Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least Squares Problem

In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares (S-NNLS) problem. We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R- GSM) to model the sparsity enforcing prior distribution for the solution. The R-GSM prior encompasses a variety of heavy-tailed densities such as the rectified Laplacian and rectified Student- t distributions with a proper choice of the mixing density. We utilize the hierarchical representation induced by the R-GSM prior and develop an evidence maximization framework based on the Expectation-Maximization (EM) algorithm. Using the EM based method, we estimate the hyper-parameters and obtain a point estimate for the solution. We refer to the proposed method as rectified sparse Bayesian learning (R-SBL). We provide four R- SBL variants that offer a range of options for computational complexity and the quality of the E-step computation. These methods include the Markov chain Monte Carlo EM, linear minimum mean-square-error estimation, approximate message passing and a diagonal approximation. Using numerical experiments, we show that the proposed R-SBL method outperforms existing S-NNLS solvers in terms of both signal and support recovery performance, and is also very robust against the structure of the design matrix.Comment: Under Review by IEEE Transactions on Signal Processin

Détection de bateaux dans les images de radar à ouverture synthétique

Le but principal de cette thèse est de développer des algorithmes efficaces et de concevoir un système pour la détection de bateaux dans les images Radar à Ouverture Synthetique (ROS.) Dans notre cas, la détection de bateaux implique en premier lieu la détection de cibles de points dans les images ROS. Ensuite, la détection d'un bateau proprement dit dépend des propriétés physiques du bateau lui-même, tel que sa taille, sa forme, sa structure, son orientation relative a la direction de regard du radar et les conditions générales de l'état de la mer. Notre stratégie est de détecter toutes les cibles de bateaux possibles dans les images de ROS, et ensuite de chercher autour de chaque candidat des évidences telle que les sillons. Les objectifs de notre recherche sont (1) d'améliorer 1'estimation des paramètres dans Ie modèle de distribution-K et de déterminer les conditions dans lesquelles un modèle alternatif (Ie Gamma, par exemple) devrait être utilise plutôt; (2) d'explorer Ie modèle PNN (Probabilistic Neural Network) comme une alternative aux modèles paramétriques actuellement utilises; (3) de concevoir un modèle de regroupement flou (FC : Fuzzy Clustering) capable de détecter les petites et grandes cibles de bateaux dans les images a un seul canal ou les images a multi-canaux; (4) de combiner la détection de sillons avec la détection de cibles de bateaux; (5) de concevoir un modèle de détection qui peut être utilisé aussi pour la détection des cibles de bateaux en zones costières.Abstract: The main purpose of this thesis is to develop efficient algorithms and design a system for ship detection from Synthetic Aperture Radar (SAR) imagery. Ship detection usually involves through detection of point targets on a radar clutter background.The detection of a ship depends on the physical properties of the ship itself, such as size, shape, and structure; its orientation relative to the radar look-direction; and the general condition of the sea state. Our strategy is to detect all possible ship targets in SAR images, and then search around each candidate for the wake as further evidence.The objectives of our research are (1) to improve estimation of the parameters in the K-distribution model and to determine the conditions in which an alternative model (Gamma, for example) should be used instead; (2) to explore a PNN (Probabilistic Neural Networks) model as an alternative to the commonly used parameteric models; (3) to design a FC (Fuzzy Clustering) model capable of detecting both small and large ship targets from single-channel images or multi-channel images; (4) to combine wake detection with ship target detection; (5) to design a detection model that can also be used to detect ship targets in coastal areas. We have developed algorithms for each of these objectives and integrated them into a system comprising six models.The system has been tested on a number of SAR images (SEASAT, ERS and RADARSAT-1, for example) and its performance has been assessed

A novel framework for MR image segmentation and quantification by using MedGA.

BACKGROUND AND OBJECTIVES: Image segmentation represents one of the most challenging issues in medical image analysis to distinguish among different adjacent tissues in a body part. In this context, appropriate image pre-processing tools can improve the result accuracy achieved by computer-assisted segmentation methods. Taking into consideration images with a bimodal intensity distribution, image binarization can be used to classify the input pictorial data into two classes, given a threshold intensity value. Unfortunately, adaptive thresholding techniques for two-class segmentation work properly only for images characterized by bimodal histograms. We aim at overcoming these limitations and automatically determining a suitable optimal threshold for bimodal Magnetic Resonance (MR) images, by designing an intelligent image analysis framework tailored to effectively assist the physicians during their decision-making tasks. METHODS: In this work, we present a novel evolutionary framework for image enhancement, automatic global thresholding, and segmentation, which is here applied to different clinical scenarios involving bimodal MR image analysis: (i) uterine fibroid segmentation in MR guided Focused Ultrasound Surgery, and (ii) brain metastatic cancer segmentation in neuro-radiosurgery therapy. Our framework exploits MedGA as a pre-processing stage. MedGA is an image enhancement method based on Genetic Algorithms that improves the threshold selection, obtained by the efficient Iterative Optimal Threshold Selection algorithm, between the underlying sub-distributions in a nearly bimodal histogram. RESULTS: The results achieved by the proposed evolutionary framework were quantitatively evaluated, showing that the use of MedGA as a pre-processing stage outperforms the conventional image enhancement methods (i.e., histogram equalization, bi-histogram equalization, Gamma transformation, and sigmoid transformation), in terms of both MR image enhancement and segmentation evaluation metrics. CONCLUSIONS: Thanks to this framework, MR image segmentation accuracy is considerably increased, allowing for measurement repeatability in clinical workflows. The proposed computational solution could be well-suited for other clinical contexts requiring MR image analysis and segmentation, aiming at providing useful insights for differential diagnosis and prognosis

