (PCA). A time dependent flat field can then be approximated by a linear combination of the mean flat field and a limited number of eigen flat fields (EFF). The weights of these EEF in a Xray projections are estimated by minimizing the total variation using a non-linear optimization algorithm. Results on synchrotron CT datasets show that the proposed technique results in projections with almost no artefacts due to flat field fluctuations. Furthermore, the reconstructions show reduced flat field induced artefacts.