## Imaging and Computing Seminar

### Justin Romberg

**Title:**

Topics in Compressed Sensing: Random Convolution and Dynamic
Updating

**Abstract:**

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.