Mauro Mangia

Rakeness in the Design of Analog-to-Information Conversion of Sparse and Localized Signals

Design of random modulation preintegration 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 nonzero 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 nonnegligible improvements in both cases.

Low-Complexity Multiclass Encryption by Compressed Sensing

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.

A Pragmatic Look at Some Compressive Sensing Architectures With Saturation and Quantization

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 design-oriented 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 ΔΣ 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 acquisition.

On Known-Plaintext Attacks to a Compressed Sensing-Based Encryption: A Quantitative Analysis

Despite its intrinsic linearity, compressed sensing may be exploited to at least partially encrypt acquired signals from unintentional receivers: in the companion paper we have shown that the simplicity of its encoding allows the definition of a general, lightweight scheme in which transmitters distribute the same information to receivers of different classes enabled to recover it with different quality levels. In this investigation we quantify the robustness of such a scheme with respect to known-plaintext attacks. The odds of such an attack are shown by theoretical means, proving that the number of candidate encoding matrices matching a typical plaintext-ciphertext pair is astronomically large, thus making the search for the true encoding infeasible. These attacks are also simulated by applying compressed sensing to a variety of signals (speech, images and electrocardiographic traces) showing how this difficulty in extracting information on the true encoding matrix from a plaintext-ciphertext pair is reflected on the quality of the signals recovered by the attacker. The results clarify that, although not perfectly secure, CS grants a noteworthy level of security that may come at almost-zero cost and especially benefit resource-limited applications.Despite the linearity of its encoding, compressed sensing (CS) may be used to provide a limited form of data protection when random encoding matrices are used to produce sets of low-dimensional measurements (ciphertexts). In this paper, we quantify by theoretical means the resistance of the least complex form of this kind of encoding against known-plaintext attacks. For both standard CS with antipodal random matrices and recent multiclass encryption schemes based on it, we show how the number of candidate encoding matrices that match a typical plaintext-ciphertext pair is so large that the search for the true encoding matrix inconclusive. Such results on the practical ineffectiveness of known-plaintext attacks underlie the fact that even closely related signal recovery under encoding matrix uncertainty is doomed to fail. Practical attacks are then exemplified by applying CS with antipodal random matrices as a multiclass encryption scheme to signals such as images and electrocardiographic tracks, showing that the extracted information on the true encoding matrix from a plaintext-ciphertext pair leads to no significant signal recovery quality increase. This theoretical and empirical evidence clarifies that, although not perfectly secure, both standard CS and multiclass encryption schemes feature a noteworthy level of security against known-plaintext attacks, therefore increasing its appeal as a negligible-cost encryption method for resource-limited sensing applications.

Hardware-Algorithms Co-Design and Implementation of an Analog-to-Information Converter for Biosignals Based on Compressed Sensing

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.

A rakeness-based design flow for Analog-to-Information conversion by Compressive Sensing

Classical design of Analog-to-Information converters based on Compressive Sensing uses random projection matrices made of independent and identically distributed entries. Leveraging on previous work, we define a complete and extremely simple design flow that quantifies the statistical dependencies in projection matrices allowing the exploitation of non-uniformities in the distribution of the energy of the input signal. The energy-driven reconstruction concept and the effect of this design technique are justified and demonstrated by simulations reporting conspicuous savings in the number of measurements needed for signal reconstruction that approach 50%.

Analog-to-information conversion of sparse and non-white signals: Statistical design of sensing waveforms

Analog to Information conversion is a new paradigm in signal digitalization. In this framework, compressed sensing theory allows to reconstruct sparse signal from a limited number of measures. In this work, we will assume that the signal is not only sparse but also localized in a given domain, so that its energy is concentrated in a subspace. We will present a formal and quantitative discussion to explain how localization of sparse signals can be exploited to improve the quality of the reconstructed signal.

A Case Study in Low-Complexity ECG Signal Encoding: How Compressing is Compressed Sensing?

When transmission or storage costs are an issue, lossy data compression enters the processing chain of resource-constrained sensor nodes. However, their limited computational power imposes the use of encoding strategies based on a small number of digital computations. In this case study, we propose the use of an embodiment of compressed sensing as a lossy digital signal compression, whose encoding stage only requires a number of fixed-point accumulations that is linear in the dimension of the encoded signal. We support this design with some evidence that for the task of compressing ECG signals, the simplicity of this scheme is well-balanced by its achieved code rates when its performances are compared against those of conventional signal compression techniques.

An ultra-low power dual-mode ECG monitor for healthcare and wellness

Technology scaling enables today the design of ultra-low cost wireless body sensor networks for wearable biomedical monitors. These devices, according to the application domain, show greatly varying tradeoffs in terms of energy consumption, resources utilization and reconstructed biosignal quality. To achieve minimal energy operation and extend battery life, several aspects must be considered, ranging from signal processing to the technological layers of the architecture. The recently proposed Rakeness-based Compressed Sensing (CS) expands the standard CS paradigm deploying the localization of input signal energy to further increase data compression without sensible RSNR degradation. This improvement can be used either to optimize the usage of a non volatile memory (NVM) to store in the device a record of the biosignal or to minimize the energy consumption for the transmission of the entire signal as well as some of its features. We specialize the sensing stage to achieve signal qualities suitable for both Healthcare (HC) and Wellness (WN), according to an external input (e.g. the patient). In this paper we envision a dual-operation wearable ECG monitor, considering a multi-core DSP for input biosignal compression and different technologies for either transmission or local storage. The experimental results show the effectiveness of the Rakeness approach (up to ≈ 70% more energy efficient than the baseline) and evaluate the energy gains considering different use case scenarios.

Generation of Antipodal Random Vectors With Prescribed Non-Stationary 2-nd Order Statistics

A Look-Up-Table-based method is proposed to generate random instances of an antipodal n-dimensional vector so that its 2-nd order statistics are as close as possible to a given specification. The method is based on linear optimization and exploits column-generation techniques to cope with the exponential complexity of the task. It yields a LUT whose storage requirements are only O(n3) and thus are compatible with hardware implementation for non-negligible n. Applications are shown in the fields of Compressive Sensing and of Ultra Wide Band systems based on Direct Sequence - Code Division Multiple Acces.