This work focuses on the development of a new family of decision-making algorithms for adaptation and learning, which are specifically tailored to decision problems and are constructed by building up on first principles from decision theory. A key observation is that estimation and decision problems are structurally different and, therefore, algorithms that have proven successful for the former need not perform well when adjusted for the latter. Exploiting classical tools from quickest detection, we propose a tailored version of Page's test, referred to as BLLR (barrier log-likelihood ratio) test, and demonstrate its applicability to real-data from the COVID-19 pandemic in Italy. The results illustrate the ability of the design tool to track the different phases of the outbreak.

Advances in multimodal imaging have revolutionized diagnostic and treatment monitoring in ophthalmic practice. In multimodal ophthalmic imaging, geometric deformations are inevitable and they contain inherent deformations arising from heterogeneity in the optical characteristics of imaging devices and patient related factors. The registration of ophthalmic images under such conditions is challenging. We propose a novel technique that overcomes these challenges, using Laplacian feature, Hessian affine feature space and phase correlation, to register blue autofluorescence, near-infrared reflectance and color fundus photographs of the ocular posterior pole with high accuracy. Our validation analysis - that used current feature detection and extraction techniques (speed-up robust features (SURF), a concept of wind approach (KAZE), and fast retina keypoint (FREAK)), and quantitative measures (Sørensen-Dice coefficient, Jaccard index, and Kullback-Leibler divergence scores) - showed that our approach has significant merit in registering multimodal images when compared with a mix-and-match SURF-KAZE-FREAK benchmark approach. Similarly, our evaluation analysis that used a state-of-the-art qualitative measure - the mean registration error (MRE) - showed that the proposed approach is significantly better than the mix-and-match SURF-KAZE-FREAK benchmark approach, as well as a cutting edge image registration technique - Linear Stack Alignment with SIFT (scale-invariant feature transform) - in registering multimodal ophthalmic images.

Estimating a time-varying signal, such as head motion from magnetic resonance imaging data, becomes particularly challenging in the face of other temporal dynamics such as functional activation. This paper describes a new Kalman filter-like framework that includes a sparse residual term in the measurement model. This additional term allows the extended Kalman filter to generate real-time motion estimates suitable for prospective motion correction when such dynamics occur. An iterative augmented Lagrangian algorithm similar to the alterating direction method of multipliers implements the update step for this Kalman filter. This paper evaluates the accuracy and convergence rate of this iterative method for small and large motion in terms of its sensitivity to parameter selection. The included experiment on a simulated functional magnetic resonance imaging acquisition demonstrates that the resulting method improves the maximum Youden's J index of the time series analysis by 2-3% versus retrospective motion correction, while the sensitivity index increases from 4.3 to 5.4 when combining prospective and retrospective correction.

Active contour models have been widely used for image segmentation purposes. However, they may fail to delineate objects of interest depicted on images with intensity inhomogeneity. To resolve this issue, a novel image feature, termed as local edge entropy, is proposed in this study to reduce the negative impact of inhomogeneity on image segmentation. An active contour model is developed on the basis of this feature, where an edge entropy fitting (EEF) energy is defined with the combination of a redesigned regularization term. Minimizing the energy in a variational level set formulation can successfully drive the motion of an initial contour curve towards optimal object boundaries. Experiments on a number of test images demonstrate that the proposed model has the capability of handling intensity inhomogeneity with reasonable segmentation accuracy.

We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework for S-NNLS based on a rectified power exponential scale mixture prior on the sparse codes. We show that the proposed framework encompasses a large class of S-NNLS algorithms and provide a computationally efficient inference procedure based on multiplicative update rules. Such update rules are convenient for solving large sets of S-NNLS problems simultaneously, which is required in contexts like sparse non-negative matrix factorization (S-NMF). We provide theoretical justification for the proposed approach by showing that the local minima of the objective function being optimized are sparse and the S-NNLS algorithms presented are guaranteed to converge to a set of stationary points of the objective function. We then extend our framework to S-NMF, showing that our framework leads to many well known S-NMF algorithms under specific choices of prior and providing a guarantee that a popular subclass of the proposed algorithms converges to a set of stationary points of the objective function. Finally, we study the performance of the proposed approaches on synthetic and real-world data.

