Multifractal analysis (MF) is a widely used signal processing tool that enables the study of scale invariance models. Classical MF assumes homogeneous MF properties, which cannot always be guaranteed in practice. Yet, the local estimation of MF parameters has barely been considered due to the challenging statistical nature of MF processes (non-Gaussian, intricate dependence), requiring large sample sizes. This present work addresses this limitation and proposes a Bayesian estimator for local MF parameters of multivariate time series. The proposed Bayesian model builds on a recently introduced statistical model for leaders (i.e., specific multiresolution quantities designed for MF analysis purposes) that enabled the Bayesian estimation of MF parameters and extends it to multivariate non-verlapping time windows. It is formulated using spatially smoothing gamma Markov random field priors that counteract the large statistical variability of estimates for short time windows. Numerical simulations demonstrate that the proposed algorithm significantly outperforms current state-of-the-art estimators.

We study the problem of decomposing a measured signal as a sum of decaying exponentials. There is a direct connection to sums of these types and positive semi-definite (PSD) Hankel matrices, where the rank of these matrices equals the number of exponentials. We propose to solve the identification problem by forming an optimization problem with a misfit function combined with a rank penalty function that also ensures the PSD-constraint. This problem is non-convex, but we show that it is possible to compute the minimum of an explicit closely related convexified problem. Moreover, this minimum can be shown to often coincide with the minimum of the original non-convex problem, and we provide a simple criterion that enables to verify if this is the case.

This paper proposes a joint segmentation and deconvolution Bayesian method for medical ultrasound (US) images. Contrary to piecewise homogeneous images, US images exhibit heavy characteristic speckle patterns correlated with the tissue structures. The generalized Gaussian distribution (GGD) has been shown to be one of the most relevant distributions for characterizing the speckle in US images. Thus, we propose a GGD-Potts model defined by a label map coupling US image segmentation and deconvolution. The Bayesian estimators of the unknown model parameters, including the US image, the label map, and all the hyperparameters are difficult to be expressed in a closed form. Thus, we investigate a Gibbs sampler to generate samples distributed according to the posterior of interest. These generated samples are finally used to compute the Bayesian estimators of the unknown parameters. The performance of the proposed Bayesian model is compared with the existing approaches via several experiments conducted on realistic synthetic data and in vivo US images.

This paper addresses the problem of single image super-resolution (SR), which consists of recovering a high- resolution image from its blurred, decimated, and noisy version. The existing algorithms for single image SR use different strate- gies to handle the decimation and blurring operators. In addition to the traditional first-order gradient methods, recent techniques investigate splitting-based methods dividing the SR problem into up-sampling and deconvolution steps that can be easily solved. Instead of following this splitting strategy, we propose to deal with the decimation and blurring operators simultaneously by taking advantage of their particular properties in the frequency domain, leading to a new fast SR approach. Specifically, an analytical solution is derived and implemented efficiently for the Gaussian prior or any other regularization that can be formulated into an l2 -regularized quadratic model, i.e., an l2 –l2 optimization problem. The flexibility of the proposed SR scheme is shown through the use of various priors/regularizations, ranging from generic image priors to learning-based approaches. In the case of non-Gaussian priors, we show how the analytical solution derived from the Gaussian case can be embedded into traditional splitting frameworks, allowing the computation cost of existing algorithms to be decreased significantly. Simulation results conducted on several images with different priors illustrate the effectiveness of our fast SR approach compared with existing techniques.

One of the remaining challenges in event-related fMRI is to discriminate between the vascular response and the neural activity in the BOLD signal. This discrimination is done by identifying the hemodynamic territories which differ in their underlying dynamics. In the literature, many approaches have been proposed to estimate these underlying dynamics, which is also known as Hemodynamic Response Function (HRF). However, most of the proposed approaches depend on a prior information regarding the shape of the parcels (territories) and their number. In this paper, we propose a novel approach which relies on the adaptive mean shift algorithm for the parcellation of the brain. A variational inference is used to estimate the unknown variables while the mean shift is embedded within a variational expectation maximization (VEM) framework to allow for estimating the parcellation and the HRF profiles without having any prior information about the number of the parcels or their shape. Results on synthetic data confirms the ability of the proposed approach to estimate accurate HRF estimates and number of parcels. It also manages to discriminate between voxels in different parcels especially at the borders between these parcels. In real data experiment, the proposed approach manages to recover HRF estimates close to the canonical shape in the bilateral occipital cortex.

