Remote sensing pushbroom-type imaging systems acquire entire columns of an image with a single detector. As a consequence, the miss-calibration of the detectors produces stripes on the image. In this context, this paper introduces a new self-calibration destriping method based on an affine response model for the detectors, called Statistical Affine Destriping (SAD). In contrast, some previous contributions were limited to a purely linear model, while many others only considered an additive structured noise model. It is based on the maximum a posteriori estimation of the gain and offset parameters attached to each detector given the observed image. Simple statistical prior assumptions are adopted: respectively, a Gaussian white noise model for the gains and offsets, and a first-order, homogeneous Markov model for the observed scene. Based on a simplification of the posterior likelihood, we propose a very efficient optimization scheme based on a constrained Majorize-Minimize principle, allowing us to process large dimension images. Moreover, simple empirical rules are given to tune the hyperparameters of the destriping method for high-resolution PLEIADES-type images. Compared to the performance of a destriping method limited to gain correction, we observe that the new version provides reliable results in a wider range of situations. We also extend the method in two directions. On the one hand, we consider that some detectors may be atypical, with very high or very low gains or offsets. On the other hand, we extend the method to multispectral image destriping.

In this paper the problem of restoration of unsupervised nonnegative sparse signals is addressed in the Bayesian framework. We introduce a new probabilistic hierarchical prior, based on the Generalized Hyperbolic (GH) distribution, which explicitly accounts for sparsity. On the one hand, this new prior allows us to take into account the non-negativity. On the other hand, thanks to the decomposition of GH distributions as continuous Gaussian mean-variance mixture, a partially collapsed Gibbs sampler (PCGS) implementation is made possible, which is shown to be more efficient in terms of convergence time than the classical Gibbs sampler.

Hyperspectral pansharpening methods, which aim to combine hyperspectral and panchromatic images, yield limited performance for scenes whose strong spatial heterogeneity induces mixed pixels. The SOSU method has been designed to handle this limitation and provided good results on agricultural and peri-urban landscapes. However, its performance was reduced on more complex urban scenes, which contain a higher proportion of mixed pixels. This article presents a new version of this method, called SOSU-2021, adapted to better process urban scenes. SOSU-2021 is tested on an urban dataset at a 1.6 m spatial resolution. We obtain better numerical results than with the previous SOSU version, and in the worst case, 56 % of the mixed pixels are better or equally processed by SOSU-2021 than by the method used as a reference.

We propose a global optimization approach to solve ℓ0-norm penalized least-squares problems, using a dedicated branch-and-bound methodology. A specific tree search strategy is built, with branching rules inspired from greedy exploration techniques. We show that the subproblem involved at each node can be evaluated via ℓ1-norm-based optimization problems with box constraints, for which an active-set algorithm is built. Our method is able to solve exactly moderate-size, yet difficult, sparse approximation problems, without resorting to mixed-integer programming (MIP) optimization. In particular, it outperforms the generic MIP solver CPLEX.

We address sparse approximation in the particular case where the dictionary is built upon the discretization of a continuous parameter. The resulting dictionary being highly correlated, equivalence between ℓ0and suboptimal solutions (e.g. greedy algorithms and convex relaxation) is not guaranteed. To tackle this issue, continuous parameter estimation has been proposed using a dictionary based on polar interpolation [1], [2]. Alternately, the exact ℓ0-norm optimization problem can be addressed on moderate size problems through Mixed Integer Programming (MIP) [3]. We propose to merge these two approaches in a new MIP formulation adapted to polar interpolation. Improvements on polar interpolation and refinements on its use in the ℓ1-norm framework are also proposed. Methods are evaluated on simulated spike train deconvolution problems, where the proposed ℓ0-norm approach with continuous dictionary achieves the best results, although with higher computing time.

Hyperspectral imaging has been an area of active research in image processing and analysis for more than 10 years, mainly for remote sensing applications. Astronomical ground-based hyperspectral imagers offer new challenges to the community, which differ from the previous ones in the nature of the observed objects, but also in the quality of the data, with a low signal-to-noise ratio and a low resolution, due to the atmospheric turbulence. In this paper, we focus on a deconvolution problem specific to hyperspectral astronomical data, to improve the study of the kinematics of galaxies. The aim is to estimate the flux, the relative velocity, and the velocity dispersion, integrated along the line-of-sight, for each spatial pixel of an observed galaxy. Thanks to the Doppler effect, this is equivalent to estimate the amplitude, center, and width of spectral emission lines, in a small spectral range, for every spatial pixel of the hyperspectral data. We consider a parametric model for the spectral lines and propose to compute the posterior mean estimators, in a Bayesian framework, using Monte Carlo Markov chain algorithms. Various estimation schemes are proposed for this nonlinear deconvolution problem, taking advantage of the linearity of the model with respect to the flux parameters. We differentiate between methods taking into account the spatial blurring of the data (deconvolution) or not (estimation). The performances of the methods are compared with classical ones, on two simulated data sets. It is shown that the proposed deconvolution method significantly improves the resolution of the estimated kinematic parameters.

