CS: Xampling, Ghost imaging via compressive sampling, Low-rank Matrix Recovery, Volume Anomaly Detection

Moshe Mishali sent me the following:

We have finished a paper draft of our implementation of the modualted wideband converter in hardware. As promised, I send you the online posting

Xampling: Analog to Digital at Sub-Nyquist Rates by Moshe Mishali, Yonina Eldar, Oleg Dounaevsky, Eli Shoshan. The abstract reads:

We present a sub-Nyquist analog-to-digital converter of wideband inputs. Our circuit realizes the recently proposed modulated wideband converter, which is a flexible platform for sampling signals according to their actual bandwidth occupation. The theoretical work enables, for example, a sub-Nyquist wideband receiver, which has no prior information on the transmitter carrier positions. Our design supports input signals with 2 GHz Nyquist rate and 120 MHz spectrum occupancy, with arbitrary transmission frequencies. The sampling rate is as low as 280 MHz. To the best of our knowledge, this is the first reported wideband hardware for sub-Nyquist conversion. Furthermore, the modular design is proven to compete with state-of-the-art Nyquist ADCs in terms of resolution bits and full-scale range. We describe the various circuit design considerations, with an emphasis on the nonordinary challenges the converter introduces: mixing a signal with a multiple set of sinusoids, rather than a single local oscillator, and generation of highly-transient periodic waveforms, with transient intervals on the order of the Nyquist rate. A series of hardware experiments validates the design and demonstrate sub-Nyquist sampling.

More about the circuit can be found here. This hardware is already listed in the compressive sensing hardware page. Thanks Moshiko !

also on arixv, here is: The effect of spatial transverse coherence property of a thermal source on Ghost imaging and Ghost imaging via compressive sampling by Wenlin Gong and Shensheng Han. The abstract reads:

Both ghost imaging (GI) and ghost imaging via compressive sampling (GICS) can nonlocally image an object. We report the influence of spatial transverse coherence property of a thermal source on GI and GICS and show that, using the same acquisition numbers, the signal-to-noise ratio (SNR) of images recovered by GI will be reduced while the quality of reconstructed images will be enhanced for GICS as the spatial transverse coherence lengths located on the object plane are decreased. Differences between GI and GICS, methods to further improve the quality and image extraction efficiency of GICS, and its potential applications are also discussed.

On the interwebs, there is also: Tight Oracle Bounds for Low-rank Matrix Recovery from a Minimal Number of Random Measurements by Emmanuel Candes and Yaniv Plan. The abstract reads:

This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that properly constrained nuclear-norm minimization stably recovers a low-rank matrix from a constant number of noisy measurements per degree of freedom; this seems to be the first result of this nature. Further, the recovery error from noisy data is within a constant of three targets: 1) the minimax risk, 2) an ‘oracle’ error that would be available if the column space of the matrix were known, and 3) a more adaptive ‘oracle’ error which would be available with the knowledge of the column space corresponding to the part of the matrix that stands above the noise. Lastly, the error bounds regarding low-rank matrices are extended to provide an error bound when the matrix has full rank with decaying singular values. The analysis in this paper is based on the restricted isometry property (RIP) introduced in [6] for vectors, and in [22] for matrices.

and finally a class presentation entitled: Volume Anomaly Detection by Joohyun Kim and Sooel Son. Maybe they should have looked at the Robust PCA technique instead ?