Image reconstruction from line-integral data: a regularization approach

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 image is first modeled as a finite Fourier series and then a set of coefficients which have low norm are searched from all those consistent with the data. The basic 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.