Expectation-maximization Formulation Research Articles

CyCoSeg: A Cyclic Collaborative Framework for Automated Medical Image Segmentation.

Deep neural networks have been tremendously successful at segmenting objects in images. However, it has been shown they still have limitations on challenging problems such as the segmentation of medical images. The main reason behind this lower success resides in the reduced size of the object in the image. In this paper we overcome this limitation through a cyclic collaborative framework, CyCoSeg. The proposed framework is based on a deep active shape model (D-ASM), which provides prior information about the shape of the object, and a semantic segmentation network (SSN). These two models collaborate to reach the desired segmentation by influencing each other: SSN helps D-ASM identify relevant keypoints in the image through an Expectation Maximization formulation, while D-ASM provides a segmentation proposal that guides the SSN. This cycle is repeated until both models converge. Extensive experimental evaluation shows CyCoSeg boosts the performance of the baseline models, including several popular SSNs, while avoiding major architectural modifications. The effectiveness of our method is demonstrated on the left ventricle segmentation on two benchmark datasets, where our approach achieves one of the most competitive results in segmentation accuracy. Furthermore, its generalization is demonstrated for lungs and kidneys segmentation in CT scans.

Relevance Vector Machines-Based Time Series Prediction for Incomplete Training Dataset: Two Comparative Approaches.

Considering that real-life time series mixed with missing points cannot be directly modeled by using most of the supervised machine learning methods, this paper proposes a novel time series prediction method based on relevance vector machines for incomplete training dataset. Given the regularity between the missing inputs and outputs constructed by the phase space reconstruction, this paper imputes the missing inputs during the learning process by the values of their corresponding missing outputs such that the elements in kernel matrix related to the missing inputs are capable of being updated. This paper designs two strategies to estimate the missing outputs. The first one is based on the expectation maximization formulation in which a joint posterior distribution over the missing outputs and the weights vector is derived as a multivariate Gaussian form, and the another maximizes the marginal likelihood function with respect to the missing outputs and other hyperparameters. To verify the performance of the two proposed computing strategies, two synthetic time series and a real-life dataset are employed. The results indicate that the proposed methods have robust and better performance over the other methods when dealing with incomplete time series training dataset.

Human-in-the-Loop SLAM

Building large-scale, globally consistent maps is a challenging problem, made more difficult in environments with limited access, sparse features, or when using data collected by novice users. For such scenarios, where state-of-the-art mapping algorithms produce globally inconsistent maps, we introduce a systematic approach to incorporating sparse human corrections, which we term Human-in-the-Loop Simultaneous Localization and Mapping (HitL-SLAM). Given an initial factor graph for pose graph SLAM, HitL-SLAM accepts approximate, potentially erroneous, and rank-deficient human input, infers the intended correction via expectation maximization (EM), back-propagates the extracted corrections over the pose graph, and finally jointly optimizes the factor graph including the human inputs as human correction factor terms, to yield globally consistent large-scale maps. We thus contribute an EM formulation for inferring potentially rank-deficient human corrections to mapping, and human correction factor extensions to the factor graphs for pose graph SLAM that result in a principled approach to joint optimization of the pose graph while simultaneously accounting for multiple forms of human correction. We present empirical results showing the effectiveness of HitL-SLAM at generating globally accurate and consistent maps even when given poor initial estimates of the map.

Fast Time-Varying Channel Estimation for OFDM Systems With Narrowband Interference

The problem of channel estimation in OFDM with narrowband interference (NBI) has been only investigated for slow time-varying channels. For the first time, a novel estimation framework is proposed for fast time-varying channels. The noise variances and channel are jointly estimated via the maximum a posteriori (MAP) expectation maximization (EM) algorithm. By considering in the EM formulation the channel as the unwanted parameter and the noise variances as the parameters to be estimated, a closed-form analytical expression for the estimation of the noise variances is obtained; the channel being given by the Kalman smoother. Mean square error (MSE) and bit error rate (BER) simulations confirm the effectiveness and robustness of the approach against mobility and its adequacy for practical interference scenarios.