Multichannel electroencephalography (EEG) is widely used in non-invasive brain computer interfaces (BCIs) for user intent inference. EEG can be assumed to be a Gaussian process with unknown mean and autocovariance, and the estimation of parameters is required for BCI inference. However, the relatively high dimensionality of the EEG feature vectors with respect to the number of labeled observations lead to rank deficient covariance matrix estimates. In this manuscript, to overcome ill-conditioned covariance estimation, we propose a structure for the covariance matrices of the multichannel EEG signals. Specifically, we assume that these covariances can be modeled as a Kronecker product of temporal and spatial covariances. Our results over the experimental data collected from the users of a letter-by-letter typing BCI show that with less number of parameter estimations, the system can achieve higher classification accuracies compared to a method that uses full unstructured covariance estimation. Moreover, in order to illustrate that the proposed Kronecker product structure could enable shortening the BCI calibration data collection sessions, using Cramer-Rao bound analysis on simulated data, we demonstrate that a model with structured covariance matrices will achieve the same estimation error as a model with no covariance structure using fewer labeled EEG observations.

The windowed Fourier transform (short time Fourier transform) and the S-transform are widely used signal processing tools for extracting frequency information from non-stationary signals. Previously, the windowed Fourier transform had been adopted for signals on graphs and has been shown to be very useful for extracting vertex-frequency information from graphs. However, high computational complexity makes these algorithms impractical. We sought to develop a fast windowed graph Fourier transform and a fast graph S-transform requiring significantly shorter computation time. The proposed schemes have been tested with synthetic test graph signals and real graph signals derived from electroencephalography recordings made during swallowing. The results showed that the proposed schemes provide significantly lower computation time in comparison with the standard windowed graph Fourier transform and the fast graph S-transform. Also, the results showed that noise has no effect on the results of the algorithm for the fast windowed graph Fourier transform or on the graph S-transform. Finally, we showed that graphs can be reconstructed from the vertex-frequency representations obtained with the proposed algorithms.

This paper studies the intrinsic connection between a generalized LASSO and a basic LASSO formulation. The former is the extended version of the latter by introducing a regularization matrix to the coefficients. We show that when the regularization matrix is even- or under-determined with full rank conditions, the generalized LASSO can be transformed into the LASSO form the Lagrangian framework. In addition, we show that some published results of LASSO can be extended to the generalized LASSO, and some variants of LASSO, , robust LASSO, can be rewritten into the generalized LASSO form and hence can be transformed into basic LASSO. Based on this connection, many existing results concerning LASSO, , efficient LASSO solvers, can be used for generalized LASSO.

This work proposes a family of greedy algorithms to jointly reconstruct a set of vectors that are (i) nonnegative and (ii) simultaneously sparse with a shared support set. The proposed algorithms generalize previous approaches that were designed to impose these constraints individually. Similar to previous greedy algorithms for sparse recovery, the proposed algorithms iteratively identify promising support indices. In contrast to previous approaches, the support index selection procedure has been adapted to prioritize indices that are consistent with both the nonnegativity and shared support constraints. Empirical results demonstrate for the first time that the combined use of simultaneous sparsity and nonnegativity constraints can substantially improve recovery performance relative to existing greedy algorithms that impose less signal structure.

In this paper we take a novel approach to the regularization of underdetermined linear systems. Typically, a prior distribution is imposed on the unknown to hopefully force a sparse solution, which often relies on uniqueness of the regularized solution (something which is typically beyond our control) to work as desired. But here we take a direct approach, by imposing the requirement that the system takes on a unique solution. Then we seek a minimal residual for which this uniqueness requirement holds. When applied to systems with non-negativity constraints or forms of regularization for which sufficient sparsity is a requirement for uniqueness, this approach necessarily gives a sparse result. The approach is based on defining a metric of distance to uniqueness for the system, and optimizing an adjustment that drives this distance to zero. We demonstrate the performance of the approach with numerical experiments.

This paper discusses the development of a slope estimation algorithm called MAPSlope for piecewise linear data that is corrupted by Gaussian noise. The number and locations of slope change points (also known as breakpoints) are assumed to be unknown though it is assumed that the possible range of slope values lies within known bounds. A stochastic hidden Markov model that is general enough to encompass real world sources of piecewise linear data is used to model the transitions between slope values and the problem of slope estimation is addressed using a Bayesian maximum a posteriori approach. The set of possible slope values is discretized, enabling the design of a dynamic programming algorithm for posterior density maximization. Numerical simulations are used to justify choice of a reasonable number of quantization levels and also to analyze mean squared error performance of the proposed algorithm. An alternating maximization algorithm is proposed for estimation of unknown model parameters and a convergence result for the method is provided. Finally, results using data from political science, finance and medical imaging applications are presented to demonstrate the practical utility of this procedure.

