Turbo Bayesian Compressed Sensing

Compressed sensing (CS) theory specifies a new signal acquisition approach, potentially allowing the acquisition of signals at a much lower data rate than the Nyquist sampling rate. In CS, the signal is not directly acquired but reconstructed from a few measurements. One of the key problems in CS is how to recover the original signal from measurements in the presence of noise. This dissertation addresses signal reconstruction problems in CS. First, a feedback structure and signal recovery algorithm, orthogonal pruning pursuit (OPP), is proposed to exploit the prior knowledge to reconstruct the signal in the noise-free situation. To handle the noise, a noise-aware signal reconstruction algorithm based on Bayesian Compressed Sensing (BCS) is developed. Moreover, a novel Turbo Bayesian Compressed Sensing (TBCS) algorithm is developed for joint signal reconstruction by exploiting both spatial and temporal redundancy. Then, the TBCS algorithm is applied to a UWB positioning system for achieving mm-accuracy with low sampling rate ADCs. Finally, hardware implementation of BCS signal reconstruction on FPGAs and GPUs is investigated. Implementation on GPUs and FPGAs of parallel Cholesky decomposition, which is a key component of BCS, is explored. Simulation results on software and hardware have demonstrated that OPP and TBCS outperform previous approaches, with UWB positioning accuracy improved by 12.8x. The accelerated computation helps enable real-time application of this work

Training Echo State Networks with Regularization through Dimensionality Reduction

In this paper we introduce a new framework to train an Echo State Network to predict real valued time-series. The method consists in projecting the output of the internal layer of the network on a space with lower dimensionality, before training the output layer to learn the target task. Notably, we enforce a regularization constraint that leads to better generalization capabilities. We evaluate the performances of our approach on several benchmark tests, using different techniques to train the readout of the network, achieving superior predictive performance when using the proposed framework. Finally, we provide an insight on the effectiveness of the implemented mechanics through a visualization of the trajectory in the phase space and relying on the methodologies of nonlinear time-series analysis. By applying our method on well known chaotic systems, we provide evidence that the lower dimensional embedding retains the dynamical properties of the underlying system better than the full-dimensional internal states of the network

Data-driven discovery of coordinates and governing equations

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam's razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom autoencoder to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional dynamical systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. It is the first method of its kind to place the discovery of coordinates and models on an equal footing.Comment: 25 pages, 6 figures; added acknowledgment

Spatio-temporal learning with the online finite and infinite echo-state Gaussian processes

Successful biological systems adapt to change. In this paper, we are principally concerned with adaptive systems that operate in environments where data arrives sequentially and is multivariate in nature, for example, sensory streams in robotic systems. We contribute two reservoir inspired methods: 1) the online echostate Gaussian process (OESGP) and 2) its infinite variant, the online infinite echostate Gaussian process (OIESGP) Both algorithms are iterative fixed-budget methods that learn from noisy time series. In particular, the OESGP combines the echo-state network with Bayesian online learning for Gaussian processes. Extending this to infinite reservoirs yields the OIESGP, which uses a novel recursive kernel with automatic relevance determination that enables spatial and temporal feature weighting. When fused with stochastic natural gradient descent, the kernel hyperparameters are iteratively adapted to better model the target system. Furthermore, insights into the underlying system can be gleamed from inspection of the resulting hyperparameters. Experiments on noisy benchmark problems (one-step prediction and system identification) demonstrate that our methods yield high accuracies relative to state-of-the-art methods, and standard kernels with sliding windows, particularly on problems with irrelevant dimensions. In addition, we describe two case studies in robotic learning-by-demonstration involving the Nao humanoid robot and the Assistive Robot Transport for Youngsters (ARTY) smart wheelchair

