Imaging and Computing Seminar

Justin Romberg

Topics in Compressed Sensing: Random Convolution and Dynamic Updating

In this talk, we will cover two topics related to compressed sensing (CS). The first has to do with making compressed sensing more "physical". Many of the essential results in CS rely on measurement devices which correlate signals against a series of random waveforms. While there are certain applications in which this can be accomplished, it often requires exotic new hardware. We will show that essentially the same theory can be developed for systems which convolve a signal with a random pulse and then sample the result, a framework which is directly applicable to a number of "active imaging" applications. We will also discuss how mathematical methods from CS can be applied to channel estimation in multiple-input multiple-output (MIMO) systems.

In the second part of the talk, we will discuss recent progress on algorithms aimed at making compressive sampling "dynamic". We will show how the solutions to L1 optimization programs can be efficiently updated as 1) the signal we are measuring changes, and 2) new measurements are added, and stale ones are removed. The algorithms are based on homotopy methods, and are somewhat analogous to recursive least-squares in that they can be reduced to a series of low-rank updates.