Reconstruction from Radon projections and orthogonal expansion on a ball

The relation between Radon transform and orthogonal expansions of a function on the unit ball in \RR^d is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to algorithms for image reconstruction from Radon data. The relation between orthogonal expansion and the singular value decomposition of the Radon transform is also exploited.Comment: 15 page

The Atacama Cosmology Telescope (ACT): Beam Profiles and First SZ Cluster Maps

The Atacama Cosmology Telescope (ACT) is currently observing the cosmic microwave background with arcminute resolution at 148 GHz, 218 GHz, and 277 GHz. In this paper, we present ACT's first results. Data have been analyzed using a maximum-likelihood map-making method which uses B-splines to model and remove the atmospheric signal. It has been used to make high-precision beam maps from which we determine the experiment's window functions. This beam information directly impacts all subsequent analyses of the data. We also used the method to map a sample of galaxy clusters via the Sunyaev-Zel'dovich (SZ) effect, and show five clusters previously detected with X-ray or SZ observations. We provide integrated Compton-y measurements for each cluster. Of particular interest is our detection of the z = 0.44 component of A3128 and our current non-detection of the low-redshift part, providing strong evidence that the further cluster is more massive as suggested by X-ray measurements. This is a compelling example of the redshift-independent mass selection of the SZ effect.Comment: 16 pages, 10 figures. Accepted for publication in ApJS. See Marriage et al. (arXiv:1010.1065) and Menanteau et al. (arXiv:1006.5126) for additional cluster result