Single-photon light detection and ranging (Lidar) devices can be used to obtain range and reflectivity information from 3D scenes. However, reconstructing the 3D surfaces from the raw waveforms can be very challenging, in particular when the number of spurious background detections is large compared to the number of signal detections. This paper introduces a new and fast detection algorithm, which can be used to assess the presence of objects/surfaces in each waveform, allowing only the histograms where the imaged surfaces are present to be further processed. The method is compared to state-of-the-art 3D reconstruction methods using synthetic and real single-photon data and the results illustrate its benefits for fast and robust target detection using single-photon data.

Cet article présente un modèle de représentation parcimonieuse pondérée pour la détection d'anomalies dans des signaux de télémesure satellite multivariés. La méthode proposée est une extension de l'état de l'art par son adaptation au cadre multivarié et l'intégration d'informations externes par l'intermédiaire d'une pondération appropriée permettant d'améliorer les performances de détection.

For linear discrete state-space models, under certain conditions, the linear least mean squares (LLMS) filter estimate has a recursive format, a.k.a. the Kalman filter (KF). Interestingly, the linear minimum variance distortionless response (LMVDR) filter, when it exists, shares exactly the same recursion as the KF, except for the initialization. If LMVDR estimators are suboptimal in mean-squared error sense, they do not depend on the prior knowledge on the initial state. Thus, the LMVDR estimators may outperform the usual LLMS estimators in case of misspecification of the prior knowledge on the initial state. In this perspective, we establish the general conditions under which existence of the LMVDRF is guaranteed. An immediate benefit is the introduction of LMVDR fixed-point and fixed-lag smoothers (and possibly other smoothers or predictors), which has not been possible so far. Indeed, the LMVDR fixed-point smoother can be used to compute recursively the solution of a generalization of the deterministic least-squares problem.

In the context of linear discrete state-space (LDSS) models, we generalize a result lately introduced in the restricted case of invertible state matrices, namely that the linear minimum variance distortionless response (LMVDR) filter shares exactly the same recursion as the linear least mean squares (LLMS) filter, aka the Kalman filter (KF), except for the initialization. An immediate benefit is the introduction of LMVDR fixed-point and fixed-lag smoothers (and possibly other smoothers or predictors), which has not been possible so far. This result is particularly noteworthy given the fact that, although LMVDR estimators are sub-optimal in mean-squared error sense, they are infinite impulse response distortionless estimators which do not depend on the prior knowledge on the mean and covariance matrix of the initial state. Thus the LMVDR estimators may outperform the usual LLMS estimators in case of misspecification of the prior knowledge on the initial state. Seen from this perspective, we also show that the LMVDR filter can be regarded as a generalization of the information filter form of the KF. On another note, LMVDR estimators may also allow to derive unexpected results, as highlighted with the LMVDR fixed-point smoother.

For linear discrete state-space models, under certain conditions, the linear least-mean-squares filter estimate has a convenient recursive predictor/corrector format, aka the Kalman filter. The purpose of this paper is to show that the linear minimum variance distortionless response (MVDR) filter shares exactly the same recursion, except for the initialization which is based on a weighted least-squares estimator. If the MVDR filter is suboptimal in mean-squared error sense, it is an infinite impulse response distortionless filter (a deconvolver) which does not depend on the prior knowledge (first- and second-order statistics) on the initial state. In other words, the MVDR filter can be pre-computed and its behaviour can be assessed in advance independently of the prior knowledge on the initial state.

Joint deconvolution and segmentation of ultrasound images is a challenging problem in medical imaging. By adopting a hierarchical Bayesian model, we propose an accelerated Markov chain Monte Carlo scheme where the tissue reflectivity function is sampled thanks to a recently introduced proximal unadjusted Langevin algorithm. This new approach is combined with a forward-backward step and a preconditioning strategy to accelerate the convergence, and with a method based on the majorization-minimization principle to solve the inner non-convex minimization problems. As demonstrated in numerical experiments conducted on both simulated and in vivo ultrasound images, the proposed method provides high-quality restoration and segmentation results and is up to six times faster than an existing Hamiltonian Monte Carlo method.

In the past years, one common way of enhancing the spatial resolution of a hyperspectral (HS) image has been to fuse it with complementary information coming from multispectral (MS) or panchromatic images. This paper proposes a new method for reconstructing a high-spatial, high-spectral image from measurements acquired after compressed sensing by multiple sensors of different spectral ranges and spatial resolutions, with specific attention to HS and MS compressed images. To solve this problem, we introduce a fusion model based on the linear spectral unmixing model classically used for HS images and investigate an optimization algorithm based on a block coordinate descent strategy. The nonnegative and sum-to-one constraints resulting from the intrinsic physical properties of abundances as well as a total variation penalization are used to regularize this ill-posed inverse problem. Simulation results conducted on realistic compressed HS and MS images show that the proposed algorithm can provide fusion results that are very close to those obtained with uncompressed images, with the advantage of using a significantly reduced number of measurements.