With the advent of high-throughput biotechnology capable of monitoring genomic signals, it becomes increasingly promising to understand molecular cellular mechanisms through systems biology approaches. One of the active research topics in systems biology is to infer gene transcriptional regulatory networks using various genomic data; this inference problem can be formulated as a linear model with latent signals associated with some regulatory proteins called transcription factors (TFs). As common statistical assumptions may not hold for genomic signals, typical latent variable algorithms such as independent component analysis (ICA) are incapable to reveal underlying true regulatory signals. Liao et al. [1] proposed to perform inference using an approach named network component analysis (NCA), the optimization of which is achieved by a least-squares fitting approach with biological knowledge constraints. However, the incompleteness of biological knowledge and its inconsistency with gene expression data are not considered in the original NCA solution, which could greatly affect the inference accuracy. To overcome these limitations, we propose a linear extraction scheme, namely regulatory component analysis (RCA), to infer underlying regulatory signals even with partial biological knowledge. Numerical simulations show a significant improvement of our proposed RCA over NCA, not only when signal-to-noise-ratio (SNR) is low, but also when the given biological knowledge is incomplete and inconsistent to gene expression data. Furthermore, real biological experiments on E. coli are performed for regulatory network inference in comparison with several typical linear latent variable methods, which again demonstrates the effectiveness and improved performance of the proposed algorithm.

With the rapid development of x-ray source and detector technologies, multi-source scanners become a hot topic in the CT field, which can acquire several projections simultaneously. Aided with the ECG-gating technique, the multi-source scanner can collect sufficient projections to reconstruct one or more specific phases of a beating heart. Hence, we are motivated to develop velocity tomography as a new dynamic imaging mode to recover the velocity field from the projections. First, we derive a velocity field constraint equation subject to the mass conservation. Then, we present a two-step general scheme to estimate the velocity field. The first step directly or indirectly computes partial derivatives. The second step iteratively determines the velocity field subject to the constraint equation and other conditions. Finally, we describe numerical experiments in the fan-beam geometry to demonstrate the correctness and utility of our scheme.

This paper addresses the problem of approximating smooth bivariate functions from the samples of their partial derivatives. The approximation is carried out under the assumption that the subspace to which the functions to be recovered are supposed to belong, possesses an approximant in the form of a principal shift-invariant (PSI) subspace. Subsequently, the desired approximation is found as the element of the PSI subspace that fits the data the best in the (2)-sense. In order to alleviate the ill-posedness of the process of finding such a solution, we take advantage of the discrete nature of the problem under consideration. The proposed approach allows the explicit construction of a projection operator which maps the measured derivatives into a stable and unique approximation of the corresponding function. Moreover, the paper develops the concept of discrete PSI subspaces, which may be of relevance for several practical settings where one is given samples of a function instead of its continuously defined values. As a final point, the application of the proposed method to the problem of phase unwrapping in homomorphic deconvolution is described.

A significant amount of attention has recently been focused on modeling of gene regulatory networks. Two frequently used large-scale modeling frameworks are Bayesian networks (BNs) and Boolean networks, the latter one being a special case of its recent stochastic extension, probabilistic Boolean networks (PBNs). PBN is a promising model class that generalizes the standard rule-based interactions of Boolean networks into the stochastic setting. Dynamic Bayesian networks (DBNs) is a general and versatile model class that is able to represent complex temporal stochastic processes and has also been proposed as a model for gene regulatory systems. In this paper, we concentrate on these two model classes and demonstrate that PBNs and a certain subclass of DBNs can represent the same joint probability distribution over their common variables. The major benefit of introducing the relationships between the models is that it opens up the possibility of applying the standard tools of DBNs to PBNs and vice versa. Hence, the standard learning tools of DBNs can be applied in the context of PBNs, and the inference methods give a natural way of handling the missing values in PBNs which are often present in gene expression measurements. Conversely, the tools for controlling the stationary behavior of the networks, tools for projecting networks onto sub-networks, and efficient learning schemes can be used for DBNs. In other words, the introduced relationships between the models extend the collection of analysis tools for both model classes.

This paper describes a unified approach to the detection of point landmarks-whose neighborhoods convey discriminant information-including multidimensional scalar, vector, and higher-order tensor data. The method is based on the interpretation of generalized correlation matrices derived from the gradient of tensor functions, a probabilistic interpretation of point landmarks, and the application of tensor algebra. Results on both synthetic and real tensor data are presented.