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Irregular point cloud distributions of grid points are used to form a tetrahedral mesh for representation of images reconstructed from projections. Previously we demonstrated that point clouds provide a significant gain in sparseness of a 3D image representation without apparent loss in resolution. Point clouds have been suggested as natural representations for factor analysis of dynamic SPECT data. In order to extract quantitative information about the kinetics of a radiotracer in the body, X-ray attenuation has to be taken into account. In this paper, we investigate attenuation correction methods that can be used with the new method of image representation. The reconstructed function is sampled on an irregular grid (cloud) of points, which is used to form a tetrahedral mesh such that a continuous function is formed by linear interpolation between the vertices of each tetrahedron. The image reconstruction relies on the underlying algorithm that computes the contribution of intensity at each point of the sinogram. The presented work investigates two methods for incorporating the attenuation map into the reconstruction algorithm. For each ray propagation direction, attenuation factors are computed for the tetrahedron vertices. The method is evaluated by applying it to the reconstruction of 210TI canine heart data acquired using the GE Millennium VH Hawkeye SPECT-CT system.