Producing megapixel cosmic microwave background maps from differential radiometer data

A major goal of cosmology is to obtain sensitive, high-resolution maps of the cosmic microwave background anisotropy. Such maps, as would be produced by the recently proposed Microwave Anisotropy Probe (MAP), will contain a wealth of primary information about conditions in the early universe. To mitigate Systematic effects when observing the microwave background, it is desirable for the raw data to be collected in differential form: as a set of temperature differences between points in the sky. However, the production of large (megapixel) maps from a set of temperature differences is a potentially severe computational challenge. We present a new technique for producing maps from differential radiometer data that has a computational cost that grows in the slowest possible way with increasing angular resolution and number of map pixels. The required CPU time is proportional to the number of differential data points, and the required random-access memory is proportional to the number of map pixels. We test our technique, and demonstrate its feasibility, by simulating 1 yr of a spaceborne anisotropy mission.