Optimal Linear Image Combination

Abstract

A simple, yet general, formalism for the optimized linear combination of astrophysical images is constructed and demonstrated. The formalism allows the user to combine multiple undersampled images to provide oversampled output at high precision. The proposed method is general and may be used for any configuration of input pixels and point spread function; it also provides the noise covariance in the output image along with a powerful metric for describing undesired distortion to the image convolution kernel. The method explicitly provides knowledge and control of the inevitable compromise between noise and fidelity in the output image. We present a first prototype implementation of the method, outlining steps taken to generate an efficient algorithm. This implementation is then put to practical use in reconstructing fully-sampled output images using simulated, undersampled input exposures that are designed to mimic the proposed \emph{Wide Field InfraRed Survey Telescope} (\emph{WFIRST}). We examine results using randomly rotated and dithered input images, while also assessing better-known "ideal" dither patterns: comparing results we illustrate the use of the method as a survey design tool. Finally, we use the method to test the robustness of linear image combination when subject to practical realities such as missing input pixels and focal plane plate scale variations.