SimpleTrack:Adaptive Trajectory Compression with Deterministic Projection Matrix for Mobile Sensor Networks

Some mobile sensor network applications require the sensor nodes to transfer their trajectories to a data sink. This paper proposes an adaptive trajectory (lossy) compression algorithm based on compressive sensing. The algorithm has two innovative elements. First, we propose a method to compute a deterministic projection matrix from a learnt dictionary. Second, we propose a method for the mobile nodes to adaptively predict the number of projections needed based on the speed of the mobile nodes. Extensive evaluation of the proposed algorithm using 6 datasets shows that our proposed algorithm can achieve sub-metre accuracy. In addition, our method of computing projection matrices outperforms two existing methods. Finally, comparison of our algorithm against a state-of-the-art trajectory compression algorithm show that our algorithm can reduce the error by 10-60 cm for the same compression ratio

Quantifying the performance of compressive sensing on scalp EEG signals

Compressive sensing is a new data compression paradigm that has shown significant promise in fields such as MRI. However, the practical performance of the theory very much depends on the characteristics of the signal being sensed. As such the utility of the technique cannot be extrapolated from one application to another. Electroencephalography (EEG) is a fundamental tool for the investigation of many neurological disorders and is increasingly also used in many non-medical applications, such as Brain-Computer Interfaces. This paper characterises in detail the practical performance of different implementations of the compressive sensing theory when applied to scalp EEG signals for the first time. The results are of particular interest for wearable EEG communication systems requiring low power, real-time compression of the EEG data. ©2010 IEEE.Accepted versio

ADDRESSING THREE PROBLEMS IN EMBEDDED SYSTEMS VIA COMPRESSIVE SENSING BASED METHODS

Compressive sensing is a mathematical theory concerning exact/approximate recovery of sparse/compressible vectors using the minimum number of measurements called projections. Its theory covers topics such as l1 optimisation, dimensionality reduction, information preserving projection matrices, random projection matrices and others. In this thesis we extend and use the theory of compressive sensing to address the challenges of limited computation power and energy supply in embedded systems. Three different problems are addressed. The first problem is to improve the efficiency of data gathering in wireless sensor networks. Many wireless sensor networks exhibit heterogeneity because of the environment. We leverage this heterogeneity and extend the theory of compressive sensing to cover non-uniform sampling to derive a new data collection protocol. We show that this protocol can realise a more accurate temporal-spatial profile for a given level of energy consumption. The second problem is to realise realtime background subtraction in embedded cameras. Background subtraction algorithms are normally computationally expensive because they use complex models to deal with subtle changes in background. Therefore existing background subtraction algorithms cannot provide realtime performance on embedded cameras which have limited processing power. By leveraging information preserving projection matrices, we derive a new background subtraction algorithm which is 4.6 times faster and more accurate than existing methods. We demonstrate that our background subtraction algorithm can realise realtime background subtraction and tracking in an embedded camera network. The third problem is to enable efficient and accurate face recognition on smartphones. The state-of-the-art face recognition algorithm is inspired by compressive sensing and is based on l1 optimisation. It also uses random projection matrices for dimensionality reduction. A key problem of using random projection matrices is that they give highly variable recognition accuracy. We propose an algorithm to optimise projection matrix to remove this performance variability. This means we can use fewer projections to achieve the same accuracy. This translates to a smaller l1 optimisation problem and reduces the computation time needed on smartphones, which have limited computation power. We demonstrate the performance of our proposed method on smartphones

Cygnus A super-resolved via convex optimisation from VLA data

We leverage the Sparsity Averaging Reweighted Analysis (SARA) approach for interferometric imaging, that is based on convex optimisation, for the super-resolution of Cyg A from observations at the frequencies 8.422GHz and 6.678GHz with the Karl G. Jansky Very Large Array (VLA). The associated average sparsity and positivity priors enable image reconstruction beyond instrumental resolution. An adaptive Preconditioned Primal-Dual algorithmic structure is developed for imaging in the presence of unknown noise levels and calibration errors. We demonstrate the superior performance of the algorithm with respect to the conventional CLEAN-based methods, reflected in super-resolved images with high fidelity. The high resolution features of the recovered images are validated by referring to maps of Cyg A at higher frequencies, more precisely 17.324GHz and 14.252GHz. We also confirm the recent discovery of a radio transient in Cyg A, revealed in the recovered images of the investigated data sets. Our matlab code is available online on GitHub.Comment: 14 pages, 7 figures (3/7 animated figures), accepted for publication in MNRA

Discussion of "Geodesic Monte Carlo on Embedded Manifolds"

