Multi-resolution radiograph alignment for motion correction in X-ray micro-tomography

Achieving sub-micron resolution in lab-based micro-tomography is challenging due to the geometric instability of the imaging hardware (spot drift, stage precision, sample motion). These instabilities manifest themselves as a distortion or motion of the radiographs relative to the expected system geometry. When the hardware instabilities are small (several microns of absolute motion), the radiograph distortions are well approximated by shift and magnification of the image. In this paper we examine the use of re-projection alignment (RA) to estimate per-radiograph motions. Our simulation results evaluate how the convergence properties of RA vary with: motion-type (smooth versus random), trajectory (helical versus space-filling) and resolution. We demonstrate that RA convergence rate and accuracy, for the space-filling trajectory, is invariant with regard to the motion-type. In addition, for the space-filling trajectory, the per-projection motions can be estimated to less than 0.25 pixel mean absolute error by performing a single quarter-resolution RA iteration followed by a single half-resolution RA iteration. The direct impact is that, for the space-filling trajectory, we need only perform one RA iteration per resolution in our iterative multi-grid reconstruction (IMGR). We also give examples of the effectiveness of RA motion correction method applied to real double-helix and space-filling trajectory micro-CT data. For double-helix Katsevich filtered-back-projection reconstruction (≈2500×2500×5000 voxels), we use a multi-resolution RA method as a pre-processing step. For the space-filling iterative reconstruction (≈2000×2000×5400 voxels), RA is applied during the IMGR iterations.