Geometric Deconvolution: A Meta-Algorithm for Limited View Computed Tomography

Images reconstructed using a limited number of projections spanning a narrow angular range suffer from a systematic geometric distortion due to the two-dimensional point spread function of the reconstruction process. Applying the projection theorem, we show that the problem of removing this distortion reduces to that of estimating the one-dimensional spread function and deconvolving projections computed for a complementary set of new angles from the initial reconstruction. A second reconstruction is performed using the deconvolved projections along with the original set of projections, thus incorporating wider angular coverage. We present here initial results of such geometric deconvolution performed via inverse filtering using fast Fourier transform techniques. While the results are noisy due to well-known problems associated with inverse filtering, they illustrate the plausibility of the underlying ideas.