2009 Poster Sessions : "Discrete Sampling" -- Reconstructing Signals With Fewest Samples

Student Name : William Wu
Advisor : Brad Osgood
Research Areas: Information Systems, Theory
Abstract :
The Goal: To perfectly reconstruct a k-sparse signal with only k samples.

We present a new approach to the age-old problem of reconstructing a signal from samples, which we call Discrete Sampling (DS). The goal mentioned directly above, while generally impossible, can be achieved using DS by leveraging known side information about the space of signals under consideration, and designing sampling patterns accordingly. To elaborate, in many applications, more may be known about our signals than simply the highest frequency present, or the sparsity factor. Exploiting such situations, Discrete Sampling (DS) can achieve perfect signal reconstruction while taking fewer samples than both the Nyquist-Shannon and Compressed Sensing (CS) paradigms. Furthermore, no on-the-fly convex optimization is required. This makes DS potentially more feasible than CS in real-time applications such as ADC/DAC circuits, where hardware limitations may render the usage of convex optimization solvers impossible. Noise analysis, sampling pattern constraints, and connections of DS with group theory and number theory are also addressed.

William Wu is a Ph.D. student in Electrical Engineering at Stanford University, advised by Brad Osgood. His research interests include discrete harmonic analysis, signal processing, combinatorics, and WLAN optimization. He earned his B.S. in Electrical Engineering and Computer Science from UC Berkeley. His hobbies include juggling, rollerblading, web design, and riddles.