The idea that compressed sensing may be used to encrypt information from unauthorized receivers has already been envisioned but never explored in depth since its security may seem compromised by the linearity of its encoding process. In this paper, we apply this simple encoding to define a general private-key encryption scheme in which a transmitter distributes the same encoded measurements to receivers of different classes, which are provided partially corrupted encoding matrices and are thus allowed to decode the acquired signal at provably different levels of recovery quality. The security properties of this scheme are thoroughly analyzed: first, the properties of our multiclass encryption are theoretically investigated by deriving performance bounds on the recovery quality attained by lower-class receivers with respect to high-class ones. Then, we perform a statistical analysis of the measurements to show that, although not perfectly secure, compressed sensing grants some level of security that comes at almost-zero cost and thus may benefit resource-limited applications. In addition to this, we report some exemplary applications of multiclass encryption by compressed sensing of speech signals, electrocardiographic tracks and images, in which quality degradation is quantified as the impossibility of some feature extraction algorithms to obtain sensitive information from suitably degraded signal recoveries

Abstract-Design of Random Modulation Pre-Integration systems based on the restricted-isometry property may be suboptimal when the energy of the signals to be acquired is not evenly distributed, i.e. when they are both sparse and localized.To counter this, we introduce an additional design criterion, that we call rakeness, accounting for the amount of energy that the measurements capture from the signal to be acquired.Hence, for localized signals a proper system tuning increases the rakeness as well as the average SNR of the samples used in its reconstruction. Yet, maximizing average SNR may go against the need of capturing all the components that are potentially non-zero in a sparse signal, i.e., against the restricted isometry requirement ensuring reconstructability.What we propose is to administer the trade-off between rakeness and restricted isometry in a statistical way by laying down an optimization problem. The solution of such an optimization problem is the statistic of the process generating the random waveforms onto which the signal is projected to obtain the measurements.The formal definition of such a problems is given as well as its solution for signals that are either localized in frequency or in more generic domain.Sample applications, to ECG signals and small images of printed letters and numbers, show that rakeness-based design leads to non-negligible improvements in both cases.

We report the design and implementation of an Analog-to-Information Converter (AIC) based on Compressed Sensing (CS). The system is realized in a CMOS 180 nm technology and targets the acquisition of bio-signals with Nyquist frequency up to 100 kHz. To maximize performance and reduce hardware complexity, we co-design hardware together with acquisition and reconstruction algorithms. The resulting AIC outperforms previously proposed solutions mainly thanks to two key features. First, we adopt a novel method to deal with saturations in the computation of CS measurements. This allows no loss in performance even when 60% of measurements saturate. Second, the system is able to adapt itself to the energy distribution of the input by exploiting the so-called rakeness to maximize the amount of information contained in the measurements. With this approach, the 16 measurement channels integrated into a single device are expected to allow the acquisition and the correct reconstruction of most biomedical signals. As a case study, measurements on real electrocardiograms (ECGs) and electromyograms (EMGs) show signals that these can be reconstructed without any noticeable degradation with a compression rate, respectively, of 8 and 10.

The paper aims to highlight relative strengths and weaknesses of some of the recently proposed architectures for hardware implementation of analog-to-information converters based on Compressive Sensing. To do so, the most common architectures are analyzed when saturation of some building blocks is taken into account, and when measurements are subject to quantization to produce a digital stream. Furthermore, the signal reconstruction is performed by established and novel algorithms (one based on linear programming and the other based on iterative guessing of the support of the target signal), as well as their specialization to the particular architecture producing the measurements. Performance is assessed both as the probability of correct support reconstruction and as the final reconstruction error. Our results help highlighting pros and cons of various architectures and giving quantitative answers to some typical designoriented questions. Among these, we show: 1) that the (Random Modulation Pre-Integration) RMPI architecture and its recently proposed adjustments are probably the most versatile approach though not always the most economic to implement; 2) that when 1-bit quantization is sought, dynamically mixing quantization and integration in a randomized Sigma-Delta architecture help bringing the performance much closer to that of multi-bit approaches; 3) for each architecture, the trade-off between number of measurements and number of bits per measurements (given a fixed bit-budget); and 4) pros and cons of the use of Gaussian versus binary random variables for signal acquisitio

Technology scaling enables today the design of ultra-low cost wireless body sensor networks for wearable biomedical monitors. The typical behaviour of such systems consists of multi-channel input biosignals acquisition data compression and final output transmission or storage. To achieve minimal energy operation and extend battery life several aspects must be considered ranging from signal processing to architectural optimizations. The recently proposed Rakeness-based Compressed Sensing (CS) paradigm deploys the localization of input signal energy to further increase compression without sensible RSNR degradation. Such output size reduction allows for trading off energy from the compression stage to the transmission or storage stage. In this paper we analyze such tradeoffs considering a multi-core DSP for input biosignal computation and different technologies for either transmission or local storage. The experimental results show the effectiveness of the Rakeness approach (on average ≈ 44% more efficient than the baseline) and assess the energy gains in a technological perspective