Sunday, October 24, 2010

CS: The Compressive Mutliplexer for Multi-Channel Compressive Sensing, Limited Feedback For Cognitive Radio Networks, Phase retrieval and a job

When I read this presentation entitled Compressed sensing with coherent and redundant dictionaries by Deanna Needell, I nearly spilled my coffee when I got to the verbose slide 21....

and the more to the point slide 22.

I know... I am a nerd. Another example for overcomplete dictionary includes voice as illustrated in a recent entry in Bob Sturm's blog entry (and comments). The audio folks are not prepared to use CS hardware because they are already getting good data from their sometimes expensive microphones. I am of the view that a CS based hardware would produce other kind of data than just quaint sound recording.

The recently developed compressive sensing (CS) framework enables the design of sub-Nyquist analog-to-digital converters. Several architectures have been proposed for the acquisition of sparse signals in large swaths of bandwidth. In this paper we consider a more flexible multi-channel signal model consisting of several discontiguous channels where the occupancy of the combined bandwidth of the channels is sparse. We introduce a new compressive acquisition architecture, the compressive multiplexer (CMUX), to sample such signals. We demonstrate that our architecture is CS-feasible and suggest a simple implementation with numerous practical advantages.
In this paper, we consider the downlink of a cognitive radio network where a cognitive base station serves multiple cognitive users on the same frequency band as a group of primary transceivers. The cognitive base station uses an orthogonal scheduling scheme (TDMA/FDMA) to serve its users. For this purpose, the base station is interested in acquiring an estimate of the interference (from the primary network) power at each of its cognitive receivers as a measure of channel quality. This can be surely achieved if we allow for the feedback (from the cognitive receivers to the cognitive base station) bandwidth to scale linearly in the number of cognitive receivers, but in densely populated networks, the cost of such an acquisition might be too high. This leads us to the question of whether we can do better in terms of bandwidth efficiency. We observe that in many scenarios – that are common in practice – where the primary network exhibits sparse changes in transmit powers from one scheduling instant to the next, it is possible to acquire this interference state with only a logarithmic scaling in feedback bandwidth. More specifically, in cognitive networks where the channels are solely determined by the positions of nodes, we can use compressed sensing to recover the interference state. In addition to being a first application of compressed sensing in the domain of limited feedback, to the best of our knowledge, this paper makes a key mathematical contribution concerning the favourable sensing properties of path-loss matrices that are composed of nonzero mean, dependent random entries. Finally, we numerically study the robustness properties of the least absolute shrinkage and selection operator (LASSO), a popular recovery algorithm, under two error models through simulations. The first model considers a varying amount of error added to all entries of the sensing matrix. The second one, a more adversarial model, considers a large amount of error added to only a fraction of the entries of the sensing matrix that are chosen uniformly at random. Simulation results establish that the LASSO recovery algorithm is robust to imperfect channel knowledge.

Behind a paywall:

Phase retrieval of diffraction from highly strained crystals by Marcus C. Newton, Ross Harder, Xiaojing Huang, Gang Xiong, and Ian K. Robinson. The abstract reads:
An important application of phase retrieval methods is to invert coherent x-ray diffraction measurements to obtain real-space images of nanoscale crystals. The phase information is currently recovered from reciprocal-space amplitude measurements by the application of iterative projective algorithms that solve the nonlinear and nonconvex optimization problem. Various algorithms have been developed each of which apply constraints in real and reciprocal space on the reconstructed object. In general, these methods rely on experimental data that is oversampled above the Nyquist frequency. To date, support-based methods have worked well, but are less successful for highly strained structures, defined as those which contain (real-space) phase information outside the range of ±π/2. As a direct result the acquired experimental data is, in general, inadvertently subsampled below the Nyquist frequency. In recent years, a new theory of “compressive sensing” has emerged, which dictates that an appropriately subsampled (or compressed) signal can be recovered exactly through iterative reconstruction and various routes to minimizing the ℓ1 norm or total variation in that signal. This has proven effective in solving several classes of convex optimization problems. Here we report on a “density-modification” phase reconstruction algorithm that applies the principles of compressive sensing to solve the nonconvex phase retrieval problem for highly strained crystalline materials. The application of a nonlinear operator in real-space minimizes the ℓ1 norm of the amplitude by a promotion-penalization (or “propenal”) operation that confines the density bandwidth. This was found to significantly aid in the reconstruction of highly strained nanocrystals. We show how this method is able to successfully reconstruct phase information that otherwise could not be recovered.

Finally, here is a job announcement at King's College, London:

Research Associate Division of Imaging Sciences & Biomedical EngineeringG6/MRE/530/10-HH21/11/2010
SummaryWe are seeking 1 post-doctoral Research Associate for 2 years to participate in a large multi-centre EPSRC funded programme grant (Intelligent imaging: motion, form and function across scale (EPSRC EP/H046410/1), a collaboration between KCL, UCL, Imperial College and The Institute of Cancer Research. The programme focuses on a multidisciplinary medical imaging approach, with the aim of providing clinicians the information they really need. It involves modelling, image processing and registration, and medical imaging physics. This post is part of a work package on improved image reconstruction, in particular MRI reconstruction including motion correction. It will be based in the Division of Imaging Sciences and Biomedical Engineering, a newly created structure in the School of Medicine at King's College London, part of King's Health Partners. It is situated on the 4th floor Lambeth Wing, St Thomas Hospital, one of the leading research hospitals in London. The Division is a unique group made of clinicians, physicists, mathematicians, chemists, biologists, and engineers working on translational research, and it has strong links with industrial partners such as Philips.

The aim of this post is to develop compressed sensing techniques for motion correction in MRI, but with a view of widening applications within the context of intelligent imaging as described by the grant proposal. More generally, the project might involve techniques beyond standard compressed sensing enabling additional prior information to be used. The compressed sensing might be used to measure motion and provide input for other motion correction developed in the lab, or even maybe directly in a generalised motion and under sampling reconstruction framework. In addition, collaboration with novel acquisition and sampling developments for example using parallel transmit techniques are likely.
DetailsSome experience in compressed sensing and MRI is required. The ideal candidate would have good knowledge of cardiac MRI, in particular aspects of acquisition and reconstruction, as well as general image reconstruction and processing techniques. Some experience of parallel MRI and parallel transmit MRI is desirable. This post is part of a large programme grant involving multiple imaging modalities, disciplines (maths, physics, medicine, biology) and institutions (UCL, KCL, Imperial College, Oxford), thus the candidate should also have the personal qualities required to work in such an environment.
SalaryThe salary will be on grade 6: from £30,747 to £33,599 plus £2323 London allowance per annum, depending on experience.
Post durationtwo years
ContactFor an information pack please see further details. Please quote reference G6/MRE/530/10-HH when applying and in all correspondence. Closing date: 17 October 2010 Creating a world-leading Academic Health Sciences Centre. Equality of Opportunity is College Policy.
Further detailsPlease see related Word document

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