A Measure of Synergy Based on Union Information.

The (PID) framework is concerned with decomposing the information that a set of (two or more) random variables (the sources) has about another variable (the target) into three types of information: unique, redundant, and synergistic. Classical information theory alone does not provide a unique way to decompose information in this manner and additional assumptions have to be made. One often overlooked way to achieve this decomposition is using a so-called measure of union information-which quantifies the information that is present in at least one of the sources-from which a synergy measure stems.

Orders between Channels and Implications for Partial Information Decomposition.

The partial information decomposition (PID) framework is concerned with decomposing the information that a set of random variables has with respect to a target variable into three types of components: redundant, synergistic, and unique. Classical information theory alone does not provide a unique way to decompose information in this manner, and additional assumptions have to be made. Recently, Kolchinsky proposed a new general axiomatic approach to obtain measures of redundant information based on choosing an order relation between information sources (equivalently, order between communication channels).

A classification-based approach to semi-supervised clustering with pairwise constraints.

In this paper, we introduce a neural network framework for semi-supervised clustering with pairwise (must-link or cannot-link) constraints. In contrast to existing approaches, we decompose semi-supervised clustering into two simpler classification tasks: the first stage uses a pair of Siamese neural networks to label the unlabeled pairs of points as must-link or cannot-link; the second stage uses the fully pairwise-labeled dataset produced by the first stage in a supervised neural-network-based clustering method. The proposed approach is motivated by the observation that binary classification (such as assigning pairwise relations) is usually easier than multi-class clustering with partial supervision.

External Patch-Based Image Restoration Using Importance Sampling.

This paper introduces a new approach to patchbased image restoration based on external datasets and importance sampling. The minimum mean squared error (MMSE) estimate of the image patches, the computation of which requires solving a multidimensional (typically intractable) integral, is approximated using samples from an external dataset. The new method, which can be interpreted as a generalization of the external non-local means (NLM), uses self-normalized importance sampling to efficiently approximate the MMSE estimates.

A Convergent Image Fusion Algorithm Using Scene-Adapted Gaussian-Mixture-Based Denoising.

We propose a new approach to image fusion, inspired by the recent plug-and-play (PnP) framework. In PnP, a denoiser is treated as a black-box and plugged into an iterative algorithm, taking the place of the proximity operator of some convex regularizer, which is formally equivalent to a denoising operation. This approach offers flexibility and excellent performance, but convergence may be hard to analyze, as most state-of-the-art denoisers lack an explicit underlying objective function.

Does Nonlinear Modeling Play a Role in Plasmid Bioprocess Monitoring Using Fourier Transform Infrared Spectra?

The monitoring of biopharmaceutical products using Fourier transform infrared (FT-IR) spectroscopy relies on calibration techniques involving the acquisition of spectra of bioprocess samples along the process. The most commonly used method for that purpose is partial least squares (PLS) regression, under the assumption that a linear model is valid. Despite being successful in the presence of small nonlinearities, linear methods may fail in the presence of strong nonlinearities.

Parametric blur estimation for blind restoration of natural images: linear motion and out-of-focus.

This paper presents a new method to estimate the parameters of two types of blurs, linear uniform motion (approximated by a line characterized by angle and length) and out-of-focus (modeled as a uniform disk characterized by its radius), for blind restoration of natural images. The method is based on the spectrum of the blurred images and is supported on a weak assumption, which is valid for the most natural images: the power-spectrum is approximately isotropic and has a power-law decay with the spatial frequency. We introduce two modifications to the radon transform, which allow the identification of the blur spectrum pattern of the two types of blurs above mentioned.

Parameter estimation for blind and non-blind deblurring using residual whiteness measures.

