One way of imaging X-ray emission from solar flares is to measure Fourier components of the spatial X-ray source distribution. We present a new Compressed Sensing-based algorithm named VIS CS, which reconstructs the spatial distribution from such Fourier components. We demonstrate the application of the algorithm on synthetic and observed solar flare X-ray data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI ) satellite and compare its performance with existing algorithms. VIS CS produces competitive results with accurate photometry and morphology, without requiring any algorithm-and X-ray source-specific parameter tuning. Its robustness and performance make this algorithm ideally suited for generation of quicklook images or large image cubes without user intervention, such as for imaging spectroscopy analysis.Back projection -The back projection algorithm performs an inverse Fourier transform where all non-measured Fourier components are assumed to be zero. The resulting reconstructions show heavy ringing artefacts