Novel tensor transform-based method of image reconstruction from limited-angle projection data

The tensor representation is an effective way to reconstruct the image from a finite number of projections, especially, when projections are limited in a small range of angles. The image is considered in the image plane and reconstruction is in the Cartesian lattice. This paper introduces a new approach for calculating the splitting-signals of the tensor transform of the discrete image f(xi, yj ) from a fine number of rayintegrals of the real image f(x,y). The properties of the tensor transform allows for calculating a large part of the 2-D discrete Fourier transform in the Cartesian lattice and obtain high quality reconstructions, even when using a small range of projections, such as [0, 30o) and down to [0, 20o). The experimental results show that the proposed method reconstructs images more accurately than the known method of convex projections and filtered back-projection.