New Theory and Algorithms for Compressive Sensing

Abstract : In this project we expanded the field of compressive sensing in both theoretical and practical ways. We first demonstrated the information scalability of CS. We applied CS principles to analog-to-digital conversion, showing ADC can be accomplished on structured high rate signals with sub-Nyquist sampling. We introduced a smashed filter to perform statistical classification problems with a rate of measurements that corresponds to the problem structure, rather than bandwidth. Second, we improved on previous work in distributed compressive sensing. We used graphical models to derive performance bounds on multi-sensor settings. Finally, we created a CS-based radar framework and applied it to both 1-D ranging and 2-D synthetic aperture problems.