Multiresolution Reconstruction for Cone-Beam Tomography from Raw Data Projections Using 3D Ridgelets

Abstract

This paper presents a novel method which reconstructs any desired 3D image resolution from raw cone-beam CT data. X-ray attenuation through the object is approximated using ridgelet basis functions which allow us to have multiresolution representation levels. Since the Radon data have preferential orientations by nature, a spherical wavelet transform is used to compute the ridgelet coefficients from the Radon shell data. The whole method uses the classical Grangeat's relation for computing derivatives of the Radon data which are then integrated and projected to a spherical wavelet representation and back-reconstructed using a modified version of the well known back-projection algorithm. Unlike previous reconstruction methods, this proposal uses a multiscale representation of the Radon data and therefore allows fast display of low-resolution data level.

3D image reconstruction using Radon transform

“…The simplicity of the FDK method has made it the most used algorithm for cone-beam reconstruction. Another important advantage, is that FDK, in contrast to the exact methods, handles data truncated in the longitudinal direction, so making such useful for a reconstruction from a stack imaging [21,22]. A confocal microscope 64 slices image of size 523×471 pixels of a nucleolus (Fig.…”