Dynamical Hyperspectral Unmixing with Variational Recurrent Neural Networks

Multitemporal hyperspectral unmixing (MTHU) is a fundamental tool in the analysis of hyperspectral image sequences. It reveals the dynamical evolution of the materials (endmembers) and of their proportions (abundances) in a given scene. However, adequately accounting for the spatial and temporal variability of the endmembers in MTHU is challenging, and has not been fully addressed so far in unsupervised frameworks. In this work, we propose an unsupervised MTHU algorithm based on variational recurrent neural networks. First, a stochastic model is proposed to represent both the dynamical evolution of the endmembers and their abundances, as well as the mixing process. Moreover, a new model based on a low-dimensional parametrization is used to represent spatial and temporal endmember variability, significantly reducing the amount of variables to be estimated. We propose to formulate MTHU as a Bayesian inference problem. However, the solution to this problem does not have an analytical solution due to the nonlinearity and non-Gaussianity of the model. Thus, we propose a solution based on deep variational inference, in which the posterior distribution of the estimated abundances and endmembers is represented by using a combination of recurrent neural networks and a physically motivated model. The parameters of the model are learned using stochastic backpropagation. Experimental results show that the proposed method outperforms state of the art MTHU algorithms

Gaussian mixture model classifiers for detection and tracking in UAV video streams.

Masters Degree. University of KwaZulu-Natal, Durban.Manual visual surveillance systems are subject to a high degree of human-error and operator fatigue. The automation of such systems often employs detectors, trackers and classifiers as fundamental building blocks. Detection, tracking and classification are especially useful and challenging in Unmanned Aerial Vehicle (UAV) based surveillance systems. Previous solutions have addressed challenges via complex classification methods. This dissertation proposes less complex Gaussian Mixture Model (GMM) based classifiers that can simplify the process; where data is represented as a reduced set of model parameters, and classification is performed in the low dimensionality parameter-space. The specification and adoption of GMM based classifiers on the UAV visual tracking feature space formed the principal contribution of the work. This methodology can be generalised to other feature spaces. This dissertation presents two main contributions in the form of submissions to ISI accredited journals. In the first paper, objectives are demonstrated with a vehicle detector incorporating a two stage GMM classifier, applied to a single feature space, namely Histogram of Oriented Gradients (HoG). While the second paper demonstrates objectives with a vehicle tracker using colour histograms (in RGB and HSV), with Gaussian Mixture Model (GMM) classifiers and a Kalman filter. The proposed works are comparable to related works with testing performed on benchmark datasets. In the tracking domain for such platforms, tracking alone is insufficient. Adaptive detection and classification can assist in search space reduction, building of knowledge priors and improved target representations. Results show that the proposed approach improves performance and robustness. Findings also indicate potential further enhancements such as a multi-mode tracker with global and local tracking based on a combination of both papers

Veni Vidi Vici, A Three-Phase Scenario For Parameter Space Analysis in Image Analysis and Visualization

Automatic analysis of the enormous sets of images is a critical task in life sciences. This faces many challenges such as: algorithms are highly parameterized, significant human input is intertwined, and lacking a standard meta-visualization approach. This paper proposes an alternative iterative approach for optimizing input parameters, saving time by minimizing the user involvement, and allowing for understanding the workflow of algorithms and discovering new ones. The main focus is on developing an interactive visualization technique that enables users to analyze the relationships between sampled input parameters and corresponding output. This technique is implemented as a prototype called Veni Vidi Vici, or "I came, I saw, I conquered." This strategy is inspired by the mathematical formulas of numbering computable functions and is developed atop ImageJ, a scientific image processing program. A case study is presented to investigate the proposed framework. Finally, the paper explores some potential future issues in the application of the proposed approach in parameter space analysis in visualization

Large Scale Inverse Problems

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation &amp Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. This collection of survey articles focusses on the large inverse problems commonly arising in simulation and forecasting in the earth sciences

