Monday, October 04, 2010

CS; CTBT's feats, TwIST, Recovery of Frequency-Sparse Signals from Compressive Measurements, Recovering Spikes from Noisy Neuronal Calcium Signals, Compressive SD-OCT, a postdoc.

I mentioned the CTBT's capabilities before (CS: Is HIFT an instance of Imaging With Nature ? The data is available.). This week-end, I came across some of Lassino Zerbo's presentations on CTBT's engineering feats. Here are some interesting slides:

Wow. I am sure I'll come back to it later.

Version 2 of the TwIST code (Two-step Iterative Shrinkage/Thresholding Algorithm for Linear Inverse Problems) is now available from the code's webpage.

Peng Zhang has a presentation on Compressed Sensing Approaches to Spectrum Sensing in Cognitive Radio Networks.

On November 1, Emmanuel Abbe (EPFL) will be making a presention at Yale a talk entitled:  A polarization approach to compressed sensing. The abstract of the presentation reads:
In 2008, a technique called channel polarization allowed to solve a problem open since 1948 by Shannon: the construction of low complexity codes that are provably capacity achieving. The polarization idea can be explained on the basis of a rather general probabilistic phenomenon: let X_1,...,X_n be i.i.d. Bernoulli(p) and transform (X_1,...,X_n) with the GF(2)-matrix that takes log(n) Kronecker products of [1 0; 1 1], then the output contains nH(p) entries which are roughly independent and uniformly distributed and n(1-H(p)) entries which are roughly deterministic given the past entries (H being the entropy function). Hence the Kronecker matrix `distills' the randomness of the original vector, and it does so at low computational cost, O(n log n). In this talk, we will use the idea behind polarization not for channel coding, but to propose a new approach to compressed sensing. With this approach, the sensing matrix has the attribute of being deterministic, whereas the signal is assumed to be statistically sparse. The reconstruction algorithm is shown to have a low complexity, and the overall scheme is based on algebraic arguments rather than convex optimization.
With reagrds to papers/preprints, here is what we have this week so far:
Recovery of Frequency-Sparse Signals from Compressive Measurements, (Slides) by Marco. Duarte and Richard Baraniuk. The abstract reads;
Compressive sensing (CS) is a new approach to simultaneous sensing and compression for sparse and compressible signals. While the discrete Fourier transform has been widely used for CS of frequency-sparse signals, it provides optimal sparse representations only for signals with components at integral frequencies. There exist redundant frames that provide compressible representations for frequency-sparse signals, but such frames are highly coherent and severely affect the performance of standard CS recovery. In this paper, we show that by modifying standard CS recovery algorithms to prevent coherent frame elements from being present in the signal estimate, it is possible to bypass the shortcomings introduced by the coherent frame. The resulting algorithm comes with theoretical guarantees and is shown to perform significantly better for frequencysparse signal recovery than its standard counterparts. The algorithm can also be extended to similar settings that use coherent frames.

Recovering Spikes from Noisy Neuronal Calcium Signals via Structured Sparse Approximation by  Eva Dyer, Marco. Duarte , Don. Johnson and Richard Baraniuk, The abstract reads:
Two-photon calcium imaging is an emerging experimental technique that enables the study of information processing within neural circuits in vivo. While the spatial resolution of this technique permits the calcium activity of individual cells within the field of view to be monitored, inferring the precise times at which a neuron emits a spike is challenging because spikes are hidden within noisy observations of the neuron’s calcium activity. To tackle this problem, we introduce the use of sparse approximation methods for recovering spikes from the time-varying calcium activity of neurons. We derive sufficient conditions for exact recovery of spikes with respect to (i) the decay rate of the spike-evoked calcium event and (ii) the maximum firing rate of the cell under test.We find—both in theory and in practice—that standard sparse recovery methods are not sufficient to recover spikes from noisy calcium signals when the firing rate of the cell is high, suggesting that in order to guarantee exact recovery of spike times, additional constraints must be incorporated into the recovery procedure. Hence, we introduce an iterative framework for structured sparse approximation that is capable of achieving superior performance over standard sparse recovery methods by taking into account knowledge that spikes are non-negative and also separated in time. We demonstrate the utility of our approach on simulated calcium signals in various amounts of additive Gaussian noise and under different degrees of model mismatch.
Behind a paywall: Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography by Xuan Liu and Jin U. Kang. The abstract reads:
We applied compressed sensing (CS) to spectral domain optical coherence tomography (SD OCT) and studied its effectiveness. We tested the CS reconstruction by randomly undersampling the k-space SD OCT signal. We achieved this by applying pseudo-random masks to sample 62.5%, 50%, and 37.5% of the CCD camera pixels. OCT images are reconstructed by solving an optimization problem that minimizes the l1 norm of a transformed image to enforce sparsity, subject to data consistency constraints. CS could allow an array detector with fewer pixels to reconstruct high resolution OCT images while reducing the total amount of data required to process the images.

