I will describe a projected Nesterov’s proximal-gradient (PNPG) approach for sparse signal reconstruction. The objective function that we wish to minimize is a sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a convex regularization term. We apply sparse signal regularization where the signal belongs to a closed convex set within the closure of the domain of the NLL; the convex-set constraint facilitates flexible NLL domains and accurate signal recovery. Signal sparsity is imposed using the ℓ₁-norm penalty on the signal's linear transform coefficients or gradient map, respectively. The PNPG approach employs projected Nesterov's acceleration step with restart and an inner iteration to compute the proximal mapping. We propose an adaptive step-size selection scheme to obtain a good local majorizing function of the NLL and reduce the time spent backtracking. Thanks to step-size adaptation, PNPG does not require Lipschitz continuity of the gradient of the NLL. We establish O(k⁻²) convergence of the PNPG scheme; our convergence-rate analysis accounts for inexactness of the iterative proximal mapping. The tuning of PNPG is largely application-independent. Tomographic and compressed-sensing reconstruction experiments with Poisson generalized linear and Gaussian linear measurement models demonstrate the performance of the proposed approach.

Health monitoring is performed on CNES spacecraft using two complementary methods: an utomatic Out-Of-Limits (OOL) checking executed on a set of critical parameters after each new telemetry reception, and a monthly monitoring of statistical features (daily minimum, mean and maximum) of another set of parameters. In this paper we present the limitations of this monitoring system and we introduce an innovative anomaly detection method based on machine-learning algorithms, developed during a collaborative R&D action between CNES and TESA (TElecommunications for Space and Aeronautics). This method has been prototyped and has shown encouraging results regarding its ability to detect actual anomalies that had slipped through the existing monitoring net. An operational-ready software implementing this method, NOSTRADAMUS, has been developed in order to further evaluate the interest of this new type of surveillance, and to consolidate the settings proposed after the R&D action. The lessons learned from the operational assessment of this system for the routine surveillance of CNES spacecraft are also presented in this paper.

This paper presents a new strategy to correct the Earth data corrupted by spurious samples that are randomly included in the multiplexed data stream provided by the MADRAS instrument. The proposed strategy relies on the construction of a trellis associated with each scan of the multi-channel image, modeling the possible occurrences of these erroneous data. A specific weight that promotes the smooth behavior of the signals recorded in each channel is assigned to each transition between trellis states. The joint detection and correction of the erroneous data are conducted using a dynamic programming algorithm for minimizing the overall cost function throughout the trellis. Simulation results obtained on synthetic and real MADRAS data demonstrate the effectiveness of the proposed solution.

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.