Bayesian network data imputation with application to survival tree analysis

Retrospective clinical datasets are often characterized by a relatively small sample size and many missing data. In this case, a common way for handling the missingness consists in discarding from the analysis patients with missing covariates, further reducing the sample size. Alternatively, if the mechanism that generated the missing allows, incomplete data can be imputed on the basis of the observed data, avoiding the reduction of the sample size and allowing methods to deal with complete data later on. Moreover, methodologies for data imputation might depend on the particular purpose and might achieve better results by considering specific characteristics of the domain. The problem of missing data treatment is studied in the context of survival tree analysis for the estimation of a prognostic patient stratification. Survival tree methods usually address this problem by using surrogate splits, that is, splitting rules that use other variables yielding similar results to the original ones. Instead, our methodology consists in modeling the dependencies among the clinical variables with a Bayesian network, which is then used to perform data imputation, thus allowing the survival tree to be applied on the completed dataset. The Bayesian network is directly learned from the incomplete data using a structural expectation–maximization (EM) procedure in which the maximization step is performed with an exact anytime method, so that the only source of approximation is due to the EM formulation itself. On both simulated and real data, our proposed methodology usually outperformed several existing methods for data imputation and the imputation so obtained improved the stratification estimated by the survival tree (especially with respect to using surrogate splits).

Factor analysis parameter estimation from incomplete data

An expectation–maximization (EM) algorithm for factor analysis parameter estimation when observations are missing is developed. In contrast to existing EM algorithms for this problem, the algorithm here is developed assuming the missing observations are not part of the complete data in the EM formulation. The resulting algorithm provides increased computational efficiency through sparse matrix operations. The algorithm is demonstrated on two sparse, high-dimensional data sets that are prohibitively large for existing algorithms: the Netflix movie recommendation data set and the Yahoo! musical item data set. The resulting factor models are applied to predict missing values using conditional mean estimation, achieving root mean square errors of 0.9001 and 24.08 on the Netflix and Yahoo! data sets, respectively.

Blind Recursive Tracking of Carrier Frequency Offset (CFO) Vector in MC-CDMA Systems

A recursive algorithm for estimating and updating the effective carrier frequency offset (CFO) vector in a multicarrier code-division multiple-access (MC-CDMA) system is proposed in this work. The recursive relation is derived based on the expectation maximization (EM) algorithm with a quadratic constraint. This new approach enables the use of linear estimation theory to tackle the CFO estimation problem with or without training data, which leads to an analytic CFO estimate in closed form. Furthermore, the multiple access interference (MAI) is mitigated using the second order statistics of the interference-plus-noise vector, which is updated in a recursive manner under the EM formulation, too. When reaching a converged estimate, a fixed-norm quadratic constraint is imposed so that the final CFO estimate is robust to an imprecise covariance matrix estimate caused by insufficient data samples. It is demonstrated by computer simulation that the performance of an MC-CDMA system without the CFO information can be restored by the proposed scheme in the sense that its bit error probability (BEP) performance is close to that with perfect CFO knowledge

An EM algorithm for shape classification based on level sets

In this paper, we propose an expectation-maximization (EM) approach to separate a shape database into different shape classes, while simultaneously estimating the shape contours that best exemplify each of the different shape classes. We begin our formulation by employing the level set function as the shape descriptor. Next, for each shape class we assume that there exists an unknown underlying level set function whose zero level set describes the contour that best represents the shapes within that shape class. The level set function for each example shape in the database is modeled as a noisy measurement of the appropriate shape class’s unknown underlying level set function. Based on this measurement model and the judicious introduction of the class labels as the hidden data, our EM formulation calculates the labels for shape classification and estimates the shape contours that best typify the different shape classes. This resulting iterative algorithm is computationally efficient, simple, and accurate. We demonstrate the utility and performance of this algorithm by applying it to two medical applications.

Expectation-maximization algorithms for image processing using multiscale models and mean- field theory, with applications to laser radar range profiling and segmentation

We describe a new class of computationally efficient algo- rithms designed to solve incomplete-data problems frequently encoun- tered in image processing and computer vision. The basis of this frame- work is the marriage of the expectation-maximization (EM) procedure with two powerful methodologies. In particular, we have incorporated optimal multiscale estimators into the EM procedure to compute esti- mates and error statistics efficiently. In addition, mean-field theory (MFT) from statistical mechanics is incorporated into the EM procedure to help solve the computational problems that arise from our use of Markov random-field (MRF) modeling of the hidden data in the EM formulation. We have applied this algorithmic framework and shown that it is effective in solving a wide variety of image-processing and computer-vision prob- lems. We demonstrate the application of our algorithmic framework to solve the problem of simultaneous anomaly detection, segmentation, and object profile estimation for noisy and speckled laser radar range images. © 2001 Society of Photo-Optical Instrumentation Engineers.