MEG and fMRI Fusion for Non-Linear Estimation of Neural and BOLD Signal Changes

The combined analysis of magnetoencephalography (MEG)/electroencephalography and functional magnetic resonance imaging (fMRI) measurements can lead to improvement in the description of the dynamical and spatial properties of brain activity. In this paper we empirically demonstrate this improvement using simulated and recorded task related MEG and fMRI activity. Neural activity estimates were derived using a dynamic Bayesian network with continuous real valued parameters by means of a sequential Monte Carlo technique. In synthetic data, we show that MEG and fMRI fusion improves estimation of the indirectly observed neural activity and smooths tracking of the blood oxygenation level dependent (BOLD) response. In recordings of task related neural activity the combination of MEG and fMRI produces a result with greater signal-to-noise ratio, that confirms the expectation arising from the nature of the experiment. The highly non-linear model of the BOLD response poses a difficult inference problem for neural activity estimation; computational requirements are also high due to the time and space complexity. We show that joint analysis of the data improves the system's behavior by stabilizing the differential equations system and by requiring fewer computational resources

Multichannel source separation and tracking with phase differences by random sample consensus

Blind audio source separation (BASS) is a fascinating problem that has been tackled from many different angles. The use case of interest in this thesis is that of multiple moving and simultaneously-active speakers in a reverberant room. This is a common situation, for example, in social gatherings. We human beings have the remarkable ability to focus attention on a particular speaker while effectively ignoring the rest. This is referred to as the ``cocktail party effect'' and has been the holy grail of source separation for many decades. Replicating this feat in real-time with a machine is the goal of BASS. Single-channel methods attempt to identify the individual speakers from a single recording. However, with the advent of hand-held consumer electronics, techniques based on microphone array processing are becoming increasingly popular. Multichannel methods record a sound field from various locations to incorporate spatial information. If the speakers move over time, we need an algorithm capable of tracking their positions in the room. For compact arrays with 1-10 cm of separation between the microphones, this can be accomplished by applying a temporal filter on estimates of the directions-of-arrival (DOA) of the speakers. In this thesis, we review recent work on BSS with inter-channel phase difference (IPD) features and provide extensions to the case of moving speakers. It is shown that IPD features compose a noisy circular-linear dataset. This data is clustered with the RANdom SAmple Consensus (RANSAC) algorithm in the presence of strong reverberation to simultaneously localize and separate speakers. The remarkable performance of RANSAC is due to its natural tendency to reject outliers. To handle the case of non-stationary speakers, a factorial wrapped Kalman filter (FWKF) and a factorial von Mises-Fisher particle filter (FvMFPF) are proposed that track source DOAs directly on the unit circle and unit sphere, respectively. These algorithms combine directional statistics, Bayesian filtering theory, and probabilistic data association techniques to track the speakers with mixtures of directional distributions

Multimodal methods for blind source separation of audio sources

The enhancement of the performance of frequency domain convolutive blind source separation (FDCBSS) techniques when applied to the problem of separating audio sources recorded in a room environment is the focus of this thesis. This challenging application is termed the cocktail party problem and the ultimate aim would be to build a machine which matches the ability of a human being to solve this task. Human beings exploit both their eyes and their ears in solving this task and hence they adopt a multimodal approach, i.e. they exploit both audio and video modalities. New multimodal methods for blind source separation of audio sources are therefore proposed in this work as a step towards realizing such a machine. The geometry of the room environment is initially exploited to improve the separation performance of a FDCBSS algorithm. The positions of the human speakers are monitored by video cameras and this information is incorporated within the FDCBSS algorithm in the form of constraints added to the underlying cross-power spectral density matrix-based cost function which measures separation performance. [Continues.