Contributed discussion and rejoinder to "Geodesic Monte Carlo on Embedded Manifolds" (arXiv:1301.6064)Comment: Discussion of arXiv:1301.6064. To appear in the Scandinavian Journal of Statistics. 18 page

Discrete Electronic Warfare Signal Processing using Compressed Sensing Based on Random Modulator Pre-Integrator

Electronic warfare receiver works in the wide electromagnetic spectrum in dense radar signal environment. Current trends in radar systems are ultra wideband and low probability of intercept radar technology. Detection of signals from various radar stations is a concern. Performance and probability of intercept are mainly dependent on high speed ADC technology. The sampling and reconstruction functions have to be optimized to capture incoming signals at the receiver to extract characteristics of the radar signal. The compressive sampling of the input signal with orthonormal base vectors, projecting the basis in the union of subspaces and recovery through convex optimisation techniques is the current traditional approach. Modern trends in signal processing suggest the random modulator pre-integrator (RMPI), which sample the input signal at information rate non-adaptively and recovery by the processing of discrete and finite vectors. Analysis of RMPI theory, application to EW receiver, simulation and recovery of EW receiver signals are discussed

Compressed sensing current mapping spatial characterization of photovoltaic devices

In this work a new measurement technique for current mapping of photovoltaic (PV) devices is developed, utilising the compressed sensing (CS) sampling theory. Conventional current mapping measurements of PV devices are realised using the light beam induced current (LBIC) measurement method. For its realization, a light beam scans a PV device and the induced current is measured for every point, generating the final current map of the device. Disadvantages of the LBIC method are the low measurement speed, the complicated and usually expensive measurement layouts and the impractical application of the method on PV modules. With the development of CS current mapping in this work, the above issues can be mitigated. Instead of applying a raster scan, a series of illumination patterns are projected onto the PV sample, acquiring fewer measurements than the pixels of the final current map. The final reconstruction of the current map is achieved by means of an optimisation algorithm. Spatially resolved electrical simulations of CS current mapping demonstrate that theoretically the proposed method is feasible. In addition, it is shown that current maps can be acquired with even 40% of the measurements a standard LBIC system would require, saving a significant amount of measurement time. The performance of CS current mapping is the same, regardless of the features a sample may contain and measurements can be applied to any type of photovoltaic device. The ability of the method to provide current maps of PV modules is demonstrated. The performance of several reconstruction algorithms is also investigated. An optical measurement setup for CS current mapping of small area PV devices was built at the National Physical Laboratory (NPL), based on a digital micromirror device (DMD). Accurate current maps can be produced with only 40% of the measurements a conventional point by point scan would need, confirming simulation results. The measurement setup is compact, straightforward to realise and uses a small number of optical elements. It can measure a small area of 1cm by 1cm, making it ideal for current mapping of small research samples. A significant signal amplification is achieved, since the patterns illuminate half of the sample. This diminishes the use of lock-in techniques, reducing the cost for current mapping of PV devices. Current maps of an optical resolution up to 27μm are acquired, without the use of any demagnification elements of the projected pattern that the DMD generates. v A scale up of this new current mapping method is demonstrated using Digital Light Processing (DLP) technology, which is based on DMD chips. A commercial DLP projector is utilised for building a proof of concept CS current mapping measurement system at the Centre of Renewable Energy Systems Technology (CREST). Current maps of individual PV cells in encapsulated modules can be acquired, something that is extremely difficult to achieve with conventional LBIC systems. Direct current mapping of a PV module with by-pass diodes is successfully applied for the first time. Specific shading strategies are developed for this purpose in order to isolate the cell under test. Due to the application of compressive sampling, current maps are acquired even if the signal-to-noise-ratio levels are so low that a point by point scan is not possible. Through the above implementations of CS current mapping of this work, the proposed technique is studied and evaluated. The results demonstrate that this novel method can offer a realistic alternative approach for current mapping of PV cells and modules that can be cost effective and straightforward to implement. In addition, this work introduces the application of the CS theory and DLP technology to PV metrology in general

Random sampling of bandlimited signals on graphs

We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure, and its performance depends on a parameter called the graph coherence. On the contrary, the second strategy is adaptive but yields optimal results. Indeed, no more than O(k log(k)) measurements are sufficient to ensure an accurate and stable recovery of all k-bandlimited signals. This second strategy is based on a careful choice of the sampling distribution, which can be estimated quickly. Then, we propose a computationally efficient decoder to reconstruct k-bandlimited signals from their samples. We prove that it yields accurate reconstructions and that it is also stable to noise. Finally, we conduct several experiments to test these techniques