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(x(i), y(j)) from a fine number of ray-integrals 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 degrees, 30 degrees) and down to [0 degrees, 20 degrees). The experimental results show that the proposed method reconstructs images more accurately than the known method of convex projections and filtered back projection.