Nonlocal prior Bayesian tomographic reconstruction

Bayesian approaches, or maximum a posteriori (MAP) methods, are effective in providing solutions to ill-posed problems in image reconstruction. Based on Bayesian theory, prior information of the target image is imposed on image reconstruction to suppress noise. Conventionally, the information in most of prior models comes from weighted differences between pixel intensities within a small local neighborhood. In this paper, we propose a novel nonlocal prior such that differences are computed over a broader neighborhoods of each pixel with weights depending on its similarity with respect to the other pixels. In such a way connectivity and continuity of the image is exploited. A two-step reconstruction algorithm using the nonlocal prior is developed. The proposed nonlocal prior Bayesian reconstruction algorithm has been applied to emission tomographic reconstructions using both computer simulated data and patient SPECT data. Compared to several existing reconstruction methods, our approach shows better performance in both lowering the noise and preserving the edges.