The Internet of Things (IoT) promises many advantages in the control and monitoring of physical systems from both efficacy and efficiency perspectives. However, in the wrong hands, the data might pose a privacy threat. In this article, we consider the tradeoff between the operational value of data collected in the IoT and the privacy of consumers. We present a general framework for quantifying this tradeoff in the IoT, and focus on a smart grid application for a proof of concept. In particular, we analyze the tradeoff between smart grid operations and how often data are collected by considering a realistic direct-load control example using thermostatically controlled loads, and we give simulation results to show how its performance degrades as the sampling frequency decreases. Additionally, we introduce a new privacy metric, which we call inferential privacy. This privacy metric assumes a strong adversary model and provides an upper bound on the adversary’s ability to infer a private parameter, independent of the algorithm he uses. Combining these two results allows us to directly consider the tradeoff between better operational performance and consumer privacy.

The phase retrieval problem has a long history and is an important problem in many areas of optics. Theoretical understanding of phase retrieval is still limited and fundamental questions such as uniqueness and stability of the recovered solution are not yet fully understood. This paper provides several additions to the theoretical understanding of sparse phase retrieval. In particular we show that if the measurement ensemble can be chosen freely, as few as 4k - 1 phaseless measurements suffice to guarantee uniqueness of a k-sparse M-dimensional real solution. We also prove that 2(k2- k + 1) Fourier magnitude measurements are sufficient under rather general conditions.

The classical shift retrieval problem considers two signals in vector form that are related by a cyclic shift. In this paper, we develop a compressive variant where the measurement of the signals is undersampled. While the standard procedure to shift retrieval is to maximize the real part of their dot product, we show that the shift can be exactly recovered from the corresponding compressed measurements if the sensing matrix satisfies certain conditions. A special case is the partial Fourier matrix. In this setting we show that the true shift can be found by as low as two measurements. We further show that the shift can often be recovered when the measurements are perturbed by noise.

While compressive sensing (CS) has been one of the most vibrant and active research fields in the past few years, most development only applies to linear models. This limits its application and excludes many areas where CS ideas could make a difference. This paper presents a novel extension of CS to the phase retrieval problem, where intensity measurements of a linear system are used to recover a complex sparse signal. We propose a novel solution using a lifting technique -- CPRL, which relaxes the NP-hard problem to a nonsmooth semidefinite program. Our analysis shows that CPRL inherits many desirable properties from CS, such as guarantees for exact recovery. We further provide scalable numerical solvers to accelerate its implementation. The source code of our algorithms will be provided to the public.

We present the first step towards a brain computer interface (BCI) for communication using real-time functional magnetic resonance imaging (fMRI). The subject in the MR scanner sees a virtual keyboard and steers a cursor to select different letters that can be combined to create words. The cursor is moved to the left by activating the left hand, to the right by activating the right hand, down by activating the left toes and up by activating the right toes. To select a letter, the subject simply rests for a number of seconds. We can thus communicate with the subject in the scanner by for example showing questions that the subject can answer. Similar BCI for communication have been made with electroencephalography (EEG). In these implementations the subject for example focuses on a letter while different rows and columns of the virtual keyboard are flashing. The system then tries to detect if the correct letter is flashing or not. In our setup we instead classify the brain activity. Our system is not limited to a communication interface, but can be used for any interface where five degrees of freedom is necessary.

A UAV navigation system relying on GPS is vulnerable to signal failure, making a drift free backup system necessary. We introduce a vision based geo-referencing system that uses pre-existing maps to reduce the long term drift. The system classifies an image according to its environmental content and thereafter matches it to an environmentally classified map over the operational area. This map matching provides a measurement of the absolute location of the UAV, that can easily be incorporated into a sensor fusion framework. Experiments show that the geo-referencing system reduces the long term drift in UAV navigation, enhancing the ability of the UAV to navigate accurately over large areas without the use of GPS.