CS: Compressive Sensing Hardware Update, Compressive estimation , General Deviants, a conference, Adaptive CS, 2 graduate asstships.

In view of the number of hits coming the Technology Review Arxiv blog, I have updated the Compressive Sensing Hardware section to include the PACS/Herschel camera. The reason,  Since MRI is one of these technologies, I don't see why I shouldn't include other hardware that already exists and for which the means of sampling has been changed to implement Compressive Sensing. I have also tried to include Hardware on described in papers as opposed to already implemented design. Both type of hardware, fit on both end of the Technology Readiness Level scale (see my entry in French on what TRLs are). Please let me know the ones I am missing. Thanks!

Wotao Yin has upgraded his website to better explain what he does in the field of Compressive Sensing. He also has an opening for two graduate students starting this coming summer. More on his webpage or on the CS Jobs page.

In a previous entry, I introduced General Deviants: An Analysis of Perturbations in Compressed Sensing by Matthew A. Herman and Thomas Strohmer. Matt Herman sent me the following describing his paper succintly:

...The main points of the paper are that we extended the general noisy CS model from

b = Ax + e
(which only accounts for simple, uncorrelated, additive noise e)

to also include a perturbation E to the measurement matrix A

b = (A+E)x + e,

and found the conditions under which recovery with Basis Pursuit was stable. The extra term Ex can be thought of as multiplicative noise and is harder to deal with than simple additive noise since it is correlated with the signal x.

It is important to consider perturbations to the measurement matrix A since the physical implementation of sensors is never perfect in the real world (thus the matrix E can represent precision errors or other non-ideal phenomena). Viewed in a different way, the matrix A can also model a channel that a signal passes through such as in radar, telecommunications, or in source separation problems. The models of these types of channels always involve assumptions and/or approximations of their physical characteristics. In that way, the matrix E can absorb errors in these assumptions. Factors such as these must be accounted for in real-world devices.

These details are also explained in the introductory first few paragraphs of our paper.

Thanks Matt !

Simon Foucart let me know that the 13th Approximation Theory conference will take place in San Antonio on March 7-10, 2010 and will feature a minisymposium on Compressive Sensing embedded in there. I'll put the date on the Compressive Sensing Calendar.

Adaptive compressed image sensing based on wavelet modeling and direct sampling by Shay Deutsch and Amir Averbuch and Shai Dekel . The abstract reads:

We present Adaptive Direct Sampling (ADS), an improved algorithm for simultaneous image acquisition and compression which does not require the data to be sampled at its highest resolution. In some cases, our approach simplifies and improves upon the existing methodology of Compressed Sensing (CS), by replacing the ‘universal’ acquisition of pseudo-random measurements with a direct and fast method of adaptive wavelet coefficient acquisition. The main advantages of this direct approach are that the decoding algorithm is significantly faster and that it allows more control over the compressed image quality, in particular, the sharpness of edges.

Finally, found on Arxiv: Compressive estimation of doubly selective channels: exploiting channel sparsity to improve spectral efficiency in multicarrier transmissions by Georg Tauboeck, Franz Hlawatsch and Holger Rauhut. The abstract reads:

We consider the estimation of doubly selective wireless channels within pulse-shaping multicarrier systems (which include OFDM systems as a special case). A pilot-assisted channel estimation technique using the methodology of compressed sensing (CS) is proposed. By exploiting a channel's delay-Doppler sparsity, CS-based channel estimation allows an increase in spectral efficiency through a reduction of the number of pilot symbols that have to be transmitted. We also present an extension of our basic channel estimator that employs a sparsity-improving basis expansion. We propose a framework for optimizing the basis and an iterative approximate basis optimization algorithm. Simulation results using three different CS recovery algorithms demonstrate significant performance gains (in terms of improved estimation accuracy or reduction of the number of pilots) relative to conventional least-squares estimation, as well as substantial advantages of using an optimized basis.

Credit Photo: MPE