Multiresolution reconstruction in fan-beam tomography

A new multiresolution tomographic reconstruction method is investigated for a flat detector fan-beam geometry. To date, almost all connections between wavelets and computerized tomography have only been considered for parallel-beam geometry. Our approach relies on the use of radial and quincunx wavelets to generalize 2D parallel multiresolution reconstruction methods to 2D divergent geometries. In this paper, an approximate inversion formula for a quincunx multiresolution scheme is demonstrated. This efficient algorithm allows one to compute both the quincunx approximation and detail coefficients of an image from its fan-beam projections without extra computational cost compared to the standard fan-beam filtered backprojection algorithm. Obtaining the scale-space representation of the object during the reconstruction process allows one to incorporate directly wavelet-based techniques such as denoising, image analysis and also local tomography. Simulations on mathematical phantoms show that our wavelet tomographic scheme is acceptable for small beam angles but deteriorates at high angles due to non verified approximations