We present the method of multiplexed imaging designed for astronomical observations of large sky areas in the IR, visible and UV frequencies. Our method relies on the sparse nature of astronomical observations. The method consists of an optical system that directs light from different locations on the focal plane of a telescope onto the same detector area and an algorithm that reconstructs the original wide-field image. In this way we can use a physically small detector to cover a wide field of view. We test our reconstruction algorithm using public space telescope data. Our tests demonstrate the reliability and power of the multiplexed imaging method. Using our method it will be possible to increase the sky area covered with space telescopes by 1-3 orders of magnitude, depending on the specific scientific goal and optical parameters. This method can significantly increase the volume of astronomical surveys, including search programs for exoplanets and transients using space and ground instruments.