Bayesian Nonparametric Unmixing of Hyperspectral Images

Hyperspectral imaging is an important tool in remote sensing, allowing for accurate analysis of vast areas. Due to a low spatial resolution, a pixel of a hyperspectral image rarely represents a single material, but rather a mixture of different spectra. HSU aims at estimating the pure spectra present in the scene of interest, referred to as endmembers, and their fractions in each pixel, referred to as abundances. Today, many HSU algorithms have been proposed, based either on a geometrical or statistical model. While most methods assume that the number of endmembers present in the scene is known, there is only little work about estimating this number from the observed data. In this work, we propose a Bayesian nonparametric framework that jointly estimates the number of endmembers, the endmembers itself, and their abundances, by making use of the Indian Buffet Process as a prior for the endmembers. Simulation results and experiments on real data demonstrate the effectiveness of the proposed algorithm, yielding results comparable with state-of-the-art methods while being able to reliably infer the number of endmembers. In scenarios with strong noise, where other algorithms provide only poor results, the proposed approach tends to overestimate the number of endmembers slightly. The additional endmembers, however, often simply represent noisy replicas of present endmembers and could easily be merged in a post-processing step

A survey on Bayesian nonparametric learning

© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM. Bayesian (machine) learning has been playing a significant role in machine learning for a long time due to its particular ability to embrace uncertainty, encode prior knowledge, and endow interpretability. On the back of Bayesian learning's great success, Bayesian nonparametric learning (BNL) has emerged as a force for further advances in this field due to its greater modelling flexibility and representation power. Instead of playing with the fixed-dimensional probabilistic distributions of Bayesian learning, BNL creates a new “game” with infinite-dimensional stochastic processes. BNL has long been recognised as a research subject in statistics, and, to date, several state-of-the-art pilot studies have demonstrated that BNL has a great deal of potential to solve real-world machine-learning tasks. However, despite these promising results, BNL has not created a huge wave in the machine-learning community. Esotericism may account for this. The books and surveys on BNL written by statisticians are overcomplicated and filled with tedious theories and proofs. Each is certainly meaningful but may scare away new researchers, especially those with computer science backgrounds. Hence, the aim of this article is to provide a plain-spoken, yet comprehensive, theoretical survey of BNL in terms that researchers in the machine-learning community can understand. It is hoped this survey will serve as a starting point for understanding and exploiting the benefits of BNL in our current scholarly endeavours. To achieve this goal, we have collated the extant studies in this field and aligned them with the steps of a standard BNL procedure-from selecting the appropriate stochastic processes through manipulation to executing the model inference algorithms. At each step, past efforts have been thoroughly summarised and discussed. In addition, we have reviewed the common methods for implementing BNL in various machine-learning tasks along with its diverse applications in the real world as examples to motivate future studies

Source Separation in the Presence of Side-information

The source separation problem involves the separation of unknown signals from their mixture. This problem is relevant in a wide range of applications from audio signal processing, communication, biomedical signal processing and art investigation to name a few. There is a vast literature on this problem which is based on either making strong assumption on the source signals or availability of additional data. This thesis proposes new algorithms for source separation with side information where one observes the linear superposition of two source signals plus two additional signals that are correlated with the mixed ones. The first algorithm is based on two ingredients: first, we learn a Gaussian mixture model (GMM) for the joint distribution of a source signal and the corresponding correlated side information signal; second, we separate the signals using standard computationally efficient conditional mean estimators. This also puts forth new recovery guarantees for this source separation algorithm. In particular, under the assumption that the signals can be perfectly described by a GMM model, we characterize necessary and sufficient conditions for reliable source separation in the asymptotic regime of low-noise as a function of the geometry of the underlying signals and their interaction. It is shown that if the subspaces spanned by the innovation components of the source signals with respect to the side information signals have zero intersection, provided that we observe a certain number of linear measurements from the mixture, then we can reliably separate the sources; otherwise we cannot. The second algorithms is based on deep learning where we introduce a novel self-supervised algorithm for the source separation problem. Source separation is intrinsically unsupervised and the lack of training data makes it a difficult task for artificial intelligence to solve. The proposed framework takes advantage of the available data and delivers near perfect separation results in real data scenarios. Our proposed frameworks – which provide new ways to incorporate side information to aid the solution of the source separation problem – are also employed in a real-world art investigation application involving the separation of mixtures of X-Ray images. The simulation results showcase the superiority of our algorithm against other state-of-the-art algorithms