Andriyan Suksmono has a blog entry (in Indonesian) on a recent display of a prototype of his Compressive Sensing - Ground Penetrating Radar technology development at IT Bandung.
Last week, I mentioned the paper by Albert Fannjiang, Pengchong Yan and Thomas Strohmer entitled Compressed Remote Sensing of Sparse Objects. In the entry, I made a mistake in my remark that the authors talked about whether or not their sensing matrix satisfied the RIP. Well that was dumb, Thomas Strohmer sent me an e-mail setting me straight on the issue:
Last week, I mentioned the paper by Albert Fannjiang, Pengchong Yan and Thomas Strohmer entitled Compressed Remote Sensing of Sparse Objects. In the entry, I made a mistake in my remark that the authors talked about whether or not their sensing matrix satisfied the RIP. Well that was dumb, Thomas Strohmer sent me an e-mail setting me straight on the issue:
You recently mentioned our paper on "Compressed Remote Sensing of Sparse Objects" .... and focused on our comment that we do not know if our sensing matrices satisfy the RIP or not. Just for clarification: our theoretical results rely on a coherence estimate, not on the RIP. Our theorems show there are explicit thresholds under which we do know exactly (an upper bound of) the coherence of our sensing matrix.
The RIP comes mainly into play since we discuss modeling errors which manifest themselves as matrix perturbation. As far as I know the only results that address sparse recovery under matrix perturbations (i.e., multiplicative noise) are with respect to the RIP. Therefore checking a different condition (e.g. nullspace condition) would not help at this point, since there are no stability results yet for matrix perturbations with respect to those other conditions that you mention.
By the way, the issue of modeling errors comes up in many compressed sensing applications but is usually neglected, since it very often would force us to analyze the transition from the continuous to the discrete setting, which was uncharted territory until now.
Emil Sidky has decided to start a page on his research and how it relates to compressive sensing. It is here. Emil is interested in performed Compressive sensing to the cone-beam or X-ray transform. On top of this, he also looking for a post-doc. As I stated earlier (Coded Imagers: What are they good for ?), I am a big believer that, as we just saw for ghost imaging, we need to reevaluate these coded aperture techniques and see how much better results can come out of using CS encoding schemes and their attendant nonlinear reconstruction techniques. While we are on the subject of CT-scans, Marcus Alley, Garry E. Gold, Robert J. Herfkens, Michael Lustig, John Pauly, and Shreyas Vasanawala were awarded the 2009 Lauterbur Award by the Society of Computed Body Tomography and Magnetic Resonance (SCBT/MR) for their outstanding research project "Faster Pediatric MRI with Compressed Sensing." Congratulations to them! Here is what I note in this press release.
"...His work sets the table for transforming MRI into a common pediatric imaging procedure replacing many CT studies and reducing the radiation burden on children."
"...His work sets the table for transforming MRI into a common pediatric imaging procedure replacing many CT studies and reducing the radiation burden on children."
In other words, Compressive sensing is likely useful to both MRI and CT and the question is Will CS tips the scale in favor of X-rays or MRI ? Will coded aperture in CT reduce the radiation burden to the point where an MRI replacement would not make an economic sense ?
The Sparsity in Machine Learning meeting featured other presentations related to Compressive Sensing. I featured the talk by Jared Tanner on Phase transitions phenomenon in Compressed Sensing on friday. There is also
- Fast methods for sparse recovery: alternatives to L1 by Mike Davies
- Algorithmic Strategies for Non-convex Optimization in Sparse Learning by Tong Zhang
- Distilled Sensing: Active sensing for sparse recovery by Rui Castro
No comments:
Post a Comment