Adaptive Langevin Sampler for Separation of t-Distribution Modelled Astrophysical Maps

We propose to model the image differentials of astrophysical source maps by Student's t-distribution and to use them in the Bayesian source separation method as priors. We introduce an efficient Markov Chain Monte Carlo (MCMC) sampling scheme to unmix the astrophysical sources and describe the derivation details. In this scheme, we use the Langevin stochastic equation for transitions, which enables parallel drawing of random samples from the posterior, and reduces the computation time significantly (by two orders of magnitude). In addition, Student's t-distribution parameters are updated throughout the iterations. The results on astrophysical source separation are assessed with two performance criteria defined in the pixel and the frequency domains.Comment: 12 pages, 6 figure

Improved Convolutive and Under-Determined Blind Audio Source Separation with MRF Smoothing

Convolutive and under-determined blind audio source separation from noisy recordings is a challenging problem. Several computational strategies have been proposed to address this problem. This study is concerned with several modifications to the expectation-minimization-based algorithm, which iteratively estimates the mixing and source parameters. This strategy assumes that any entry in each source spectrogram is modeled using superimposed Gaussian components, which are mutually and individually independent across frequency and time bins. In our approach, we resolve this issue by considering a locally smooth temporal and frequency structure in the power source spectrograms. Local smoothness is enforced by incorporating a Gibbs prior in the complete data likelihood function, which models the interactions between neighboring spectrogram bins using a Markov random field. Simulations using audio files derived from stereo audio source separation evaluation campaign 2008 demonstrate high efficiency with the proposed improvement

Landslide mapping from multi-sensor data through improved change detection-based Markov random field

Abstract Accurate landslide inventory mapping is essential for quantitative hazard and risk assessment. Although multi-temporal change detection techniques have contributed greatly to landslide inventory preparation, it is still challenging to generate quality change detection images (CDIs) for accurate landslide mapping. The recently proposed change detection-based Markov random field (CDMRF) provides an effective approach for rapid mapping of landslides with minimum user interventions. However, when CDI is generated by change vector analysis (CVA) alone, the CDMRF method may suffer from noise especially when the pre- and post-event remote sensing images are acquired under different atmospheric, illumination, and phenological conditions. This paper improved such CDMRF approach by integrating normalized difference vegetation index (NDVI), principal component analysis (PCA), and independent component analysis (ICA) generated CDIs with MRF for landslide inventory mapping from multi-sensor data. To justify the effectiveness and applicability, the improved methods were applied to map rainfall-, typhoon-, and earthquake-triggered landslides from the pre- and post-event satellite images acquired by very high resolution QuickBird, high resolution FORMOSAT-2, and moderate resolution Sentinel-2. Moreover, they were tested on pre-event Landsat-8 and post-event Sentinel-2 datasets, indicating that they are operational for landslide inventory mapping from combined multi-temporal and multi-sensor data. The results demonstrate that the improved δNDVI-, PCA-, and ICA-based approaches perform much better than CVA-based CDMRF in terms of completeness, correctness, Kappa coefficient, and F-measures. To the best of our knowledge, it is the first time that NDVI, PCA, and ICA are integrated with MRF for landslide inventory mapping from multi-sensor data. It is anticipated that this research can be a starting point for developing new change detection techniques that can readily generate quality CDI and for applying advanced machine learning algorithms (e.g., deep learning) to automatic detection of natural hazards from multi-sensor time series data

Doctor of Philosophy

dissertationFunctional magnetic resonance imaging (fMRI) measures the change of oxygen consumption level in the blood vessels of the human brain, hence indirectly detecting the neuronal activity. Resting-state fMRI (rs-fMRI) is used to identify the intrinsic functional patterns of the brain when there is no external stimulus. Accurate estimation of intrinsic activity is important for understanding the functional organization and dynamics of the brain, as well as differences in the functional networks of patients with mental disorders. This dissertation aims to robustly estimate the functional connectivities and networks of the human brain using rs-fMRI data of multiple subjects. We use Markov random field (MRF), an undirected graphical model to represent the statistical dependency among the functional network variables. Graphical models describe multivariate probability distributions that can be factorized and represented by a graph. By defining the nodes and the edges along with their weights according to our assumptions, we build soft constraints into the graph structure as prior information. We explore various approximate optimization methods including variational Bayesian, graph cuts, and Markov chain Monte Carlo sampling (MCMC). We develop the random field models to solve three related problems. In the first problem, the goal is to detect the pairwise connectivity between gray matter voxels in a rs-fMRI dataset of the single subject. We define a six-dimensional graph to represent our prior information that two voxels are more likely to be connected if their spatial neighbors are connected. The posterior mean of the connectivity variables are estimated by variational inference, also known as mean field theory in statistical physics. The proposed method proves to outperform the standard spatial smoothing and is able to detect finer patterns of brain activity. Our second work aims to identify multiple functional systems. We define a Potts model, a special case of MRF, on the network label variables, and define von Mises-Fisher distribution on the normalized fMRI signal. The inference is significantly more difficult than the binary classification in the previous problem. We use MCMC to draw samples from the posterior distribution of network labels. In the third application, we extend the graphical model to the multiple subject scenario. By building a graph including the network labels of both a group map and the subject label maps, we define a hierarchical model that has richer structure than the flat single-subject model, and captures the shared patterns as well as the variation among the subjects. All three solutions are data-driven Bayesian methods, which estimate model parameters from the data. The experiments show that by the regularization of MRF, the functional network maps we estimate are more accurate and more consistent across multiple sessions