CS: Beyond Nyquist, Domain decomposition methods for CS, an internship, CS workshop on Youtube and Optical Imaging and Spectroscopy book and blog

Today, we have two papers, an internship offer, some news from Duke and a new blog:

Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals by Joel Tropp, Jason Laska, Marco Duarte, Justin Romberg, and Richard Baraniuk. The abstract reads:

Wideband analog signals push contemporary analog-to-digital conversion systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient, because the signals of interest contain only a small number of significant frequencies relative to the bandlimit, although the locations of the frequencies may not be known a priori. For this type of sparse signal, other sampling strategies are possible. This paper describes a new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components. Let K denote the total number of frequencies in the signal, and let W denote its bandlimit in Hz. Simulations show that the random demodulator requires just O(K log(W=K)) samples per second to stably reconstruct the signal. This sampling rate is exponentially lower than the Nyquist rate of W Hz. In contrast with Nyquist sampling, one must use nonlinear methods, such as convex programming, to recover the signal from the samples taken by the random demodulator. Finally, the paper provides a theoretical analysis of the system’s performance.

Domain decomposition methods for compressed sensing by Massimo Fornasier, Andreas Langer, Carola-Bibiane Schönlieb. The abstract reads:

We present several domain decomposition algorithms for sequential and parallel minimization of functionals formed by a discrepancy term with respect to data and total variation constraints. The convergence properties of the algorithms are analyzed. We provide several numerical experiments, showing the successful application of the algorithms for the restoration 1D and 2D signals in interpolation/inpainting problems respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.

Amit Agrawal is looking for interns at MERL this summer: Summer Internship (2009) at Mitsubishi Electric Research Labs (MERL)

Starting May 2009 We are looking for a student with experience and interest in one or more of the following topics Computational Imaging/Photography Active illumination LightFields and Applications Motion Deblurring Coded Aperture Techniques Project details are at http://www.merl.com/people/agrawal/index.html
* The student research background should include computer vision and image processing projects.
* Programming experience in Matlab, C/C++
* The student may also submit his/her own proposal for a research project.
* Competitive pay, fun working environment. Please send email to agrawal at merl dot com with resume, dates of availability and area of interest.

While there is no obvious relation to Compressive Sensing, work like the one performed by Roummel Marcia, Zachary Harmany, and Rebecca Willett in their latest paper entitled Compressive Coded Aperture Imaging should be a clue that much work can expand in that area with CS provinding much solid theoretical underpinnings. I have added this announcement to the Compressive Sensing Jobs list.

Rebecca Willett just mentioned to me that the upcoming Compressive Sensing Workshop will be videoed and is expected to be put on the Youtube channel of the meeting. I need to buy myself some popcorn. If somebody wants to be a reporter for NB, it would be nice if you could also have photos of the numerous posters of the poster session. I'll feature each and every one of them on the blog, promise.

Also from Duke, if you recall I mentioned earlier that David Brady would have a book out in 2009 entitled: Optical Imaging and Spectroscopy. Looks like the book already has an attendant website with Matlab and Mathematica codes for each chapter. Chapter 8 featuring some CS reconstruction. The website is at: http://opticalimaging.org/. More Importantly, the book also has an attendant blog: http://opticalimaging.org/OISblog/


Credit Photo: NASA/JPL/Space Science Institute, Saturn rings taken on February 01, 2009