This letter introduces a novel approach for graph classification in the context of sensor network data analysis using machine learning methods. It is based on exploiting both sensor positions and their functional connectivity for the inference of a graph class. The original idea is to formulate interaction forces between the graph vertices and exploit them as features of the graph functional connectivity. This letter also discusses the fusion of these features with classical ones extracted from sensor signals and structural features of the learned underlying graph. This original framework is found to be relevant for machine learning tasks, for instance the classification of multivariate EEG signals, where the force feature representation allows to distinguish between different mental workload levels. Experiments conducted with real data illustrate the usefulness of the proposed framework.

Blood flow observation is of high interest in cardiovascular disease diagnosis and assessment. For this purpose, 2D Phase-Contrast MRI is widely used in the clinical routine. 4D flow MRI sequences, which dynamically image the anatomic shape and velocity vectors within a region of interest, are promising but rarely used due to their low resolution and signal-to-noise ratio (SNR). Computational fluid dynamics (CFD) simulation is considered as a reference solution for resolution enhancement. However, its precision relies on image segmentation and a clinical expertise for the definition of the vessel borders. The main contribution of this paper is a Segmentation-Free Super-Resolution (SFSR) algorithm. Based on inverse problem methodology, SFSR relies on minimizing a compound criterion involving: a data fidelity term, a fluid mechanics term, and a spatial velocity smoothing term. The proposed algorithm is evaluated with respect to state-of-the-art solutions, in terms of quantification error and computation time, on a synthetic 3D dataset with several noise levels, resulting in a 59% RMSE improvement and factor 2 super-resolution with a noise standard deviation of 5% of the Venc. Finally, its performance is demonstrated, with a scale factor of 2 and 3, on a pulsed flow phantom dataset with more complex patterns. The application on in-vivo were achievable within the 10 min. computation time.

Interest in 4D blood flow MRI grows due to its ability to image the anatomic shape and the three velocity components within a volume along the cardiac cycle. However, some biomarkers’ quantification from these data can be inaccurate due to the low resolution of the images. The reference method to improve the spatial resolution numerically is to run computational fluid dynamic (CFD) simulations in order to deduce the associated images in a higher resolution grid. However, such approaches induce complex time-consuming steps and require precise estimates of the vessel wall and the inlet velocity. In this work, an original segmentation-free super-resolution (SR) solution is proposed using an inverse problem resolution approach by the minimization of a compound criterion involving three terms, a mechanical term based on Navier-Stokes equations, and a velocity smoothness promoting term, and a spatially weighted data fidelity term. The proposed solution has been validated regarding estimation error and computation time on simulated data and experimental acquisition from a phantom. Super-resolved velocity reconstruction demonstrates promising performance, even without segmentation knowledge, compared to state-of-the-art solutions.

This paper addresses the problem of rank tracking in real time hyperspectral image unmixing. Based on the On-line Alternating Direction Method of Multipliers (ADMM), we propose a new hyperspectral unmixing approach that integrates prior information as well as joint sparsity regularization, allowing to select only the active components on each sample of the image. This results in a semi-supervised algorithm, well adapted for on-line rank tracking for pushbroom imager. Experimental results on synthetic and real data sets demonstrate the effectiveness of our method for parameter estimation and rank change detection.

Relaxation signal inside each voxel of magnetic resonance images (MRI) is commonly fitted by a multi-exponential decay curve. The estimation of a discrete multi-component relaxation model parameters from magnitude MRI data is a challenging nonlinear inverse problem since it should be conducted on the entire image voxels under non-Gaussian noise statistics. This paper proposes an efficient algorithm allowing the joint estimation of relaxation time values and their amplitudes using different criteria taking into account a Rician noise model, combined with a spatial regularization accounting for low spatial variability of relaxation time constants and amplitudes between neighboring voxels. The Rician noise hypothesis is accounted for either by an adapted nonlinear least squares algorithm applied to a corrected least squares criterion or by a majorization-minimization approach applied to the maximum likelihood criterion. In order to solve the resulting large-scale non-negativity constrained optimization problem with a reduced numerical complexity and computing time, an optimization algorithm based on a majorization approach ensuring separability of variables between voxels is proposed. The minimization is carried out iteratively using an adapted Levenberg-Marquardt algorithm that ensures convergence by imposing a sufficient decrease of the objective function and the non-negativity of the parameters. The importance of the regularization alongside the Rician noise incorporation is shown both visually and numerically on a simulated phantom and on magnitude MRI images acquired on fruit samples.