In other news, Laurent Jacques sent me the following postdoc announcement at UCL in Belgium (also posted on the compressive sensing jobs page)

October 1, 2010. Postdoc position,:"Optical Inverse Problem Solving in 3-D Deflectometry” (starting date: January 1st, 2011, application deadline: November 12th, 2010. )      

Optical Framework:

Improved functional performance is a general trend in ocular surgery today. As an example, multifocal intraocular lens (IOL) achieves different optical powers, as such to enable good near and distant vision. There are two types of multifocal lenses. A refractive multifocal lens is made of concentric rings whose refractive powers alternate from centre to periphery. Diffractive multifocal lens uses light diffraction at an interference grid made of micrometric steps. Such complex surfaces are a real challenge both for manufacturing and for characterization.
This position opening takes place in a 3-year regional project (DETROIT), funded by the Belgian Walloon Region. This project aims at characterizing surfaces by optical deflectometry. The principle is to measure the deviation of the light reflected by each point of the surface. This technique is an interesting alternative to interferometry in order to estimate the surface topography. Indeed measuring the deviation angle instead of the height has several advantages. It is insensitive to vibrations as it is not based on interferences. It is more effective in detecting local details and object contours than height measurement. In deflectometry, the shape of an object is numerically reconstructed from the gradient data with a high accuracy. As an example, 10nm flatness deviation over a 50mm window glass can be observed with high accuracy instrument.
Experimentally, the very short radius of curvature of the IOLs requires the use of wide acceptance optics as such to collect light that is reflected in a large range of angles. The drawback is the very narrow field of view. In order to reduce the acquisition time, a device that images the whole lens shall be preferred but inevitable distortion of the image will be numerically corrected based on the knowledge of instrument response. This solution is challenging but very attractive for industrial perspectives.

Numerical Methods:

Nowadays, assuming that a signal (e.g., a 1-D signal, an image or a volume of data) has a sparse representation, namely that this signal is linearly described with few elements taken in a suitable basis, is an ubiquitous hypothesis validated in many different scientific domains. Interestingly, this sparsity assumption is the heart of methods solving inverse problems, namely those estimating a signal from some linear distorting observations. Sparsity stabilizes (or regularizes) these signal estimation techniques often based on L1-norm (or Total Variation norm) minimization and greedy methods.
This postdoc position concerns the application of the sparsity principle for modeling and solving the optical inverse problem described in the previous section, that is, the reconstruction of the undistorted image of the IOL from the experimental measurements.

Job description:

The postdoc will be in charge of the numerical reconstruction development of the undistorted IOL image from the experimental measurements, taking into account (and modeling) the particularities of the sensing systems. Calibration of the response of the instrument will be carried out by another partner of the project. However, a close collaboration between the two teams is necessary. Moreover, the postdoc will co-supervise a PhD student working on the same topic and funded by the same project.
The optical development takes place in the 3-year project DETROIT. It involves two industrial partners, Physiol and Lambda-X and 3 university partners. Physiol is well-known for its development of IOL. Lambda-X has a large experience in optical characterization of optical components by means of deflectometry. The leading academic partner is the Atomic, Molecular and Optical Physics Laboratory (IMCN-PAMO) of University of Louvain (UCL, Louvain-la-Neuve, Belgium), helped by two other Belgian university partners: the Active Structures Laboratory of the University of Brussels (ASL, ULB), in charge of the development of fast adaptive optics, and the Communications and Remote Sensing laboratory (ICTEAM-TELE, UCL) which is responsible of the IOL image reconstruction and post-processing algorithms.
Research activity will be carried out in the ICTEAM-TELE Laboratory, and partly at IMCN-PAMO and at Lambda-X offices in Nivelles, Belgium.

Candidate's Profile:

PhD in Physics, Electrical Engineering, Computer Science or Applied Mathematics; Good knowledge of signal/image processing and classical optics are mandatory; Knowledge (even partial) in the following topics constitutes assets: Multispectral Imaging, Coded Aperture, Spatial Light Modulator, Convex Optimization methods, Sparsity Models, Image DeNoising and Debluring, Compressed Sensing. Programming experience with Matlab, C and/or C++. Good communications skills, both written and oral; Speaking fluently in English or French is required. Writing in English is mandatory.

We offer:

  • A research position in a dynamic and advanced high-tech environment, working on leading-edge technologies in collaboration with industrial partners.
  • 1-year contract (starting date: 1/1/2011)
  • gross salary range: 35 000 - 45 000 Euros


Applications should include a full CV, including list of publications, and must be sent before November 12th, 2010.
Names and complete addresses of referees are welcome.
Please send applications by email to (and replace _DOT_ and _AT_):
laurent _DOT_ jacques _AT_ uclouvain _DOT_ be
        ph _DOT_ antoine _AT_ uclouvain _DOT_ be 
Questions about the subject or the position should be addressed to the same email address.

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