The improved performance of both X-ray sources and detectors in recent times has seen a number of studies obtain rapid time-resolved data (i.e. spectra, patterns) from multiple positions within a single sample or else from a sample ensemble via the performing of time-resolved imaging/tomography experiments . These 'chemical imaging' techniques have reached a stage whereby they enable the study of functional materials and devices in four or more dimensions i.e. obtaining spatially resolved (1D/2D) spectra/patterns in 2D/3D from an evolving sample, such as a catalytic reactor, a fuel cell or a Li-ion battery, as a function of time (1D) or imposed operating condition/state (e.g. temperature, pressure, potential, chemical environment) 20-26 . The quantity and speed of this data acquisition poses challenges to traditional image reconstruction and analysis techniques. The limits to what is currently achievable with chemical imaging techniques is currently often determined by the density of sampling required for the sinogram in order to achieve good quality image reconstructions. Algorithms for improved reconstruction with more sparsely sampled sinograms are needed to unlock new levels of spatial and temporal resolution in chemical imaging.