In a low-statistics PET imaging context, the positive bias in regions of low activity is a burning issue. To overcome this problem, algorithms without the built-in non-negativity constraint may be used. They allow negative voxels in the image to reduce, or even to cancel the bias. However, such algorithms increase the variance and are difficult to interpret since the resulting images contain negative activities, which do not hold a physical meaning when dealing with radioactive concentration. In this paper, a post-processing approach is proposed to remove these negative values while preserving the local mean activities. Its original idea is to transfer the value of each voxel with negative activity to its direct neighbors under the constraint of preserving the local means of the image. In that respect, the proposed approach is formalized as a linear programming problem with a specific symmetric structure, which makes it solvable in a very efficient way by a dual-simplex-like iterative algorithm. The relevance of the proposed approach is discussed on simulated and on experimental data. Acquired data from an yttrium-90 phantom show that on images produced by a non-constrained algorithm, a much lower variance in the cold area is obtained after the post-processing step, at the price of a slightly increased bias. More specifically, when compared with the classical OSEM algorithm, images are improved, both in terms of bias and of variance.

The extraction of multi-exponential decay parameters from multi-temporal images corrupted with Rician noise and with limited time samples proves to be a challenging problem frequently encountered in clinical and food MRI studies. This work aims at proposing a method for the estimation of multi-exponential transverse relaxation times from noisy magnitude MRI images. A spatially regularized Maximum-Likelihood estimator accounting for the Rician distribution of the noise is introduced. To deal with the large-scale optimization problem, a Majoration-Minimization approach coupled with an adapted non-linear least squares algorithm is implemented. The proposed algorithm is numerically fast, stable and leads to accurate results. Its effectiveness is illustrated by an application to a simulated phantom and to magnitude multi spin echo MRI images acquired from a tomato sample.

The estimation of the state of lateral dynamics of a vehicle is usually performed using information gathered by several sensors, such as cameras, radars, odometers, and accelerometers. However, some quantities and their variations cannot be measured directly in all driving situations whereas they are required for vehicle control. Among these unmeasured quantities, one can find road curvature. This paper proposes to apply nonlinear observers to provide such information, in addition to other quantities related to the vehicle state, in the context of Traffic Jump Pilot. The first contribution of this paper is to formulate the nonlinear dynamics model and then to design two nonlinear observers based on High-Gain and Sliding Mode techniques. Furthermore, in order to ensure their efficient applications in a real situation, an experimental methodology is developed in order to optimize their performances by finding an optimal set of gain values. In that respect, a large database of real driving conditions and different road curvature scenarios is recorded for the performances evaluation and then a recent multi-objective optimization algorithm is used to find the optimal tuning parameters of the observers. The effectiveness of the proposed methodology is illustrated through an application to a driving test, which is not in the database. The use of this optimization tool is a novelty in the context of nonlinear observation and control, which allows getting optimized observers that can be efficiently applied to experimental data.

Primal-dual interior-point methods are used in image processing to solve inversion problems that can be reduced to constrained convex minimization. Such iterative methods require the solution of a sequence of linear systems which are used to derive descent directions. This approach is very consuming in terms of computing time and memory usage for large-scale problems, unless the involved matrices have a specific structure. This is the case in the spectral unmixing problem where these matrices are block-diagonal when no spatial regularization is considered. Here, we consider the edge-preserving regularized case and we propose to tackle the linear system solving using a majorization-minimization (MM) approach based on separable quadratic majorant functions. The resulting systems have the same structure as in the non-regularized case and can thereby be solved efficiently. The interior-point algorithm is speeded-up while remaining convergent. An example of spectral unmixing is proposed to illustrate the efficiency of this approach.

This paper deals with the reconstruction of relaxation time distributions in Nuclear Magnetic Resonance (NMR) spectroscopy. This large scale and ill-posed inverse problem is solved by the iterative minimization of a regularized objective function allowing to encode some prior assumptions on the sought distribution. The numerical optimization of the criterion is performed using a primal-dual interior point algorithm allowing to handle the non-negativity constraint. The performances of the proposed approach are illustrated through the processing of real data from a two-dimensional NMR experiment.

We consider a hyperspectral image restoration problem in which the solution is known to be nonnegative. The image estimate is obtained as the constrained minimizer of a convex criterion incorporating prior information on its spatial and spectral regularity. We previously proposed a fast algorithm for Tikhonov regularization. Here, we adapt this algorithm to edge-preserving image restoration.

We present a low computational cost bit allocation procedure dedicated to wavelet compression performed by entropy coded lattice vector quantization (ECLVQ). This approach is based on a previously proposed statistical model called multidimensional mixture of generalized Gaussian densities. Here, we focus on the distribution estimation step which requires to be as fast as possible. We show that the method of moments (MoM) can be used successfully as an alternative to Monte Carlo Markov chain approach (MCMC); this method allows not only to reduce the computational complexity but also to maintain a good estimation performance. Experimental results show the efficiency of our approach in terms of CPU time.

