Compressive Sensing Literature for the Week-End.

Here are three CS papers for the weekend and an intriguing paper on BCI utilization with no calibration period. Enjoy!


Sub-Nyquist Sampling: Bridging Theory and Practice by Moshe Mishali, Yonina Eldar. The abstract reads:

Sampling theory encompasses all aspects related to the conversion of continuous-time signals to discrete streams of numbers. The famous Shannon-Nyquist theorem has become a landmark in the development of digital signal processing. In modern applications, an increasingly number of functions is being pushed forward to sophisticated software algorithms, leaving only those delicate finely-tuned tasks for the circuit level.

In this paper, we review sampling strategies which target reduction of the ADC rate below Nyquist. Our survey covers classic works from the early 50's of the previous century through recent publications from the past several years. The prime focus is bridging theory and practice, that is to pinpoint the potential of sub-Nyquist strategies to emerge from the math to the hardware. In that spirit, we integrate contemporary theoretical viewpoints, which study signal modeling in a union of subspaces, together with a taste of practical aspects, namely how the avant-garde modalities boil down to concrete signal processing systems. Our hope is that this presentation style will attract the interest of both researchers and engineers in the hope of promoting the sub-Nyquist premise into practical applications, and encouraging further research into this exciting new frontier.

OFDM pilot allocation for sparse channel estimation by Pooria Pakrooh, Arash Amini, Farrokh Marvasti. The abstract reads:

In communication systems, efficient use of the spectrum is an indispensable concern. Recently the use of compressed sensing for the purpose of estimating Orthogonal Frequency Division Multiplexing (OFDM) sparse multipath channels has been proposed to decrease the transmitted overhead in form of the pilot subcarriers which are essential for channel estimation. In this paper, we investigate the problem of deterministic pilot allocation in OFDM systems. The method is based on minimizing the coherence of the submatrix of the unitary Discrete Fourier Transform (DFT) matrix associated with the pilot subcarriers. Unlike the usual case of equidistant pilot subcarriers, we show that non-uniform patterns based on cyclic difference sets are optimal. In cases where there are no difference sets, we perform a greedy search method for finding a suboptimal solution. We also investigate the performance of the recovery methods such as Orthogonal Matching Pursuit (OMP) and Iterative Method with Adaptive Thresholding (IMAT) for estimation of the channel taps.

Tight Measurement Bounds for Exact Recovery of Structured Sparse Signals by Nikhil Rao, Benjamin Recht, Robert Nowak. The abstract reads:

Standard compressive sensing results state that to exactly recover an s sparse signal in R^p, one requires O(s\cdotlog p) measurements. While this bound is extremely useful in practice, often real world signals are not only sparse, but also exhibit structure in the sparsity pattern. We focus on group-structured patterns in this paper. Under this model, groups of signal coefficients are active (or inactive) together. The groups are predefined, but the particular set of groups that are active (i.e., in the signal support) must be learned from measurements. We show that exploiting knowledge of groups can further reduce the number of measurements required for exact signal recovery, and derive near optimal bounds for the same. The number of measurements needed only depends on the number of groups under consideration, and not the particulars of the groups (e.g., compositions, sizes, extents, overlaps, etc.). The results are also shown to predict experimental performance quite well.

A Subject-Independent Brain-Computer Interface based on Smoothed, Second-Order Baselining by Boris Reuderink, Jason Farquhar, Mannes Poel, Anton Nijholt.

Image Credit: NASA/JPL/Space Science Institute
N00172964.jpg was taken on June 22, 2011 and received on Earth June 23, 2011. The camera was pointing toward TITAN at approximately 817,420 kilometers away, and the image was taken using the CL1 and CB3 filters. This image has not been validated or calibrated.