CS: Sparse Brain Network Recovery under Compressed Sensing, Compressive Radar Imaging Using White Stochastic Waveforms, Compressive Sensing in the Limit

Wow! just Wow! We have two very application oriented interesting papers today:

Sparse Brain Network Recovery under Compressed Sensing by Hyekyoung Lee, Dong Soo Lee, Hyejin Kang, Boong-Nyun Kim, Moo K. Chung. The abstract reads:

Partial correlation is a useful connectivity measure for brain networks, especially, when it is needed to remove the confounding e ffects in highly correlated networks. Since it is difficult to estimate the exact partial correlation under the small-n large-p situation, a sparseness constraint is generally introduced. In this paper, we consider the sparse linear regression model with a l1-norm penalty, a.k.a., least absolute shrinkage and selection operator (LASSO), for estimating sparse brain connectivity. LASSO is a well-known decoding algorithm in the compressed sensing (CS). The CS theory states that LASSO can reconstruct the exact sparse signal even from a small set of noisy measurements. We briefly show that the penalized linear regression for partial correlation estimation is related with CS. It opens a new possibility that the proposed framework can be used for a sparse brain network recovery. As an illustration, we construct sparse brain networks of 97 regions of interest (ROIs) obtained from FDG-PET data for the autism spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. As a model validation, we check their reproducibilities by leave-one-out cross validation and compare the clustered structures derived from the brain networks of ASD and PedCon.

I don't think I have this type of quality work in Autism related studies. Kudos to this team. On a related note,  if you are interested in going for a PhD that deals with how compressed sensing translates into medical application, you may want to check the PhD program at King's College in London. Check the title of Dr. Batchelor. More information can be found here.

In a different direction, we get to use the Donoho-Tanner phase transition to calibrate a hardware system. I like very much this idea:

Compressive Radar Imaging Using White Stochastic Waveforms by Mahesh C. Shastry, Ram M. Narayanan and Muralidhar Rangaswamy. The abstract reads:

In this paper, we apply the principles of compressive sampling to ultra-wideband (UWB) stochastic waveform radar. The theory of compressive sampling says that it is possible to recover a signal that is parsimonious when represented in a particular basis, by acquiring few projections on to an appropriate basis set. Drawing on literature in compressive sampling, we develop the theory behind stochastic waveformbased compressive imaging. We show that using stochastic waveforms for radar imaging, it is possible to estimate target parameters and detect targets by sampling at a rate that is considerably slower than the Nyquist rate and recovering using compressive sensing algorithms. Thus, it is theoretically possible to increase the bandwidth (and hence the spatial resolution) of an ultra-wideband radar system using stochastic waveforms, without significant additions to the data acquisition system. Further, there is virtually no degradation in the performance of a UWB stochastic waveform radar system that employs compressive sampling. We present numerical simulations to show that the performance guarantees provided by theoretical results are achieved in realistic scenarios.

And finally a poster on  Compressive Sensing in the Limit by Yaser Eftekhari, Amir H. Banihashemi, IoannisLambadaris whose goal is to

Study the asymptotic behaviour of Node-Based Verification-Based (NBVB) algorithms over random regular bipartite graphs in the context of compressive sensing.