This paper proposes a new Bayesian strategy for the smooth estimation of altimetric parameters. The altimetric signal is assumed to be corrupted by a thermal and speckle noise distributed according to an independent and non-identically Gaussian distribution. We introduce a prior enforcing a smooth temporal evolution of the altimetric parameters which improves their physical interpretation. The posterior distribution of the resulting model is optimized using a gradient descent algorithm which allows us to compute the maximum a posteriori estimator of the unknown model parameters. This algorithm has a low computational cost that is suitable for real-time applications. The proposed Bayesian strategy and the corresponding estimation algorithm are evaluated using both synthetic and real data associated with conventional and delay/Doppler altimetry. The analysis of real Jason-2 and CryoSat-2 waveforms shows an improvement in parameter estimation when compared to state-of-the-art estimation algorithms.

In high-grade gliomas, the tumor boundaries and the degree of infiltration are difficult to define due to their heterogeneous composition and diffuse growth pattern. Magnetic Resonance Spectroscopic Imaging (MRSI) is a non-invasive technique able to provide information on brain tumor biology not available from conventional anatomical imaging. In this paper we propose a blind source separation (BSS) algorithm for brain tissue classification and visualization of tumor spread using MRSI data. The proposed algorithm imposes relaxed non-negativity in the direct domain along with spatial-spectral regularizations in a transformed domain. The optimization problem is efficiently solved in a two-step approach using the concept of proximity operators. Vertex component analysis (VCA) is proposed to estimate the number of sources. Comparisons with state-of-the-art BSS algorithms on in-vivo MRSI data show the efficiency of the proposed algorithm. The presented method provides patterns that can easily be related to a specific tissue (normal, tumor, necrosis, hypoxia, edema or infiltration). Unlike other BSS methods dedicated to MRSI data, it can handle spectra with negative peaks and results are not sensitive to the initialization strategy. In addition, it is robust against noisy or bad-quality spectra.

fMRI experiments are usually conducted over a population of interest for investigating brain activity across different regions stimuli and objects. Multi-subject analysis proceeds in two steps, intra-subject analysis is performed sequentially on each individual and then group-level analysis is addressed to report significant results at the population level. This paper considers an existing Joint Parcellation Detection Estimation (JPDE) model which performs joint hemodynamic parcellation, brain dynamics estimation and evoked activity detection. The hierarchy of the JPDE model is extended for multi-subject analysis in order to perform group-level parcellation. Then, the corresponding underlying dynamics is estimated in each parcel while the detection and estimation steps are iterated over each individual. Validation on synthetic and real fMRI data shows its robustness in inferring the group-level parcellation and the corresponding hemodynamic profiles.

This paper addresses the problem of super-resolution (SR) for medical ultrasound (US) images. Contrary to device-based approaches, we investigate a post-processing method to invert the direct linear model of US image formation. Given the ill-posedness of single image SR, we proposed an ℓp-norm (1 ≤ p ≤ 2) regularizer for the US tissue reflectivity function/image to be estimated. To solve the associated optimization problem, we propose a novel way to explore the decimation and blurring operators simultaneously. As a consequence, we are able to compute the analytical solution for the ℓ2-norm regularized SR problem and to embed the analytical solution to an alternating direction method of multipliers for the ℓp-norm regularized SR problem. The behavior of the proposed algorithm is illustrated using synthetic, simulated and in vivo US data.

Passive intermodulation products may occur when two or more carriers are transmitted through a passive device such as a filter, a transmission line or an antenna or if they are reflected from one object. These products are generally due to distributed non-linearity along the transmission path or the reflector of the antenna. We show that ray optics can be used to determine easily the directions in which these products are in phase and reinforced. This is particularly significant for multihorn fed reflector antennas, for multiple antennas systems and for higher dynamic in measurement of passive intermodulation.

