Principal Component Analysis (PCA) is a well-established approach commonly used for dimensionality reduction. However, its computational cost and memory requirements hamper the adoption of PCA in heavily resource-constrained embedded platforms. Streaming approaches have been proposed that may enable embedded implementations of the PCA. Among them, the History PCA (HPCA) algorithm stands out for its robustness to the variability in parameters and accuracy. This paper presents a parallel and memory-efficient implementation of HPCA in a structural health monitoring (SHM) application based on a heterogeneous network with sensor nodes measuring three-axial accelerations and gateways collecting measurements from several nodes and sending them to the cloud storage and analytic facility. In the targeted application, standard PCA reaches 15× compression factor with an average reconstruction signal to noise ratio of 16 dB and a negligible impact on the accuracy in the tracking of structural modal frequencies. By embedding HPCA on our SHM network gateways, we achieve the same compression factor as standard PCA, with more than 1000× reduction in data memory footprint for running the algorithm. Furthermore, we parallelize HPCA on the gateway, and we achieve a speedup of 7.1× (on 8 cores). Finally, we explore a fixed-point HPCA implementation on sensors (network end-nodes), that maximally distributes compression workload, minimizes required communication bandwidth, and maintains the same quality of reconstruction as HPCA in floating-point, with a compression factor of 10×.

The recovery of sparse signals given their linear mapping on lower-dimensional spaces can be partitioned into a support estimation phase and a coefficient estimation phase. We propose to estimate the support with an oracle based on a deep neural network trained jointly with the linear mapping at the encoder. The divination of the oracle is then used to estimate the coefficients by pseudo-inversion. This architecture allows the definition of an encoding-decoding scheme with state-of-the-art recovery capabilities when applied to biological signals such as ECG and EEG, thus allowing extremely low-complex encoders. As an additional feature, oracle-based recovery is able to self-assess, by indicating with remarkable accuracy chunks of signals that may have been reconstructed with a non-satisfactory quality. This self-assessment capability is unique in the CS literature and paves the way for further improvements depending on the requirements of the specific application. As an example, our scheme is able to satisfyingly compress by a factor of 2.67 an ECG or EEG signal with a complexity equivalent to only 24 signed sums per processed sample.

Large monitoring systems produce data that is often compressed to be transmitted over the network. For latency or security reasons, compressed data may be processed at the edge, i.e., along the path from sensors to the cloud, for some purposes such as anomaly detection. However, the performance of a detector distinguishing between normal and anomalous behavior may be affected by the loss of information due to compression. We here analyze how lossy compression affects the performance of a generic anomaly detector. This relationship is formalized in terms of information-theoretic quantities. Within such a framework we leverage a Gaussian assumption to derive analytical results regarding the importance of white noise as a representative of both the average and asymptotic anomalies. Moreover, in an anomaly-agnostic scenario, we also show the existence of a level of compression for which an anomaly is undetectable though compression is not completely destructive. Numerical evidence confirms that the proposed information-theoretic quantities anticipate the performance of practical compressors and detectors in the case of Gaussian and non-Gaussian signals allowing an assessment of the tradeoff between compression and detection.

The amount of data generated by distributed monitoring systems that can be exploited for anomaly detection, along with real-time, bandwidth, and scalability requirements leads to the abandonment of centralized approaches in favor of processing closer to where data is generated. This increases the interest in algorithms coping with the limited computational resources of gateways or sensor nodes. We here propose two dual and lightweight methods for anomaly detection based on generalized spectral analysis. We monitor the signal energy laying along with the principal and principal signal subspaces and call for an anomaly when such energy changes significantly with respect to normal conditions. A streaming approach for the online estimation of the needed subspaces is also proposed. The methods are tested by applying them to synthetic data and real-world sensor readings. The synthetic setting is used for design space exploration and highlights the trade-off between accuracy and computational cost. The real-world example deals with structural health monitoring and shows how, despite the extremely low computations costs, our methods are able to detect permanent and transient anomalies that would classically be detected by full spectral analysis.

We investigate the advantage of a two-step approach in the recovery of Compressed Sensing (CS) encoded signals in a realistic environment. First, the support of the signal is computed from the compressed measurements exploiting a Deep Neural Network (DNN). Once the support is known, the input signal can be easily recovered by a pseudoinverse operation. We consider a case study involving realistic biomedical signals and a processing architecture based on a limited precision fixed-point arithmetic unit for the implementation of the DNN and the pseudoinverse operation. In this setting, we show that the proposed approach results in a performance improvement of more than 5 dB in terms of average reconstructed signal to noise ratio (ARSNR) compared to CS state-of-the-art approach. This has been possible thanks to two main contributions reported in this paper. The first one is a theoretical investigation of the relationship between the definition of support and both the properties of the input signal and the adopted compression technique. The second one relies on replacing the pseudoinverse operation with a least mean square filter, whose small sensitivity to numerical errors grants advantages in architectures relying on limited precision fixed-point arithmetic units.