Abstract
In this paper, we study the problem of projection kernel design for the reconstruction of high-dimensional signals from low-dimensional measurements in the presence of side information, assuming that the signal of interest and the side information signal are described by a joint Gaussian mixture model (GMM). In particular, we consider the case where the projection kernel for the signal of interest is random, whereas the projection kernel associated to the side information is designed. We then derive sufficient conditions on the number of measurements needed to guarantee that the minimum mean-squared error (MMSE) tends to zero in the low-noise regime. Our results demonstrate that the use of a designed kernel to capture side information can lead to substantial gains in relation to a random one, in terms of the number of linear projections required for reliable reconstruction. © 2016 IEEE.

Abstract
We develop a general framework for compressive linear-projection measurements with side information. Side information is an additional signal correlated with the signal of interest. We investigate the impact of side information on classification and signal recovery from low-dimensional measurements. Motivated by real applications, two special cases of the general model are studied. In the first, a joint Gaussian mixture model is manifested on the signal and side information. The second example again employs a Gaussian mixture model for the signal, with side information drawn from a mixture in the exponential family. Theoretical results on recovery and classification accuracy are derived. The presence of side information is shown to yield improved performance, both theoretically and experimentally. © 2016 IEEE.

Abstract
This paper investigates the impact of projection design on the reconstruction of high-dimensional signals from low-dimensional measurements in the presence of side information. In particular, we assume that both the signal of interest and the side information are described by a joint Gaussian mixture model (GMM) distribution. Sharp necessary and sufficient conditions on the number of measurements needed to guarantee that the average reconstruction error approaches zero in the low-noise regime are derived, for both cases when the side information is available at the decoder or at the decoder and encoder. Numerical results are also presented to showcase the impact of projection design on applications with real imaging data in the presence of side information. © 2016 IEEE.

Abstract
Achievable secrecy rates over a multiple-input multiple-output multipleeavesdropper (MIMOME) wiretap channel are considered, when the legitimate users have perfect knowledge only of the legitimate channel state and the eavesdropper channel is drawn from a (possibly unknown) continuous probability density. Legitimate users are assumed to deploy more antennas than the eavesdropper. A signaling transmission based on K-class Gaussian mixture model (GMM) distributions is proposed, which can be considered as an artificial-noise augmented signal, where the noise statistics are data-dependent. The proposed scheme is shown to achieve the secrecy capacity, log K, in the high signal-to-noise ratio (SNR) regime. Moreover, the tradeoff between secrecy and reliability at finite SNR is explored via the characterization of an upper bound to the error probability at the legitimate receiver, an upper bound to themutual information leakage to the eavesdropper and via numerical simulations. © Springer International Publishing Switzerland 2016.

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
This paper studies how to optimally capture side information to aid in the reconstruction of high-dimensional signals from low-dimensional random linear and noisy measurements, by assuming that both the signal of interest and the side information signal are drawn from a joint Gaussian mixture model. In particular, we derive sufficient and (occasionally) necessary conditions on the number of linear measurements for the signal reconstruction minimum mean squared error (MMSE) to approach zero in the low-noise regime; moreover, we also derive closed-form linear side information measurement designs for the reconstruction MMSE to approach zero in the low-noise regime. Our designs suggest that a linear projection kernel that optimally captures side information is such that it measures the attributes of side information that are maximally correlated with the signal of interest. A number of experiments both with synthetic and real data confirm that our theoretical results are well aligned with numerical ones. Finally, we offer a case study associated with a panchromatic sharpening (pan sharpening) application in the presence of compressive hyperspectral data that demonstrates that our proposed linear side information measurement designs can lead to reconstruction peak signal-to-noise ratio (PSNR) gains in excess of 2 dB over other approaches in this practical application.