Passive intermodulation products may occur when two or more carriers are transmitted through a passive device such as a filter, a transmission line or an antenna or if they are reflected from one object. These products are generally due to distributed non-linearity along the transmission path or the reflector of the antenna. We show that ray optics can be used to determine easily the directions in which these products are in phase and reinforced. This is particularly significant for multihorn fed reflector antennas, for multiple antennas systems and for higher dynamic in measurement of passive intermodulation.

Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational inference techniques. This has driven the development of statistical SP methods based on stochastic simulation and optimization. Stochastic simulation and optimization algorithms are computationally intensive tools for performing statistical inference in models that are analytically intractable and beyond the scope of deterministic inference methods. They have been recently successfully applied to manydifficultproblemsinvolving complex statistical models and sophisticated (often Bayesian) statistical inference techniques. This survey paper offers an introduction to stochastic simulation and optimization methods in signal and image processing. The paper addresses a variety of high-dimensional Markov chain Monte Carlo (MCMC) methods as well as deterministic surrogate methods, such as variational Bayes, the Bethe approach, belief and expectation propagation and approximate message passing algorithms. It also discusses a range of optimization methods that have been adopted to solve stochastic problems, as well as stochastic methods for deterministic optimization. Subsequently, areas of overlap between simulation.

Mixing phenomena in hyperspectral images depend on a variety of factors, such as the resolution of observation devices, the properties of materials, and how these materials interact with incident light in the scene. Different parametric and nonparametric models have been considered to address hyperspectral unmixing problems. The simplest one is the linear mixing model. Nevertheless, it has been recognized that the mixing phenomena can also be nonlinear. The corresponding nonlinear analysis techniques are necessarily more challenging and complex than those employed for linear unmixing. Within this context, it makes sense to detect the nonlinearly mixed pixels in an image prior to its analysis, and then employ the simplest possible unmixing technique to analyze each pixel. In this paper, we propose a technique for detecting nonlinearly mixed pixels. The detection approach is based on the comparison of the reconstruction errors using both a Gaussian process regression model and a linear regression model. The two errors are combined into a detection statistics for which a probability density function can be reasonably approximated. We also propose an iterative endmember extraction algorithm to be employed in combination with the detection algorithm. The proposed detect-then-unmix strategy, which consists of extracting endmembers, detecting nonlinearly mixed pixels and unmixing, is tested with synthetic and real images.

Increasing the sampling rate of Analog-to-Digital Converters (ADC) is a main challenge in many fields and especially in telecommunications. Time-Interleaved ADCs (TI-ADC) were introduced as a technical solution to reach high sampling rates by time interleaving and multiplexing several lowrate ADCs at the price of a perfect synchronization between them. Indeed, as the signal reconstruction formulas are derived under the assumption of uniform sampling, a desynchronization between the elementary ADCs must be compensated upstream with an online calibration and expensive hardware corrections of the sampling device. Based on the observation that desynchronized TI-ADCs can be effectively modeled using a Periodic Non-uniform Sampling (PNS) scheme, we develop a general method to blindly estimate the time delays involved in PNS. The proposed strategy exploits the signal stationarity properties and thus is simple and quite generalizable to other applications. Moreover, contrarily to state-ofthe-art methods, it applies to bandpass signals which is the more judicious application framework of the PNS scheme.

Texture analysis is an image processing task that can be conducted using the mathematical framework of multifractal analysis to study the regularity fluctuations of image intensity and the practical tools for their assessment, such as (wavelet) leaders. A recently introduced statistical model for leaders enables the Bayesian estimation of multifractal parameters. It significantly improves performance over standard (linear regression based) estimation. However, the computational cost induced by the associated nonstandard posterior distributions limits its application. The present work proposes an alternative Bayesian model for multifractal analysis that leads to more efficient algorithms. It relies on three original contributions: A novel generative model for the Fourier coefficients of log-leaders; an appropriate reparametrization for handling its inherent constraints ; a data-augmented Bayesian model yielding standard conditional posterior distributions that can be sampled exactly. Numerical simulations using synthetic multifractal images demonstrate the excellent performance of the proposed algorithm, both in terms of estimation quality and computational cost.