This paper presents a data-driven strategy for the detection of failures impacting the flight control system. Early and robust detection of Oscillatory Failure Case (OFC) allows the aircraft structural design to be optimized, which in turn helps improve the aircraft environmental footprint thanks to weight saving. Compared to existing model-based techniques already used on in-service Airbus aircraft, this paper studies a novel signal processing approach based on distance and correlation. It is shown that a mixed similarity index between Euclidean distance and logarithmic invariant divergence gives promising detection results. This paper details the proposed approach by insisting on practical constraints due to implementation in embedded real-time systems such as the flight control computer. Preliminary results obtained from a Verification & Validation (V&V) on-going campaign are presented.

Linear mixture models are commonly used to represent a hyperspectral data cube as linear combinations of endmember spectra. However, determining the number of endmembers for images embedded in noise is a crucial task. This paper proposes a fully automatic approach for estimating the number of endmembers in hyperspectral images. The estimation is based on recent results of random matrix theory related to the so-called spiked population model. More precisely, we study the gap between successive eigenvalues of the sample covariance matrix constructed from high-dimensional noisy samples. The resulting estimation strategy is fully automatic and robust to correlated noise owing to the consideration of a noise-whitening step. This strategy is validated on both synthetic and real images. The experimental results are very promising and show the accuracy of this algorithm with respect to state-of-the-art algorithms.

Magnetic resonance spectroscopic imaging (MRSI) is a non-invasive technique able to provide the spatial distribu- tion of relevant biochemical compounds commonly used as biomarkers of disease. Information provided by MRSI can be used as a valuable insight for the diagnosis, treatment and follow-up of several diseases such as cancer or neurological disorders. Obtaining accurate metabolite concentrations from in vivo MRSI signals is a crucial require- ment for the clinical utility of this technique. Despite the numerous publications on the topic, accurate quantification is still a challenging problem due to the low signal-to-noise ratio of the data, overlap of spectral lines and the pres- ence of nuisance components. We propose a novel quantification method, which alleviates these limitations by exploiting a spatio-spectral regularization scheme. In contrast to previous methods, the regularization terms are not expressed directly on the parameters being sought, but on appropriate transformed domains. In order to quan- tify all signals simultaneously in the MRSI grid, while introducing prior information, a fast proximal optimization al- gorithm is proposed. Experiments on synthetic MRSI data demonstrate that the error in the estimated metabolite concentrations is reduced by a mean of 41% with the proposed scheme. Results on in vivo brain MRSI data show the benefit of the proposed approach, which is able to fit overlapping peaks correctly and to capture metabolites that are missed by single-voxel methods due to their lower concentrations.

The SPOT 6-7 satellite ground segment includes a systematic and automatic cloud detection step in order to feed a catalogue with a binary cloud mask and an appropriate confidence measure. In order to significantly improve the SPOT cloud detection and get rid of frequent manual re-labelings, we study a new automatic cloud detection technique that is adapted to large datasets. The proposed method is based on a modified distributed boosting algorithm. Experiments conducted using the framework Apache Spark on a SPOT 6 image database with various landscapes and cloud coverage show promising results.

This paper presents a high-resolution hyperspectral image fusion algorithm based on spectral unmixing. The widely used linear observation model (with additive Gaussian noise) is combined with the linear spectral mixture model to form the data terms. The non-negativity and sum-to-one constraints, resulting from the intrinsic physical properties of the abundances (i.e., fractions of the materials contained in each pixel), are introduced to regularize the ill-posed image fusion problem. The joint fusion and unmixing problem is formulated as the minimization of a cost function with respect to the mixing matrix (which contains the spectral signatures of the pure material, referred to as endmembers), and the abundance maps, with non-negativity and sum-to-one constraints. This optimization problem is attacked with an alternating optimization strategy. The two resulting sub-problems are convex and are solved efficiently using the alternating direction method of multipliers. Simulation results, including comparisons with the state-of-the-art, document the effectiveness and competitiveness of the proposed unmixing based fusion algorithm.