MAP Tomographic Reconstruction with a Spatially Adaptive Hierarchical Image Model

A method for penalized likelihood tomographic reconstruction is presented which is based on a spatially adaptive stochastic image model. The model imposes onto the image a smoothing Gaussian prior whose parameters follow a Gamma distribution. Three variations of the model are examined: (i) a stationary model, where the Gamma distribution has the same constant parameter for the entire image, (ii) a non stationary model, where this parameter varies with respect to location and (iii) a non stationary directional model where the parameter varies also with respect to orientation (horizontal or vertical direction). In all cases, the MAP criterion provides a closed form solution for both the unknown image and the parameters of the model. Numerical experiments showed that the reconstructions obtained using the proposed image priors outperform the state of the art EM based methods.