Sparseness Measures of Signals for Compressive Sampling

Recent theoretical developments in compressive sampling (or compressed sensing) show that if a signal has a sparse representation in some basis, then it is possible to capture the signal information via a small number of projections. Furthermore, the signal can be accurately reconstructed using low complexity algorithms. Although the information encoding process may be agnostic to signal type - random projections can capture the information with high probability - accurate reconstruction of the signal often depends on proper selection of a reconstruction basis. In this paper, we evaluate techniques for measuring sparseness, including some not traditionally used in signal processing, and apply them to compressive sampling with the goal of selecting the best basis for signal reconstruction.