Attenuation map reconstruction using topology constrained labeling

In order to derive a quantitative reconstructed image in various types of emission CT (ECT), such as SPECT and PET, it is necessary to examine the gamma ray attenuation coefficient distribution inside the body, called the attenuation map, by transmission CT (TCT), and to apply attenuation correction. This paper proposes a new method in which the attenuation map is reconstructed from the incomplete TCT projection data or ECT projection data. The conventional attenuation map reconstruction method is performed, assuming that each pixel of the attenuation map takes a continuous value. In the proposed method, in contrast, the attenuation map is reconstructed by region segmentation in which the pixel value takes only discrete values. The problem is formulated as a labeling problem in which the label image minimizing the energy function is to be determined. In order to avoid local minima, the solution is derived by stochastic relaxation. In the conventional formulation of image region segmentation, however, the search space for the solution is too wide, and it is difficult to derive an accurate attenuation map if the measured data are incomplete. Consequently, this paper proposes topology constrained labeling, in which topology constraints, that is, a priori information on the topology (the number of regions and the connection relations among the regions) of the attenuation map to which the region segmentation is applied, are used, and (he solution search space is constrained. Simulation experiments, as well as an experiment using the actual PET data, were performed, and the effectiveness of the topology constrained labeling has been demonstrated. (C) 2003 Wiley Periodicals, Inc.