This paper proposes accelerated subspace optimization methods in the context of image restoration. Subspace optimization methods belong to the class of iterative descent algorithms for unconstrained optimization. At each iteration of such methods, a stepsize vector allowing the best combination of several search directions is computed through a multidimensional search. It is usually obtained by an inner iterative second-order method ruled by a stopping criterion that guarantees the convergence of the outer algorithm. As an alternative, we propose an original multidimensional search strategy based on the majorize-minimize principle. It leads to a closed-form stepsize formula that ensures the convergence of the subspace algorithm whatever the number of inner iterations. The practical efficiency of the proposed scheme is illustrated in the context of edge-preserving image restoration.

This paper deals with the reconstruction of T1-T2 correlation spectra in Nuclear Magnetic Resonance (NMR) spectroscopy. The ill-posed character of this inverse problem and its large size are the main difficulties of the reconstruction. While maximum entropy is retained as an adequate regularization approach, the choice of an efficient optimization algorithm remains a challenging task. Our proposal is to apply a nonlinear conjugate gradient algorithm with two original features. Firstly, a theoretically well stated line search strategy suitable for the entropy function is applied to ensure a monotonic decrease of the criterion. Secondly, an appropriate preconditioning structure based on a truncated singular value decomposition of the forward model matrix is used to speed up the algorithm convergence. The resulting method reveals far more efficient than the classical Skilling and Bryan method and its applicability is illustrated through real NMR data processing.

Bayesian positive source separation (BPSS) is a useful unsupervised approach for hyperspectral data unmixing, where numerical nonnegativity of spectra and abundances has to be ensured, such as in remote sensing. Moreover, it is sensible to impose a sum-to-one (full additivity) constraint to the estimated source abundances in each pixel. Even though nonnegativity and full additivity are two necessary properties to get physically interpretable results, the use of BPSS algorithms has so far been limited by high computation time and large memory requirements due to the Markov chain Monte Carlo calculations. An implementation strategy that allows one to apply these algorithms on a full hyperspectral image, as it is typical in earth and planetary science, is introduced. The effects of pixel selection and the impact of such sampling on the relevance of the estimated component spectra and abundance maps, as well as on the computation times, are discussed. For that purpose, two different data sets have been used: a synthetic one and a real hyperspectral image from Mars.

Independent component analysis (ICA) is a very popular method that has shown success in blind source separation, feature extraction and unsupervised recognition. In recent years ICA has been largely studied by researchers from the signal processing community. This paper addresses a more in-depth study on the use of this method, applied to hyper-spectral images used for remote sensing purposes. In a first part, source separation is addressed. Since the independence of sources is usually not verified in hyperspectral real data images, ICA, if used alone, is not a suitable tool to unmix sources. We propose a hierarchical approximation for the use of ICA as a pre-processing step for a Bayesian Positive Source Separation method. In a second part, the use of ICA for dimensionality reduction is studied in the frame of hyperspectral data classification. Experimental results show the effectiveness of ICA when used for hyperspectral image pre-processing for the two considered applications.

Entropy-coded lattice vector quantization (ECLVQ) with codebooks dedicated to independent identically distributed (i.i.d.) generalized Gaussian sources have proven their high coding performances in the wavelet domain. It is well known that wavelet coefficients with high magnitude (corresponding to edges and textures) tend to be clustered in a few amount of vectors. In this paper, we first show that this property has a major influence on the performances of ECLVQ schemes. Since this clustering property cannot be taken into account by the classical i.i.d. assumption, our first proposal is to model the joint distribution of vectors by a multidimensional mixture of generalized Gaussian (MMGG) densities. The main outcome of this MMGG model is to provide a theoretical framework to simply derive from i.i.d. R- D models, the corresponding MMGG R- D models. In a second part, a new codebook better suited to wavelet coding is proposed: the so-called dead zone lattice vector quantizers (DZLVQ). It consists of generalizing the scalar dead zone to vector quantization by thresholding vectors according to their energy. We show that DZLVQ improves the rate-distortion tradeoff. Experimental results are provided for the pyramidal LVQ scheme under the assumption of a multidimensional mixture of Laplacian (MML) densities. Results performed on a set of real life images show the precision of the analytical R- D curves and the efficiency of the DZLVQ scheme.

A main issue in source separation is to deal with the indeterminacies. Well known are the ordering and scale ambiguities, but other types of indeterminacies may also occur. In this paper we address these indeterminacies in the case of non-negative sources and non-negative mixing coefficients. On the one hand, we fully develop the case of two sources. On the other hand, in the general case we formulate necessary conditions for the uniqueness of the solution (up to ordering and scale ambiguities).

The paper considers the problem of source separation in the particular case where both the sources and the mixing coefficients are positive. The proposed method addresses the problem in a Bayesian framework. We assume a gamma distribution for the spectra and the mixing coefficients. This prior distribution enforces the non-negativity. This leads to an original method for positive source separation. A simulation example is presented to illustrate the effectiveness of the method.