Three-dimensional tomographic reconstruction through two-dimensional multiresolution backprojection steps according to Marr's method

A novel algorithm for 3-D tomographic reconstruction is proposed. The proposed algorithm is based on multiresolution techniques for local inversion of the 3-D Radon transform in confined subvolumes within the entire object space. Directional wavelet functions of the form psi(m,n)(x) = 2(j/2) psi(2(j)W(m,n)x) are employed in a sequel of double filtering and 2-D backprojection operations performed on vertical and horizontal reconstruction planes using the method suggested by Marr and others. The densities of the 3-D object are found initially as backprojections of coarse wavelet functions of this form at directions on vertical and horizontal planes that intersect the object. As the algorithm evolves, finer planar wavelets intersecting a subvolume of medical interest within the original object may be used to reconstruct its details by double backprojection steps on vertical and horizontal planes in a similar fashion. Reduction in the complexity of the reconstruction algorithm is achieved due to the good localization properties of planar wavelets that render the details of the projections with small errors. Experimental results that illustrate multiresolution reconstruction at four successive levels of resolution are given for wavelets belonging to the Daubechies family. (C) 2009 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3089883]