Review on Sparse-Based Multipath Estimation and Mitigation: Intense Solution to Counteract the Effects in Software GPS Receivers

Multipath is the major concern in GPS receivers that fade the actual GPS signal causes positioning error up to 10 m so special care need to be taken to mitigate the multipath effects. Numerous methods like hardware based antenna arrays technique, receiver based narrow correlator receiver, double -delta discriminator, Adaptive Multipath Estimator, Wavelet Transformation and Particle filter, Kalman filter based post receiver methods etc. used to resolve the problem. But some of the methods can only reduce code multipath error but not effective in eliminating carrier multipath error. Most of these techniques are based on the assumption that the Line-of-Sight (LOS) signal is stronger than the Non-Line of-Sight (NLOS) signals. However, in the scenarios where the LOS signal is weaker than the composite multipath signal, this approach may result in a bias in code tracking. In this chapter, different types of multipath mitigation and its limitation are described. The recent development in sparse signal processing based blind channel estimation is investigated to compensate the multipath error. The Rayleigh and Rician fading model with different multipath parameters are simulated to test the urban scenario. The inverse problem of finding the GPS signal is addressed based on the deconvolution approach. To solve linear inverse problems, the suitable kind of appropriate objective function has been formulated to find the signal of interest. By exploiting this methods, the signal is observed and the carrier and code tracking loop parameters are computed with minimal error

Bayesian framework for multiple acoustic source tracking

Acoustic source (speaker) tracking in the room environment plays an important role in many speech and audio applications such as multimedia, hearing aids and hands-free speech communication and teleconferencing systems; the position information can be fed into a higher processing stage for high-quality speech acquisition, enhancement of a specific speech signal in the presence of other competing talkers, or keeping a camera focused on the speaker in a video-conferencing scenario. Most of existing systems focus on the single source tracking problem, which assumes one and only one source is active all the time, and the state to be estimated is simply the source position. However, in practical scenarios, multiple speakers may be simultaneously active, and the tracking algorithm should be able to localise each individual source and estimate the number of sources. This thesis contains three contributions towards solutions to multiple acoustic source tracking in a moderate noisy and reverberant environment. The first contribution of this thesis is proposing a time-delay of arrival (TDOA) estimation approach for multiple sources. Although the phase transform (PHAT) weighted generalised cross-correlation (GCC) method has been employed to extract the TDOAs of multiple sources, it is primarily used for a single source scenario and its performance for multiple TDOA estimation has not been comprehensively studied. The proposed approach combines the degenerate unmixing estimation technique (DUET) and GCC method. Since the speech mixtures are assumed window-disjoint orthogonal (WDO) in the time-frequency domain, the spectrograms can be separated by employing DUET, and the GCC method can then be applied to the spectrogram of each individual source. The probabilities of detection and false alarm are also proposed to evaluate the TDOA estimation performance under a series of experimental parameters. Next, considering multiple acoustic sources may appear nonconcurrently, an extended Kalman particle filtering (EKPF) is developed for a special multiple acoustic source tracking problem, namely “nonconcurrent multiple acoustic tracking (NMAT)”. The extended Kalman filter (EKF) is used to approximate the optimum weights, and the subsequent particle filtering (PF) naturally takes the previous position estimates as well as the current TDOA measurements into account. The proposed approach is thus able to lock on the sharp change of the source position quickly, and avoid the tracking-lag in the general sequential importance resampling (SIR) PF. Finally, these investigations are extended into an approach to track the multiple unknown and time-varying number of acoustic sources. The DUET-GCC method is used to obtain the TDOA measurements for multiple sources and a random finite set (RFS) based Rao-blackwellised PF is employed and modified to track the sources. Each particle has a RFS form encapsulating the states of all sources and is capable of addressing source dynamics: source survival, new source appearance and source deactivation. A data association variable is defined to depict the source dynamic and its relation to the measurements. The Rao-blackwellisation step is used to decompose the state: the source positions are marginalised by using an EKF, and only the data association variable needs to be handled by a PF. The performances of all the proposed approaches are extensively studied under different noisy and reverberant environments, and are favorably comparable with the existing tracking techniques