## References

a complete list of our contribution on this topic

### Journal papers

M. Mangia, F. Pareschi, V. Cambareri, R. Rovatti and G. Setti, "Rakeness-Based Design of Sparse Projection Matrices for Low-Complexity Compressed Sensing," IEEE Trans. on Circuits and Systems, vol.64, no.5, pp.1201-1213, May 2017 doi: 10.1109/TCSI.2017.2649572

*abstract* - Compressed Sensing (CS) can be introduced in the processing chain of a sensor node as a mean to globally reduce its operating cost, while maximizing the quality of the acquired signal. We exploit CS as a simple early-digital compression stage that performs a multiplication of the signal by a matrix. The operating costs (e.g., the consumed power) of such an encoding stage depend on the number of rows of the matrix, but also on the value and position of the rows' coefficients. Our novel design flow yields optimized sparse matrices with very few rows. It is a non-trivial extension of the rakeness-based approach to CS and yields an extremely lightweight stage implemented by a very small number of possibly signed sums with an excellent compression performance. By means of a general signal model we explore different corners of the design space and show that, for example, our method is capable of compressing the signal by a factor larger than 2.5 while not considering 30% of the original samples (so that they may not be acquired at all, leaving the analog front-end and ADC stages inactive) and by processing each of the considered samples with not more than three signed sums.

F. Pareschi, P. Albertini, G. Frattini, M. Mangia, R. Rovatti and G. Setti, "Hardware-Algorithms Co-design and Implementation of an Analog-to-Information Converter for Biosignals based on Compressed Sensing," IEEE Trans. Biomedical Circuits and Systems, vol.10, no.1, pp.149-162, Feb. 2016 doi: 10.1109/TBCAS.2015.2444276

*abstract* - 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.

V. Cambareri, M. Mangia, F. Pareschi, R. Rovatti, G. Setti, G., "On Known-Plaintext Attacks to a Compressed Sensing-based Encryption: a Quantitative Analysis," IEEE Trans. on Information Forensics and Security, vol.10, no.10, pp.2182-2195, Oct. 2015 - doi: 10.1109/TIFS.2015.2450676

*abstract* - Despite the linearity of its encoding, compressed sensing 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 compressed sensing 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 compressed sensing 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 compressed sensing and multiclass encryption schemes feature a noteworthy level of security against knownplaintext attacks, therefore increasing its appeal as a negligiblecost encryption method for resource-limited sensing applications.

V. Cambareri, M. Mangia, F. Pareschi, R. Rovatti, G. Setti, G., "Low-Complexity Multiclass Encryption by Compressed Sensing," IEEE Trans. on Signal Processing, vol.63, no.9, pp.2183-2195, May 2015 - doi: 10.1109/TSP.2015.2407315

*abstract* - 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.

V. Cambareri, M. Mangia, F. Pareschi, R. Rovatti, G. Setti, G., "A Case Study in Low-Complexity ECG Signal Encoding: How Compressing is Compressed Sensing?," IEEE Signal Processing Letters, IEEE, vol.22, no.10, pp.1743-1747, Oct. 2015 - doi: 10.1109/LSP.2015.2428431

*abstract* - 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.

M. Mangia, R. Rovatti and G. Setti, "Rakeness in the Design of Analog-to-Information Conversion of Sparse and Localized Signals," IEEE Trans. on Circuits and Systems I: Regular Papers, vol.59, no.5, pp.1001-1014, May 2012 (it won the IEEE Guillemin-Cauer Best Paper Award 2013 ) - doi: 10.1109/TCSI.2012.2191312

*abstract* - 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.

J. Haboba, M. Mangia, F. Pareschi, R. Rovatti, G. Setti, G., "A Pragmatic Look at Some Compressive Sensing Architectures With Saturation and Quantization," *Emerging and Selected Topics in Circuits and Systems, IEEE Journal on*, vol.2, no.3, pp.443-459, Sept. 2012 - 10.1109/JETCAS.2012.2220392

*abstract* - 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.

A. Caprara, F. Furini, A. Lodi, M. Mangia, R. Rovatti, G. Setti, G., "Generation of Antipodal Random Vectors With Prescribed Non-Stationary 2-nd Order Statistics," IEEE Trans. on Signal Processing, vol.62, no.6, pp.1603-1612, March, 2014 - doi: 10.1109/TSP.2014.2302737

*abstract* - 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.

### Some Conferences papers

D. Bortolotti, M. Mangia, A. Bartolini, R. Rovatti, G. Setti, L. Benini, "An ultra-low power dual-mode ECG monitor for healthcare and wellness," Design, Automation & Test in Europe Conference (DATE),2015, pp. 1611-1616, Marc 2015

Mangia, M.; Pareschi, F.; Rovatti, R.; Setti, G., "Leakage compensation in analog random modulation pre-integration architectures for biosignal acquisition," Biomedical Circuits and Systems Conference (BioCAS), 2014 IEEE, pp.432-435, Oct. 2014

M. Mangia, M. Paleari, P. Ariano, R. Rovatti, G. Setti, "Compressed Sensing based on Rakeness for surface ElectroMyoGraphy," Biomedical Circuits and Systems Conference (BioCAS), 2014 IEEE, pp. 204 - 207, Oct. 2014

D. Bortolotti, M. Mangia, A. Bartolini, R. Rovatti, G. Setti, L. Benini, "Rakeness-based Compressed Sensing on Ultra-Low Power Multi-Core Biomedical Processors," Design & Architectures for Signal & Image Processing (DASIP), 2014 IEEE, pp.1-8, Sep. 2014

M. Mangia, R. Rovatti, G. Setti, P. Vandergheynst, "Combining Spread Spectrum Compressive Sensing with rakeness for low frequency modulation in RMPI architecture," International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2014 IEEE, pp.4146-4150, May 2014

M. Mangia, J. Haboba, R. Rovatti, G. Setti, "Rakeness-based approach to compressed sensing of ECGs," Biomedical Circuits and Systems Conference (BioCAS), 2011 IEEE, pp.424-427, Oct. 2011

M. Mangia, R. Rovatti, G. Setti, "Analog-to-information conversion of sparse and non-white signals: Statistical design of sensing waveforms," International Symposium on Circuits and Systems (ISCAS), 2011 IEEE, pp.2129-2132, Oct. 2011 (it won the IEEE ISCAS 2011 Best Student Paper Award doi: 10.1109/ISCAS.2011.5938019)