Texture analysis can be embedded in the mathematical framework of multifractal (MF) analysis, enabling the study of the fluctuations in regularity of image intensity and providing practical tools for their assessment, wavelet leaders. A statistical model for leaders was proposed permitting Bayesian estimation of MF parameters for images yielding improved estimation quality over linear regression based estimation. This present work proposes an extension of this Bayesian model for patch-wise MF analysis of images. Classical MF analysis assumes space homogeneity of the MF properties whereas here we assume MF properties may change between texture elements and we do not know where the changes are located. This paper proposes a joint Bayesian model for patches formulated using spatially smoothing gamma Markov Random Field priors to counterbalance the increased statistical variability of estimates caused by small patch sizes. Numerical simulations based on synthetic multifractal images demonstrate that the proposed algorithm outperforms previous formulations and standard estimators.

This paper addresses the problem of blind deconvolution of medical ultrasound (US) images. Specifically, a parametric model for the point spread function (PSF) established experimentally is used, i.e., the US PSF can be modeled by a Gaussian function modulated by a sinusoidal function. Given this parametric model, the estimation of the PSF in a blind deconvolution problem can be reduced to the estimation of its parameters. Moreover, due to the ill-posedness of blind deconvolution problem, an ℓp-norm (0 <; p ≤ 2) regularization term (including the widely considered ℓ1-norm, ℓ2-norm regularization terms) for the ultrasound tissue reflectivity function (TRF) is employed, based on the assumption of generalized Gaussian distributed US images. An alternating optimization approach is proposed for the estimations of the US PSF and TRF. The behavior of the proposed algorithm is illustrated using simulated and in vivo US data.

Several random access (RA) techniques have been proposed recently for the satellite return link. The main objective of these techniques is to resolve packets collisions in order to enhance the limited throughput of traditional RA schemes. In this context, Multi-Replica Decoding using Correlation based Localisation (MARSALA) has been introduced and has shown good performance with DVB-RCS2 coding scheme and equi-powered transmissions. However, it has been shown in the literature that alternative coding schemes and packets power distributions can have a positive impact on RA performance. Therefore, in this paper, we investigate the behaviour of MARSALA with various coding schemes and various packet power distributions, then we propose a configuration for optimal performance. This paper also introduces the enhancement of MARSALA RA scheme by adding MRC to optimize replicas combination and study the impact on the throughput. We compare two different MRC techniques and we evaluate, via simulations, the gain achieved using MRC with different coding schemes and unbalanced packets. The simulation results demonstrate that the proposed enhancements to MARSALA show substantial performance gain, i.e. throughput achieved for a target Packet Loss Ratio (PLR).

This paper studies a maritime vessel detection method based on the fusion of data obtained from two different sensors, namely a synthetic aperture radar (SAR) and an automatic identification system (AIS) embedded in a satellite. Contrary to most methods widely used in the literature, the present work proposes to jointly exploit information from SAR and AIS raw data in order to detect the absence or presence of a ship using a binary hypothesis testing problem. This detection problem is handled by a generalized likelihood ratio detector whose test statistics has a simple closed form expression. The distribution of the test statistics is derived under both hypotheses, allowing the corresponding receiver operational characteristics (ROCs) to be computed. The ROCs are then used to compare the detection performance obtained with different sensors showing the interest of combining information from AIS and radar.

The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article, we attempttomeasuretheproximityoftwostationaryfieldsbya real and positive number between 0 and 1. The extremal values will correspond to uncorrelation and linear dependence, similartoacorrelationcoefficientwhichmeasureslinearlinks between two random variables. We show that these ”indices of coherence” are generally not symmetric, and not unique. We study and we illustrate this problem together for onedimensional and two-dimensional fields in the framework of stationary processes.

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.