Wednesday, June 15, 2011

Compressive Sensing Literature This Week (part two).

Alexandre Thiery has a blog entry on compressive sensing. Zhilin talks about some Misunderstandings on Sparse Bayesian Learning (SBL) for Compressed Sensing (2), while Bob is implementing CMP in MPTK and  Pardis talks about the Paper of the Day (Po'D): Encoding vs. Training with Sparse Coding Edition. The Google also found the following papers on the interwebs:

Compressive sampling is a technique of recovering sparse N-dimensional signals from low-dimensional sketches, i.e., their linear images in Rm; m N: The main question associated with this technique is construction of linear operators that allow faithful recovery of the signal from its sketch. The most frequently used sufficient condition for robust recovery is the near-isometry property of the operator when restricted to k-sparse signals. We study 1-matrices of dimensions m N that satisfy the restricted isometry property of order k (k-RIP). As our main set of results, we describe a general method of constructing sampling matrices for which a statistical version of k-RIP holds. We also show that m N matrices with k-RIP and m = O(k2log N) can be constructed with time complexity O(k2N log N):

Poisson Compressed Sensing by Rebecca Willett and Maxim Raginsky. The abstract reads:
Compressed sensing has profound implications for the design of new imaging and network systems, particularly when physical and economic limitations require that these systems be as small and inexpensive as possible. However, several aspects of compressed sensing theory are inapplicable to real-world systems in which noise is signal-dependent and unbounded. In this work we discuss some of the key theoretical challenges associated with the application of compressed sensing to practical hardware systems and develop performance bounds for compressed sensing in the presence of Poisson noise. We develop two novel sensing paradigms, based on either pseudo-random dense sensing matrices or expander graphs, which satisfy physical feasibility constraints. In these settings, as the overall intensity of the underlying signal increases, an upper bound on the reconstruction error decays at an appropriate rate (depending on the compressibility of the signal), but for a fixed signal intensity, the error bound actually grows with the number of measurements or sensors. This surprising fact is both proved theoretically and justified based on physical intuition.

Dynamic Range and Compressive Sensing Acquisition Receivers by John Treichler, Mark Davenport, Jason Laska, and Richard Baraniuk. The abstract reads:
Compressive sensing (CS) exploits the sparsity present in many signal environments to reduce the number of measure- ments needed for digital acquisition and processing. We have previously introduced the concept and feasibility of using CS techniques to build a wideband signal acquisition systems. This paper extends that work to examine such a receiver’s performance as a function of several key design parameters. In particular we show that that the system noise figure is predictably degraded as the subsampling implicit in CS is made more aggressive. Conversely we show that the dynamic range of a CS-based system can be substantially improved as the subsampling factor grows. The ability to control these aspects of performance provides an engineer new degrees of freedom in the design of wideband acquisition systems. A specific practical example, a multi-collector emitter geoloca- tion system, is included to illustrate that point.

Network Tomography via Compressed Sensing by Mohammad H. Firooz, Sumit Roy. The abstract reads:

In network tomography, we seek to infer link status parameters (such as delay) inside a network through end-toend probe sending between (external) boundary nodes. The main challenge here is to estimate link-level attributes from end-to-end measurements. In this paper by using the idea of combinatorial compressed sensing, we provide conditions on network routing matrix under which it is possible to estimate links delay from end-to-end delay measurements. We also provide an upper-bound on the estimation error. Moreover, for a given network, we show how to design its routing matrix to achieve the minimum number of probes needed to be sent in order to estimate delay of the links inside the network.

On the web but no preprint:

Image Credit: NASA/JPL/Space Science Institute, N00172726.jpg was taken on June 11, 2011 and received on Earth June 13, 2011. The camera was pointing toward JANUS, and the image was taken using the CL1 and CL2 filters.

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