How to Make Maps from Cosmic Microwave Background Data without Losing Information

Abstract

The next generation of cosmic microwave background (CMB) experiments can measure cosmological parameters with unprecedented accuracy—in principle. To achieve this in practice when faced with such gigantic data sets, elaborate data analysis methods are needed to make it computationally feasible. An important step in the data pipeline is to make a map, which typically reduces the size of the data set by orders of magnitude. We compare 10 map-making methods and find that for the Gaussian case, both the method used by the COBE Differential Microwave Radiometer (DMR) team and various forms of Wiener filtering are optimal in the sense that the map retains all cosmological information that was present in the time-ordered data (TOD). Specifically, one obtains just as small error bars on cosmological parameters when estimating them from the map as one could have obtained by estimating them directly from the TOD. The method of simply averaging the observations of each pixel (for total-power detectors), on the contrary, is found generally to destroy information, as does the maximum entropy method and most other nonlinear map-making techniques. Since it is also numerically feasible, the COBE method is the natural choice for large data sets. Other lossless (e.g., Wiener-filtered) maps can then be computed directly from the COBE method map.