A machine learning route between band mapping and band structure

The electronic band structure (BS) of solid state materials imprints the multidimensional and multi-valued functional relations between energy and momenta of periodically confined electrons. Photoemission spectroscopy is a powerful tool for its comprehensive characterization. A common task in photoemission band mapping is to recover the underlying quasiparticle dispersion, which we call band structure reconstruction. Traditional methods often focus on specific regions of interests yet require extensive human oversight. To cope with the growing size and scale of photoemission data, we develop a generic machine-learning approach leveraging the information within electronic structure calculations for this task. We demonstrate its capability by reconstructing all fourteen valence bands of tungsten diselenide and validate the accuracy on various synthetic data. The reconstruction uncovers previously inaccessible momentum-space structural information on both global and local scales in conjunction with theory, while realizing a path towards integrating band mapping data into materials science databases

Three more Decades in Array Signal Processing Research: An Optimization and Structure Exploitation Perspective

The signal processing community currently witnesses the emergence of sensor array processing and Direction-of-Arrival (DoA) estimation in various modern applications, such as automotive radar, mobile user and millimeter wave indoor localization, drone surveillance, as well as in new paradigms, such as joint sensing and communication in future wireless systems. This trend is further enhanced by technology leaps and availability of powerful and affordable multi-antenna hardware platforms. The history of advances in super resolution DoA estimation techniques is long, starting from the early parametric multi-source methods such as the computationally expensive maximum likelihood (ML) techniques to the early subspace-based techniques such as Pisarenko and MUSIC. Inspired by the seminal review paper Two Decades of Array Signal Processing Research: The Parametric Approach by Krim and Viberg published in the IEEE Signal Processing Magazine, we are looking back at another three decades in Array Signal Processing Research under the classical narrowband array processing model based on second order statistics. We revisit major trends in the field and retell the story of array signal processing from a modern optimization and structure exploitation perspective. In our overview, through prominent examples, we illustrate how different DoA estimation methods can be cast as optimization problems with side constraints originating from prior knowledge regarding the structure of the measurement system. Due to space limitations, our review of the DoA estimation research in the past three decades is by no means complete. For didactic reasons, we mainly focus on developments in the field that easily relate the traditional multi-source estimation criteria and choose simple illustrative examples.Comment: 16 pages, 8 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Empirical Bayesian significance measure of neuronal spike response

Background: Functional connectivity analyses of multiple neurons provide a powerful bottom-up approach to reveal functions of local neuronal circuits by using simultaneous recording of neuronal activity. A statistical methodology, generalized linear modeling (GLM) of the spike response function, is one of the most promising methodologies to reduce false link discoveries arising from pseudo-correlation based on common inputs. Although recent advancement of fluorescent imaging techniques has increased the number of simultaneously recoded neurons up to the hundreds or thousands, the amount of information per pair of neurons has not correspondingly increased, partly because of the instruments' limitations, and partly because the number of neuron pairs increase in a quadratic manner. Consequently, the estimation of GLM suffers from large statistical uncertainty caused by the shortage in effective information. Results: In this study, we propose a new combination of GLM and empirical Bayesian testing for the estimation of spike response functions that enables both conservative false discovery control and powerful functional connectivity detection. We compared our proposed method's performance with those of sparse estimation of GLM and classical Granger causality testing. Our method achieved high detection performance of functional connectivity with conservative estimation of false discovery rate and q values in case of information shortage due to short observation time. We also showed that empirical Bayesian testing on arbitrary statistics in place of likelihood-ratio statistics reduce the computational cost without decreasing the detection performance. When our proposed method was applied to a functional multi-neuron calcium imaging dataset from the rat hippocampal region, we found significant functional connections that are possibly mediated by AMPA and NMDA receptors. Conclusions: The proposed empirical Bayesian testing framework with GLM is promising especially when the amount of information per a neuron pair is small because of growing size of observed network

Model-based Filtering of Interfering Signals in Ultrasonic Time Delay Estimations

This work presents model-based algorithmic approaches for interference-invariant time delay estimation, which are specifically suited for the estimation of small time delay differences with a necessary resolution well below the sampling time. Therefore, the methods can be applied particularly well for transit-time ultrasonic flow measurements, since the problem of interfering signals is especially prominent in this application