  Many imaging technologies rely on tomographic reconstruction, which requires
solving a multidimensional inverse problem given a finite number of
projections. Backprojection is a popular class of algorithm for tomographic
reconstruction, however it typically results in poor image reconstructions when
the projection angles are sparse and/or if the sensors characteristics are not
uniform. Several deep learning based algorithms have been developed to solve
this inverse problem and reconstruct the image using a limited number of
projections. However these algorithms typically require examples of the
ground-truth (i.e. examples of reconstructed images) to yield good performance.
In this paper, we introduce an unsupervised sparse-view backprojection
algorithm, which does not require ground-truth. The algorithm consists of two
modules in a generator-projector framework; a convolutional neural network and
a spatial transformer network. We evaluated our algorithm using computed
tomography (CT) images of the human chest. We show that our algorithm
significantly out-performs filtered backprojection when the projection angles
are very sparse, as well as when the sensor characteristics vary for different
angles. Our approach has practical applications for medical imaging and other
imaging modalities (e.g. radar) where sparse and/or non-uniform projections may
be acquired due to time or sampling constraints.
