Modern imaging instruments generally provide multi-value datasets, which means that for a given image pixel, we do not only have one measurement (such as the intensity) but a set of ancillary data. This could be information on color, but in general this extra data set can also be much more complex. The proposed interdisciplinary project intends to develop the next generation of sparse representation methods for complex multi-valued astronomical data in order to probe the fine structure and extract information in high dimensional astronomical data sets. Objectives: Our project will have three main scientific directions: i) Find new decompositions for sparse representation of complex multi-valued data, ii) develop new scheme for data restoration, component separation, data compression using the new sparse representations and iii) apply the new developed techniques on astronomical data. Originality: New sparse representations for such data set is essential for fundamental progress in a wide range of problem areas where traditional multiscale methods have now run their course. Expected results: Our effort will result in three main deliverables. Theory: Coherent, comprehensive knowledge, showing what can and cannot be accomplished with sparse representation. Tools: A wide range of practical algorithms and a unified, publicly available software environment -- SparseAstro-Lab -- deploying them. Applications: Our main initial focus will be on the analysis of data in astronomy, such as those coming soon from the satellites PLANCK, HERSCHELL or GLAST.