The reliability of a recently introduced nonlinear estimation method for tomographic imaging is discussed in full detail. It is shown how a proper choice of the functional spaces to which unknown quantities belong and the exploitation of the expected properties of the object under test and of all the available a priori information positively affect robustness against false solutions of the inversion procedure. The developed arguments allow the authors to understand causes of possible false solutions, suggesting possible countermeasures. In particular, it is shown how the proposed approach allows the authors to achieve accurate and reliable reconstructions in a set of cases larger than the range of applicability of other "false solutions free" approaches. Numerical analyses confirm the validity of the approach and the effectiveness of developed inversion procedures through practical examples.

We present a statistical method to solve the height estimation problem in interferometric synthetic aperture radar (InSAR) applications. It is based on the use of multifrequency SAR raw datasets obtained by partitioning in subbands the available raw data spectrum, and on a Bayesian estimator using Markov random fields to model the a priori distribution of the unknown images. The method allows recovering topographic profiles affected by strong height discontinuities and allows to perform efficient noise rejections.

A nonlinear estimation approach to solving the inverse scattering problem, and reconstructing the space-varying complex permittivity of unknown objects is considered. The bilinear operator equations governing the scattering are approximated into finite dimensional spaces on the basis of the finite degrees of freedom of data, and on the simple concept that one cannot expect to reconstruct an arbitrary function from a finite number of independent equations. As a consequence, a discrete model, well suited to numerical inversion, is developed. The particular bilinear nature of the equations, and a suitable choice of contrast and field unknowns allows the functional adopted in the estimation to be minimized in an accurate and numerically efficient manner. Numerical experiments show how the method is capable, when a proper number of searched unknowns is adopted, to manage the possible convergence to local minima (which is a typical question in nonlinear inverse problems), and validate the effectiveness of the proposed approach.

Deep learning (DL) in remote sensing has nowadays become an effective operative tool: it is largely used in applications, such as change detection, image restoration, segmentation, detection, and classification. With reference to the synthetic aperture radar (SAR) domain, the application of DL techniques is not straightforward due to the nontrivial interpretation of SAR images, especially caused by the presence of speckle. Several DL solutions for SAR despeckling have been proposed in the last few years. Most of these solutions focus on the definition of different network architectures with similar cost functions, not involving SAR image properties. In this article, a convolutional neural network (CNN) with a multi-objective cost function taking care of spatial and statistical properties of the SAR image is proposed. This is achieved by the definition of a peculiar loss function obtained by the weighted combination of three different terms. Each of these terms is dedicated mainly to one of the following SAR image characteristics: spatial details, speckle statistical properties, and strong scatterers identification. Their combination allows balancing these effects. Moreover, a specifically designed architecture is proposed to effectively extract distinctive features within the considered framework. Experiments on simulated and real SAR images show the accuracy of the proposed method compared with the state-of-art despeckling algorithms, both from a quantitative and qualitative point of view. The importance of considering such SAR properties in the cost function is crucial for correct noise rejection and details preservation in different underlined scenarios, such as homogeneous, heterogeneous, and extremely heterogeneous.

The aim of this paper is twofold. First, why and how exploitation of multifrequency information is of great usefulness in inverse scattering problems is discussed. Second, three different solution strategies, all based on a recently introduced approach, are presented, discussed, and compared in the actual case of noise affected data in the two-dimensional (2D) scalar case. The first one is a (nonlinear) frequency-hopping technique, which favorably compares with approaches of the same kind that use linear inversion steps. As a second approach, the contemporary use of the different frequencies data is considered. Contrary to common assumptions, it is shown that such an approach may perform better than the previous one, the different performances between the two being dictated by the spatial frequency content of the unknown contrast. Finally, a hybrid and, to the best of the authors' knowledge, novel strategy, which exploits the advantages of the the previous ones, is introduced and discussed.