Image deblurring (ID) is an ill-posed problem typically addressed by using regularization, or prior knowledge, on the unknown image (and also on the blur operator, in the blind case). ID is often formulated as an optimization problem, where the objective function includes a data term encouraging the estimated image (and blur, in blind ID) to explain the observed data well (typically, the squared norm of a residual) plus a regularizer that penalizes solutions deemed undesirable. The performance of this approach depends critically (among other things) on the relative weight of the regularizer (the regularization parameter) and on the number of iterations of the algorithm used to address the optimization problem.

Activity recognition using a mixture of vector fields.

The analysis of moving objects in image sequences (video) has been one of the major themes in computer vision. In this paper, we focus on video-surveillance tasks; more specifically, we consider pedestrian trajectories and propose modeling them through a small set of motion/vector fields together with a space-varying switching mechanism. Despite the diversity of motion patterns that can occur in a given scene, we show that it is often possible to find a relatively small number of typical behaviors, and model each of these behaviors by a "simple" motion field.

Towards a classification approach using meta-biclustering: impact of discretization in the analysis of expression time series.

Biclustering has been recognized as a remarkably effective method for discovering local temporal expression patterns and unraveling potential regulatory mechanisms, essential to understanding complex biomedical processes, such as disease progression and drug response. In this work, we propose a classification approach based on meta-biclusters (a set of similar biclusters) applied to prognostic prediction. We use real clinical expression time series to predict the response of patients with multiple sclerosis to treatment with Interferon-β.

Statistical classification of road pavements using near field vehicle rolling noise measurements.

Low noise surfaces have been increasingly considered as a viable and cost-effective alternative to acoustical barriers. However, road planners and administrators frequently lack information on the correlation between the type of road surface and the resulting noise emission profile. To address this problem, a method to identify and classify different types of road pavements was developed, whereby near field road noise is analyzed using statistical learning methods.

An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems.

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly nonsmooth) regularizer is minimized under the constraint that the solution explains the observations sufficiently well. Although the regularizer and constraint are usually convex, several particular features of these problems (huge dimensionality, nonsmoothness) preclude the use of off-the-shelf optimization tools and have stimulated a considerable amount of research. In this paper, we propose a new efficient algorithm to handle one class of constrained problems (often known as basis pursuit denoising) tailored to image recovery applications.

Restoration of Poissonian images using alternating direction optimization.

Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state-of-the-art regularizers (such as those based upon multiscale representations or total variation) is still an active research area, since the associated optimization problems are quite challenging. In this paper, we propose an approach to deconvolving Poissonian images, which is based upon an alternating direction optimization method.

Fast image recovery using variable splitting and constrained optimization.

We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an l2 data-fidelity term and a nonsmooth regularizer. This formulation allows both wavelet-based (with orthogonal or frame-based representations) regularization or total-variation regularization. Our approach is based on a variable splitting to obtain an equivalent constrained optimization formulation, which is then addressed with an augmented Lagrangian method.

Multiplicative noise removal using variable splitting and constrained optimization.

Multiplicative noise (also known as speckle noise) models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. These models introduce two additional layers of difficulties with respect to the standard Gaussian additive noise scenario: (1) the noise is multiplied by (rather than added to) the original image; (2) the noise is not Gaussian, with Rayleigh and Gamma being commonly used densities. These two features of multiplicative noise models preclude the direct application of most state-of-the-art algorithms, which are designed for solving unconstrained optimization problems where the objective has two terms: a quadratic data term (log-likelihood), reflecting the additive and Gaussian nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.

Near-infrared hyperspectral unmixing based on a minimum volume criterion for fast and accurate chemometric characterization of counterfeit tablets.

A rapid detection of the nonauthenticity of suspect tablets is a key first step in the fight against pharmaceutical counterfeiting. The chemical characterization of these tablets is the logical next step to evaluate their impact on patient health and help authorities in tracking their source. Hyperspectral unmixing of near-infrared (NIR) image data is an emerging effective technology to infer the number of compounds, their spectral signatures, and the mixing fractions in a given tablet, with a resolution of a few tens of micrometers.

Determination of the composition of counterfeit Heptodin tablets by near infrared chemical imaging and classical least squares estimation.

