Discrete Signal Processing on Graphs: Frequency Analysis

Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In contrast to traditional time and image signals, data in these domains are supported by arbitrary graphs. Signal processing on graphs extends concepts and techniques from traditional signal processing to data indexed by generic graphs. This paper studies the concepts of low and high frequencies on graphs, and low-, high-, and band-pass graph filters. In traditional signal processing, there concepts are easily defined because of a natural frequency ordering that has a physical interpretation. For signals residing on graphs, in general, there is no obvious frequency ordering. We propose a definition of total variation for graph signals that naturally leads to a frequency ordering on graphs and defines low-, high-, and band-pass graph signals and filters. We study the design of graph filters with specified frequency response, and illustrate our approach with applications to sensor malfunction detection and data classification

A deep learning approach for anomaly identification in PZT sensors using point contact method

The implementation of piezoelectric sensors is degraded due to surface defects, delamination, and extreme weathering conditions, to mention a few. Hence, the sensor needs to be diagnosed before the efficacious implementation in the structural health monitoring (SHM) framework. To rescue the problem, a novel experimental method based on Coulomb coupling is utilised to visualise the evolution of elastic waves and interaction with the surface anomaly in the lead zirconate titanate (PZT) substrate. Recently, machine learning (ML) has been expeditiously becoming an essential technology for scientific computing, with several possibilities to advance the field of SHM. This study employs a deep learning-based autoencoder neural network in conjunction with image registration and peak signal-to-noise ratio (PSNR) to diagnose the surface anomaly in the PZT substrate. The autoencoder extracts the significant damage-sensitive features from the complex waveform big data. Further, it provides a nonlinear input–output model that is well suited for the non-linear interaction of the wave with the surface anomaly and boundary of the substrate. The measured time-series waveform data is provided as input into the autoencoder network. The mean absolute error (MAE) between the input and output of the deep learning model is evaluated to detect the anomaly. The MAEs are sensitive to the anomaly that lies in the PZT substrate. Further, the challenge arising from offset and distortion is addressed with ad hoc image registration technique. Finally, the localisation and quantification of the anomaly are performed by computing PSNR values. This work proposes an advanced, efficient damage detection algorithm in the scenario of big data that is ubiquitous in SHM

Level based sampling techniques for energy conservation in large scale wireless sensor networks

As the size and node density of wireless sensor networks (WSN) increase,the energy conservation problem becomes more critical and the conventional methods become inadequate. This dissertation addresses two different problems in large scale WSNs where all sensors are involved in monitoring,but the traditional practice of periodic transmissions of observations from all sensors would drain excessive amount of energy. In the first problem,monitoring of the spatial distribution of a two dimensional correlated signal is considered using a large scale WSN. It is assumed that sensor observations are heavily affected by noise. We present an approach that is based on detecting contour lines of the signal distribution to estimate the spatial distribution of the signal without involving all sensors in the network. Energy efficient algorithms are proposed for detecting and tracking the temporal variation of the contours. Optimal contour levels that minimize the estimation error and a practical approach for selection of contour levels are explored. Performance of the proposed algorithm is explored with different types of contour levels and detection parameters. In the second problem,a WSN is considered that performs health monitoring of equipment from a power substation. The monitoring applications require transmissions of sensor observations from all sensor nodes on a regular basis to the base station,which is very costly in terms of communication cost. To address this problem,an efficient sampling technique using level-crossings (LCS) is proposed. This technique saves communication cost by suppressing transmissions of data samples that do not convey much information. The performance and cost of LCS for several different level-selection schemes are investigated. The number of required levels and the maximum sampling period for practical implementation of LCS are studied. Finally,in an experimental implementation of LCS with MICAzmote,the performance and cost of LCS for temperature sensing with uniform,logarithmic and a combined version of uniform and logarithmically spaced levels are compared with that using periodic sampling

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1