The severity of stages estimation during hemorrhage using error correcting output codes method

As a beneficial component with critical impact, computer-aided decision making systems have infiltrated many fields, such as economics, medicine, architecture and agriculture. The latent capabilities for facilitating human work propel high-speed development of such systems. Effective decisions provided by such systems greatly reduce the expense of labor, energy, budget, etc. The computer-aided decision making system for traumatic injuries is one type of such systems that supplies suggestive opinions when dealing with the injuries resulted from accidents, battle, or illness. The functions may involve judging the type of illness, allocating the wounded according to battle injuries, deciding the severity of symptoms for illness or injuries, managing the resources in the context of traumatic events, etc. The proposed computer-aided decision making system aims at estimating the severity of blood volume loss. Specifically speaking, accompanying many traumatic injuries, severe hemorrhage, a potentially life-threatening condition that requires immediate treatment, is a significant loss of blood volume in process resulting in decreased blood and oxygen perfusion of vital organs. Hemorrhage and blood loss can occur in different levels such as mild, moderate, or severe. Our proposed system will assist physicians by estimating information such as the severity of blood volume loss and hemorrhage , so that timely measures can be taken to not only save lives but also reduce the long-term complications as well as the cost caused by unmatched operations and treatments. The general framework of the proposed research contains three tasks and many novel and transformative concepts are integrated into the system. First is the preprocessing of the raw signals. In this stage, adaptive filtering is adopted and customized to filter noise, and two detection algorithms (QRS complex detection and Systolic/Diastolic wave detection) are designed. The second process is to extract features. The proposed system combines features from time domain, frequency domain, nonlinear analysis, and multi-model analysis to better represent the patterns when hemorrhage happens. Third, a machine learning algorithm is designed for classification of patterns. A novel machine learning algorithm, as a new version of error correcting output code (ECOC), is designed and investigated for high accuracy and real-time decision making. The features and characteristics of this machine learning method are essential for the proposed computer-aided trauma decision making system. The proposed system is tested agasint Lower Body Negative Pressure (LBNP) dataset, and the results indicate the accuracy and reliability of the proposed system

Bayesian Approaches For Modeling Variation

A core focus of statistics is determining how much of the variation in data may be attributed to the signal of interest, and how much to noise. When the sources of variation are many and complex, a Bayesian approach to data analysis offers a number of advantages. In this thesis, we propose and implement new Bayesian methods for modeling variation in two general settings. The first setting is high-dimensional linear regression where the unknown error variance is also of interest. Here, we show that a commonly used class of conjugate shrinkage priors can lead to underestimation of the error variance. We then extend the Spike-and-Slab Lasso (SSL, Rockova and George, 2018) to the unknown variance case, using an alternative, independent prior framework. This extended procedure outperforms both the fixed variance approach and alternative penalized likelihood methods on both simulated and real data. For the second setting, we move from univariate response data where the predictors are known, to multivariate response data in which potential predictors are unobserved. In this setting, we first consider the problem of biclustering, where a motivating example is to find subsets of genes which have similar expression in a subset of patients. For this task, we propose a new biclustering method called Spike-and-Slab Lasso Biclustering (SSLB). SSLB utilizes the SSL prior to find a doubly-sparse factorization of the data matrix via a fast EM algorithm. Applied to both a microarray dataset and a single-cell RNA-sequencing dataset, SSLB recovers biologically meaningful signal in the data. The second problem we consider in this setting is nonlinear factor analysis. The goal here is to find low-dimensional, unobserved ``factors\u27\u27 which drive the variation in the high-dimensional observed data in a potentially nonlinear fashion. For this purpose, we develop factor analysis BART (faBART), an MCMC algorithm which alternates sampling from the posterior of (a) the factors and (b) a functional approximation to the mapping from the factors to the data. The latter step utilizes Bayesian Additive Regression Trees (BART, Chipman et al., 2010). On a variety of simulation settings, we demonstrate that with only the observed data as the input, faBART is able to recover both the unobserved factors and the nonlinear mapping