According to the WHO definition for counterfeit medicines, several categories can be established, e.g., medicines containing the correct active pharmaceutical ingredient (API) but different excipients, medicines containing low levels of API, no API or even a substitute API.

An EM algorithm for wavelet-based image restoration.

This paper introduces an expectation-maximization (EM) algorithm for image restoration (deconvolution) based on a penalized likelihood formulated in the wavelet domain. Regularization is achieved by promoting a reconstruction with low-complexity, expressed in the wavelet coefficients, taking advantage of the well known sparsity of wavelet representations. Previous works have investigated wavelet-based restoration but, except for certain special cases, the resulting criteria are solved approximately or require demanding optimization methods.

A new twIst: two-step iterative shrinkage/thresholding algorithms for image restoration.

Iterative shrinkage/thresholding (IST) algorithms have been recently proposed to handle a class of convex unconstrained optimization problems arising in image restoration and other linear inverse problems. This class of problems results from combining a linear observation model with a nonquadratic regularizer (e.g.

Majorization-minimization algorithms for wavelet-based image restoration.

Standard formulations of image/signal deconvolution under wavelet-based priors/regularizers lead to very high-dimensional optimization problems involving the following difficulties: the non-Gaussian (heavy-tailed) wavelet priors lead to objective functions which are nonquadratic, usually nondifferentiable, and sometimes even nonconvex; the presence of the convolution operator destroys the separability which underlies the simplicity of wavelet-based denoising. This paper presents a unified view of several recently proposed algorithms for handling this class of optimization problems, placing them in a common majorization-minimization (MM) framework. One of the classes of algorithms considered (when using quadratic bounds on nondifferentiable log-priors) shares the infamous "singularity issue" (SI) of "iteratively reweighted least squares" (IRLS) algorithms: the possibility of having to handle infinite weights, which may cause both numerical and convergence issues.

Sparse multinomial logistic regression: fast algorithms and generalization bounds.

Recently developed methods for learning sparse classifiers are among the state-of-the-art in supervised learning. These methods learn classifiers that incorporate weighted sums of basis functions with sparsity-promoting priors encouraging the weight estimates to be either significantly large or exactly zero. From a learning-theoretic perspective, these methods control the capacity of the learned classifier by minimizing the number of basis functions used, resulting in better generalization.

Orientation in manhattan: equiprojective classes and sequential estimation.

The problem of inferring 3D orientation of a camera from video sequences has been mostly addressed by first computing correspondences of image features. This intermediate step is now seen as the main bottleneck of those approaches. In this paper, we propose a new 3D orientation estimation method for urban (indoor and outdoor) environments, which avoids correspondences between frames.

Simultaneous feature selection and clustering using mixture models.

Clustering is a common unsupervised learning technique used to discover group structure in a set of data. While there exist many algorithms for clustering, the important issue of feature selection, that is, what attributes of the data should be used by the clustering algorithms, is rarely touched upon. Feature selection for clustering is difficult because, unlike in supervised learning, there are no class labels for the data and, thus, no obvious criteria to guide the search.

A Bayesian approach to joint feature selection and classifier design.

This paper adopts a Bayesian approach to simultaneously learn both an optimal nonlinear classifier and a subset of predictor variables (or features) that are most relevant to the classification task. The approach uses heavy-tailed priors to promote sparsity in the utilization of both basis functions and features; these priors act as regularizers for the likelihood function that rewards good classification on the training data. We derive an expectation-maximization (EM) algorithm to efficiently compute a maximum a posteriori (MAP) point estimate of the various parameters.

Segmentation of fetal ultrasound images.

This paper describes a new method for segmentation of fetal anatomic structures from echographic images. More specifically, we estimate and measure the contours of the femur and of cranial cross-sections of fetal bodies, which can thus be automatically measured. Contour estimation is formulated as a statistical estimation problem, where both the contour and the observation model parameters are unknown.