Soft X-ray microscopy coupled with low energy X-ray fluorescence is a powerful tool for investigating complex biological systems like cells and tissues. Due to certain characteristics of X-ray sources, sample stage motors, and detectors, the examination of large areas at high resolutions is very time consuming, often confining the analysis only to a restricted number of pre-selected representative regions. Here we propose and demonstrate a compressive sensing method that provides an alternative approach for overcoming such limitations and can be applied to different kinds of samples and other microscopy and analytical techniques.