Enhanced Spatial Resolution in 2D CT-Reconstruction without Filtered Back-Projection: DIRECTT

We report on novel developments of the DIRECTT (Direct Iterative Reconstruction of Computed Tomography Trajectories) algorithm. Details are discussed for model calculations in order to elucidate its universal character for parallel and fan beam geometry. Our approach represents a promising alternative to the conventional filtered back-projection (FP). Instead of Fourier transforming single projections DIRECTT traces single sinoidal-like trajectories in Radon space which are selected from the set of all possible trajectories by appropriate criteria such as their angular averaged (filtered) weight or contrast to adjacent trajectories. The respective reconstruction elements are added to form an array. The projection (Radon transform) of these elements is then subtracted from the original data set. The obtained residual sinogram is treated the same way in the subsequent iteration steps until a pre-selected criterion of convergence is reached. A very precise projection of a gapless reconstruction array is essential for enhanced spatial resolution also taking into account the actual size and shape of its elements (in this case squares). Abandonment of the spatial filtering overcomes some serious restrictions of the FP: (i) Nyquist’s theorem does not refer to the detector pixel sampling (for each single projection!) but holds for the non-equidistant angular oversampling, i.e. the achievable spatial resolution is no longer limited to twice the detector pixel size but can be enhanced considerably (even to subpixels in terms of detector elements) by choosing appropriate small increments of rotation, (ii) there is no need for complete data sets, even missing projections are well tolerated, and (iii) region-of-interest reconstructions perform without considerable artifacts.