Paper of the Day (Po’D): My EUSIPCO Papers Day 2 Edition

Tomorrow at EUSIPCO 2012, I present my third paper. And to remind myself of what I did, I present a Po’D:
B. L. Sturm, “When ‘exact recovery’ is exact recovery in compressed sensing simulation,” Proc. European Signal Processing Conference, Bucharest, Romania, Aug. 2012.

This paper is essentially described in this post, with a link to a failed submission that confused both reviewers. My EUSIPCO submission also confused a reviewer, but this time four other reviewers were not confused — so I made some progress! Nonetheless, I made considerable changes for the camera ready paper to make its purpose even more clear, and to make as sure as I could that every claim is correct. I also changed the title from “When ‘exact recovery’ is exact recovery in compressive sampling” — adding the “simulation” bit to make the following more clear.
This paper is entirely a practical paper. It has not even an ounce of CS theory, and so it does not make any sort of contribution to CS theory. It is the first of a few papers I am writing about the effects of the decisions we make in simulating algorithms for recovering signals from compressive sampling. This interest grows out of reading many papers with differing experimental designs, not to mention
my empirical work.

In simulating a CS recovery algorithm over the phase plane, we have to make a choice of when a signal is recovered. Of course, the definition of exact recovery should come from the application; but in these times of prolific algorithm design, we need to just simulate and compare. In this paper, I look closely at two common definitions that have been used: one based on support, and another based on normalized squared error.
I seek to answer when they are the same, and what is the meaning of the parameter on the latter. I look at both noisy and noiseless conditions, making particular assumptions on the signals (which I call the “best case scenario”), and answer these questions in ways that show how these two exact recovery criteria are related, and how to set the parameter of one of them.

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