Sparse continuous signal recovery

Reinhard Heckel1 and Kannan Ramchandran

Swiss National Science Foundation P2EZP2_159065

In this project we consider the problem of recovering a signal that is sparse in a continuous dictionary. A concrete example is a signal that is sparse in the continuous dictionary of time-frequecy shifts of a random window function, a problem that arises in radar [1]. We show that the time-frequency shifts can be recovered perfectly, by solving a convex program, provided they are sufficiently separated. A similar problem arises in Multiple Input, Multiple Output (MIMO) radar systems and a variety of other signal processing problems related to localization and line spectral estimation. Important directions of future research are the design of computationally efficient, e.g., sub-linear, algorithms to address such problems.

Figure 1
Figure 1: Super-resolution radar: the effect of band and time-limitation