Sparse X-ray tomography for medical imaging

X-ray tomography is based on recording several radiographs of a target along different projection directions. The inner structure of the target is then recovered from the data, interpreted as a collection of line integrals over a non-negative X-ray attenuation function. In recent years, mathematical methods have enabled three-dimensional medical X-ray imaging using much lower radiation dose than before. The idea is to collect fewer projection images than traditional computerized tomography machines and then use advanced inversion mathematics to reconstruct the tissue from such incomplete data. One particularly successful methodology is to regularize the inversion by enforcing sparsity in some suitable basis. In this talk we discuss the traditional total variation regularization, leading to sparsity in the image gradient, and sparsity in the shearlet basis. Computational results are shown, based on both simulated and measured data. Also, discussed is a commercial dental low-dose X-ray imaging product based on sparsity-promoting inversion. Special attention is given to automatic choice of regularization parameters.