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Scuba half-degree extragalactic survey : data reduction by Iterative deconvolution Lepage, Kyle Quentin

Abstract

A generalization of an iterative algorithm used to reduce large data sets consisting of observations of the cosmic microwave background is presented. In particular, the algorithm is modified to reduce data sets obtained by arbitrary observations. The generalized algorithm is applied, in simulation, to a data set consisting of complicated observations taken during a Scuba HAlf Degree Extragalactic Survey (SHADES). The algorithm is found to be unstable. The generalized time-order algorithm is reformulated as a difference equation whose solution gives the Nth iteration reduced data map in analytical form. Within the analytical framework, the convergence properties of the algorithm are determined, a stable, known work-around explained, and the converged map shown to be optimal in the least-squares sense. The known work-around, a modification of the generalized iterative algorithm, trades stability for ideal behaviour at the edge of the reduced data map. Using simulations of a sky populated by a realistic source count model, it is shown that the deleterious effect of the modified algorithm towards the edge of the map is negligible as compared to the statistical noise for most of the half-degree square map. Simulations of the modified algorithm applied to data taken with the SHADES measurement strategy with Gaussian noise added, reveal the presence of streaking and large scale fluctuations in the converged map. The streaking which is demonstrated to be affected only by the measurement strategy, is indicative of a band-diagonal pixel-pixel covariance matrix, and is absent in noiseless simulations. The large scale fluctuations are indicative of non-negligible, far off-diagonal terms in the pixel-pixel covariance matrix, and are also absent in noiseless simulations. The effect of different observation strategies on the streaking is investigated by simulation. The presence of the amplified large scale noise is explained by linear systems theory. The determination of the optimal observation strategy is formulated as the task of determining the linear combination of absolute power measurements which will yield a desired pixel-pixel covariance matrix. This problem is discussed. An un-deconvolved map of real SHADES data is produced. Sources are detected in the un-deconvolved map using Bayesian techniques.

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