This paper introduces a new self-calibration destriping technique for pushbroom-type satellite imaging systems. Self-calibration means that no specific training data are required. It is based on the statistical estimation of each detector gain from the observed image, assuming a linear response. Both theoretical and practical behaviors are studied. Our technique is shown to outperform simpler techniques based on column averages in terms of gain estimation precision while keeping the computational cost within admissible limits.

The Soil Moisture and Ocean Salinity (SMOS) mission is a European Space Agency project aimed at global monitoring of surface SMOS from radiometric L-band observations. This letter is concerned with the reduction of the systematic error (or bias) in the reconstruction of radiometric brightness temperature maps from SMOS interferometric measurements. A recent and efficient method has been proposed for reducing this error. However, a residual bias still persists. A new approach for reducing this bias down to residual values less than 0.1 K is presented here and illustrated with numerical simulations.

Synthetic aperture imaging radiometers (SAIR) are powerful instruments for high-resolution observation of the Earth surface at low microwave frequencies. This article deals with the impact of correlators and receivers failures on the reconstruction process which aims at inverting the interferometric data for retrieving the radiometric brightness temperature distribution of the scene under observation. Numerical simulations are carried out for the SMOS space mission, a project led by the European Space Agency and devoted to the remote sensing of soil moisture and ocean salinity from a low orbit platform.

Line spectra estimation is addressed for irregularly sampled astrophysical data. A formulation with a large number of discretized frequencies is used and sparseness is encouraged via a Bernoulli-Gaussian (BG) model on the corresponding amplitudes. Contrary to classic BG models, here the frequency parameters are not constrained on a fixed grid, theoretically enabling unlimited frequency precision. We propose a posterior mean unsupervised estimation scheme combined with an hybrid MCMC algorithm, that allows us to derive crucial information in an astrophysical context, such as confidence levels and variances for each detected spectral line. Simulations confirm the validity of this model with satisfactory estimation results, in addition to a more solid behaviour than parametric methods towards classic astrophysical perturbations

High resolution spectral analysis has recently been addressed as an inverse problem, and solutions are currently proposed through the regularization framework. In this paper, we focus on regularized spectral analysis of unevenly sampled data for line spectra estimation. First, we study the structural differences of the model between regular sampling, missing data (where the sampling is regular, but with missing data) and irregular sampling cases. Then, consequences for the computation of the solution are emphasized. We propose an approximation of the irregular sampling model to compute the nonquadratic regularization solution at a cost comparable to the other sampling cases. Finally, algorithmic implementation is discussed and applications to simulated data are presented.

We focus on the nonlinear inverse problem of diffraction tomography. We set the problem as one of estimation within the Bayesian framework and define the solution as the maximum a posteriori (MAP) estimate which corresponds to the global minimum of a multimodal criterion. The objective of this paper is to present a new deterministic single site update algorithm specially designed to compute this solution. The term of fidelity to the data, function of one pixel value, can be written as a second order rational fraction. Thus, the 1-D MAP criterion can be evaluated and minimized-at a very low computational cost. Moreover, for certain MRF models the global minimum can even be computed explicitly as roots of a polynomial. The proposed algorithm turns these properties to advantage and moreover performs the updates of intermediate quantities at a particularly low cost compared to the criterion evaluation. Even if not guaranteed to converge towards the global minimum, the algorithm has shown itself to give satisfactory practical results.

The authors propose a new method to solve the nonlinear inverse problem of tomographic imaging using microwave or ultrasound probing, beyond the classical first order Born or Rytov approximations. The relation between the data and the measurement is given by two coupled nonlinear equations. The authors set this problem as one of estimation and propose a solution within the Bayesian probability framework. The maximum a posteriori estimate determination leads to a multi-modal criterion minimisation. Global minimisation using simulated annealing is not practicable due to the high calculation cost. The authors propose a feasible deterministic relaxation algorithm inspired by the graduated nonconvexity principle to perform this minimisation.