2D image reconstruction from sparse line-integral data

The problem of reconstructing images on the basis of very sparse and noisy line-integral data is addressed. The strategy adopted has been that of the standard Tikhonov regularization theory which allows a unique and stable solution to be selected for an ill-posed, ill-conditioned inverse problem. The performances of two different stabilizers measuring the energy and smoothness of the solution have been investigated for the reconstruction of a particular test image. The fundamental result obtained was that regularization can improve the quality of reconstructed images with respect to the traditional least squares method for particularly small data sets and low signal-to-noise ratios. © 1991.