Bayesian multiresolution method for local X-ray tomography in dental radiology

Dental tomographic cone-beam X-ray imaging devices record truncated projections and reconstruct a region of interest (ROI) inside the head. Image reconstruction from the resulting local tomography data is an ill-posed inverse problem. A Bayesian multiresolution method is proposed for the local tomography reconstruction. The inverse problem is formulated in a well-posed statistical form where a prior model of the tissues compensates for the incomplete projection data. Tissues are represented in a reduced wavelet basis, and prior information is modeled in terms of a Besov norm penalty. The number of unknowns in the inverse problem is reduced by abandoning fine-scale wavelets outside the ROI. Compared to traditional voxel based reconstruction methods, this multiresolution approach allows significant reduction in number of unknown parameters without loss of reconstruction accuracy inside the ROI, as shown by two dimensional examples using simulated local tomography data.