Abstract
This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the probability of misclassification to zero in the low-noise regime, both for random measurements and designed ones. Such bounds reveal two important operational regimes that are a function of the characteristics of the source: 1) when the number of classes is less than or equal to the dimension of the space spanned by signals in each class, reliable classification is possible in the low-noise regime by using a one-vs-all measurement design; 2) when the dimension of the spaces spanned by signals in each class is lower than the number of classes, reliable classification is guaranteed in the low-noise regime by using a simple random measurement design. Simulation results both with synthetic and real data show that our analysis is sharp, in the sense that it is able to gauge the number of measurements required to drive the misclassification probability to zero in the low-noise regime.

Abstract

Abstract
We introduce a framework for the reconstruction of the amplitude, phase, and polarization of an optical vector-field using measurements acquired by an imaging device characterized by an integral transform with an unknown spatially variant kernel. By incorporating effective regularization terms, this new approach is able to recover an optical vector-field with respect to an arbitrary representation system, which may be different from the one used for device calibration. In particular, it enables the recovery of an optical vector-field with respect to a Fourier basis, which is shown to yield indicative features of increased scattering associated with tissue abnormalities. We demonstrate the effectiveness of our approach using synthetic holographic images and biological tissue samples in an experimental setting, where the measurements of an optical vector-field are acquired by a multicore fiber endoscope, and observe that indeed the recovered Fourier coefficients are useful in distinguishing healthy tissues from tumors in early stages of oesophageal cancer.

Abstract
This paper determines to within a single measurement the minimum number of measurements required to successfully reconstruct a signal drawn from a Gaussian mixture model in the low-noise regime. The method is to develop upper and lower bounds that are a function of the maximum dimension of the linear subspaces spanned by the Gaussian mixture components. The method not only reveals the existence or absence of a minimum mean-squared error (MMSE) error floor (phase transition) but also provides insight into the MMSE decay via multivariate generalizations of the MMSE dimension and the MMSE power offset, which are a function of the interaction between the geometrical properties of the kernel and the Gaussian mixture. These results apply not only to standard linear random Gaussian measurements but also to linear kernels that minimize the MMSE. It is shown that optimal kernels do not change the number of measurements associated with theMMSE phase transition, rather they affect the sensed power required to achieve a target MMSE in the low-noise regime. Overall, our bounds are tighter and sharper than standard bounds on the minimum number of measurements needed to recover sparse signals associated with a union of subspaces model, as they are not asymptotic in the signal dimension or signal sparsity.

Abstract
In this paper, we study the fundamental limits of secret-key agreement over MIMO quasi-static fading channels. We provide closed-form expressions for the secret-key capacity in both the asymptotic high-power and low-power regimes. The optimal signaling strategy for the low-power regime is shown to be independent of the eavesdropper's channel and secret-key capacity is achieved by transmitting random Gaussian symbols along the direction corresponding to the maximal eigenvalue of the legitimate channel matrix. Hence, by beamforming and waterfilling over the main channel alone, one obtains a semi-blind key-agreement strategy in which the knowledge of the eavesdropper's channel is only required for privacy amplification. We also derive the probability that a target secret-key rate is not achieved by the optimal low-power signaling when assuming only statistical CSI about the eavesdropper's channel.

Abstract
We consider a wiretap multiple-input multiple-output multiple-eavesdropper (MIMOME) channel, where agent Alice aims at transmitting a secret message to agent Bob, while leaking no information on it to an eavesdropper agent Eve. We assume that Alice has more antennas than both Bob and Eve, and that she has only statistical knowledge of the channel towards Eve. We focus on the low-noise regime, and assess the secrecy rates that are achievable when the secret message determines the distribution of a multivariate Gaussian mixture model (GMM) from which a realization is generated and transmitted over the channel. In particular, we show that if Eve has fewer antennas than Bob, secret transmission is always possible at low-noise. Moreover, we show that in the low-noise limit the secrecy capacity of our scheme coincides with its unconstrained capacity, by providing a class of covariance matrices that allow to attain such limit without the need of wiretap coding.