Uncertainty assessment for reconstructions based on deformable geometry

Deformable geometric models can be used in the concannot be solved with conventional reconstruction algorithms, as text of Bayesian analysis to solve ill-posed tomographic reconstrucshown in Reference [5] , for example. Our ability to obtain an tion problems. The uncertainties associated with a Bayesian analysis excellent reconstruction emphasizes the advantage of using demay be assessed by generating a set of random samples from the formable models in tomography when objects have a relatively posterior, which may be accomplished using a Markov Chain Monte simple shape and possess uniform density. MCMC provides the Carlo (MCMC) technique. We demonstrate the combination of these means to verify the reliability of our reconstruction. Conventional techniques for a reconstruction of a two-dimensional object from two approaches to uncertainty estimation are not adequate to treat this orthogonal noisy projections. The reconstructed object is modeled in problem because of the nonlinear relation between the data and terms of a deformable geometrically defined boundary with a uniform the model parameters and, hence, the potential nonGaussian nainterior density yielding a nonlinear reconstruction problem. We show how an MCMC sequence can be used to estimate uncertainties in ture of the posterior distribution. the location of the edge of the reconstructed object. q 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 506–512, 1997 II. BAYESIAN ANALYSIS Bayesian analysis provides the ultimate means of the analysis of uncertainties in the interpretation of data with respect to models.