In the past, I have mentioned that one of the big issue when one was trying to arrange a Compressive Sensing system (or any system for that matter) was the issue of calibration. But in compressive sensing, it takes a particular importance as the mixing or multiplexing is supposedly random. Let's take the example of the MIT Random Lens Imager (by Rob Fergus, Antonio Torralba, and William T. Freeman) featured in one of Rich Baraniuk's presentation on Compressive Sensing:
(this video and others can be found on the Compressive Sensing Hardware page [Update: It looks like the video was removed])
After having constructed such a system, one is bound to go through a lengthy calibration process of taking pictures of known elements and their response on the sensor with the eventual expectation that with enough such calibration photos one would be able to build the Point Spread Function or the Camera Response Function. The MIT paper takes the right point of view that the PSF should also be sparse and tries to devise this PSF for a small part of the sensor (they use only a 32x32 section of the CMOS/CDD, see figure 7) and one wonders how one can speed up this process now that we have faster reconstruction algorithms as the MIT report came out in 2006. This issue of finding the (here random) mixing system is known in the literature as blind deconvolution. I did a search on this keyword in my e-mail box that contains the daily dump of my webcrawler and found the following papers that I may or may not have covered:
Non-Iterative Valid Blind Deconvolution of Sparsifiable Images using an Inverse Filter by Andrew Yagle. The abstract reads:
We propose a new non-iterative algorithm for the blind deconvolution problem of reconstructing both a sparsifiable image and a point-spread function (PSF) from their valid 2D convolution. No support constraint is needed for either the image or the PSF, nor is non-negativity of the image. The only requirements are that the PSF be modelled as having a finite support inverse or equalizing filter (IF), and that the product of the (known) numbers of nonzero pixels in this inverse filter and the sparsified image be less than the total number of image pixels. The algorithm requires only the solution of a large linear system of equations and a small rank-one matrix decomposition.
- L. Zhang, A. Cichocki and S. Amari, Geometrical structures of FIR manifold and their application to multichannel blind deconvolution
- Bo Zhang, Ph.D. dissertation: Contributions to fluorescence microscopy in biological imaging: PSF modeling, image restoration, and super-resolution detection
- Anat Levin, Yair Weiss, Fredo Durand, William T. Freeman, Understanding and Evaluating Blind Deconvolution Algorithms
- Kyle Herrity, Raviv Raich and Alfred O. Hero, "Blind deconvolution for sparse molecular imaging
- Kyle Herrity, Raviv Raich and A.O. Hero, "Blind reconstruction of sparse images with unknown point spread function
Let us note that this is not the same case studied by Yaron Rachlin and Dror Baron in The Secrecy of Compressive Sensing Measurements. In that case, the inputs AND the mixing matrix are unknowns.
I also found this job on the interwebs: a postdoc at University of Edinburgh, Scotland, I am adding it to the Compressive Sensing Jobs page:
University of Edinburgh School of Engineering: Research Associate in "Compressed Sensing SAR"
* Vacancy Reference: 3011316
* Department: School of Engineering
* Job Title: Research Associate in "Compressed Sensing SAR"
* Job Function: Academic
* Job Type: Full Time
* Live Date: 29-Jul-2009
* Expiry Date: 20-Aug-2009
* Salary Scale: £20,226 - £23,449
* Internal job: No. Anybody can apply for this position.
* Further Information: Further Information
* Conditions Of Employment: View Conditions of Employment
School of Engineering: Research Associate in "Compressed Sensing SAR"
This post is to investigate a compressed sensing coding techniques for use in Synthetic Aperture Radar (SAR) remote sensing applications.
The purpose of "Compressed sensing SAR" is to provide SAR imaging with a superior compression system that has the capability of practically transmitting large quantities of SAR data to the receiving station over restricted bandwidth with minimal on board computation. The communication or data storage bottleneck is a key factor currently limiting coverage and/or resolution in SAR instruments. Our unique approach to addressing this problem is to utilize the new concept of "compressed sensing" to remove this bottleneck. Compressed sensing has the potential to provide a compression scheme that is bandwidth efficient while requiring minimal on-board processing. The project will explore the feasibility of such a technique and design and evaluate a proof of concept compression system. In addition, you will have the opportunity to work closely with other members of the sparse representations research group within the Institute for Digital Communications.
You will have a PhD (or have recently submitted) or equivalent in engineering, computer science or related discipline, and have a strong background in signal processing. The appointment will be for two years starting on 1st October 2009 or as soon as possible thereafter.
Fixed Term: 2 years