The recent serendipitous discovery of a new population of short duration X-ray transients, thought to be associated with collisions of compact objects or stellar explosions in distant galaxies, has motivated efforts to build up statistical samples by mining X-ray telescope archives. Most searches to date however, do not fully exploit recent developments in the signal and imaging processing research domains to optimise searches for short X-ray flashes. This paper addresses this issue by presenting a new source detection pipeline, STATiX (Space and Time Algorithm for Transients in X-rays), which directly operates on 3-dimensional X-ray data cubes consisting of two spatial and one temporal dimension. The algorithm leverages wavelet transforms and the principles of sparsity to denoise X-ray observations and then detect source candidates on the denoised data cubes. The light curves of the detected sources are then characterised using the Bayesian blocks algorithm to identify flaring periods. We describe the implementation of STATiX in the case of XMM-Newton data, present extensive validation and performance verification tests based on simulations and also apply the pipeline to a small subset of seven XMM-Newton observations, which are known to contain transients sources. In addition to known flares in the selected fields we report a previously unknown short duration transient found by our algorithm that is likely associated with a flaring Galactic star. This discovery demonstrates the potential of applying STATiX to the full XMM-Newton archive.