My recent research interests mainly focus on algorithm design, theoretic analysis, and applications of Compressive Sensing (CS). CS is a revolutionary methodology of simultaneously sensing and compressing signals, and builds a new sampling theorem beyond the Nyquist rate. We are currently interested in some fundamental issues of optimal sensing matrix design, fast and accurate sparse signal recovery algorithms, dictionary learning, and theoretical but more practical bounds for sparse signal recovery. For optimal sensing matrix design, conventional approaches are mostly based on reducing mutual coherence between a pair of sensing matrix and sparsifying basis. This seems to be intuitive and reasonable but the resultant optimal sensing matrix does not necessarily lead to good performance of sparse signal recovery. We will investigate this topic by exploring and comparing the existing criteria. For sparse signal recovery, many algorithms have been proposed. However, we find that the theoretic recovery bound and practical performance are still not consistent. In fact, it is very often that the theoretical bounds are too strict to fit practical situations. Our goal will be to close the gap between them.
Our representative results on compressive sensing are summarized as follows:
(1) We have proposed a sparse Fast Fourier Transform (sFFT) method that can be faster than MIT’s methods (also known as state-of-the-art) with better reconstructed results. The advantage also includes the easy selection of parameters and easy implementation for sFFT without needing to know sparsity of a signal.
(2) We have developed compressed sensing detector design for space shift keying for MIMO systems, compressed sensing-based clone identification method for sensor networks, and compressed sensing-based cooperative spectrum sensing for cognitive radio networks.
(3) We have presented a distributed compressive video sensing (DCVS) method to simultaneously sensing and compressing videos.