Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL) divergence. In this paper, we focus on the following parametric family: mixtures of isotropic Gaussians (i.e., with diagonal covariance matrices proportional to the identity) and uniform weights. We develop a variational framework and provide efficient algorithms suited for this family. In contrast with mixtures of Gaussian with generic covariance matrices, this choice presents a balance between accurate approximations of multimodal Bayesian posteriors, while being memory and computationally efficient. Our algorithms implement gradient descent on the location of the mixture components (the modes of the Gaussians), and either (an entropic) Mirror or Bures descent on their variance parameters. We illustrate the performance of our algorithms on numerical experiments.

Remote control vehicles require the transmission of large amounts of data, and video is one of the most important sources for the driver. To ensure reliable video transmission, the encoded video stream is transmitted simultaneously over multiple channels. However, this solution incurs a high transmission cost. To address this issue, it is necessary to use more efficient video encoding methods that can make the video stream robust to noise. Moreover it should have a less complexity to adapt to the real time requirement. In this paper, we propose a low-complexity, low-latency 2-channel Multiple Description Coding (MDC) solution with an adaptive Instantaneous Decoder Refresh (IDR) frame period, which is compatible with the HEVC standard with adaptive redundancy adjustment. This method shows a better resistance to high packet loss rates with lower complexity.

Along with Markov chain Monte Carlo (MCMC) methods, variational inference (VI) has emerged as a central computational approach to large-scale Bayesian inference. Rather than sampling from the true posterior $\pi$, VI aims at producing a simple but effective approximation $\hat \pi$ to $\pi$ for which summary statistics are easy to compute. However, unlike the well-studied MCMC methodology, algorithmic guarantees for VI are still relatively less well-understood. In this work, we propose principled methods for VI, in which $\hat \pi$ is taken to be a Gaussian or a mixture of Gaussians, which rest upon the theory of gradient flows on the Bures--Wasserstein space of Gaussian measures. Akin to MCMC, it comes with strong theoretical guarantees when $\pi$ is log-concave.

The recently introduced noniterative imaging method entitled “direct sampling method” (DSM) is known to be fast, robust, and effective for inverse scattering problems in the multistatic configuration but fails when applied to the monostatic one. To the best of our knowledge, no explanation of this failure has been provided yet. Thanks to the framework of the asymptotic and the far-field hypothesis in the 2-D scalar configuration, an analytical expression of the DSM indicator function in terms of the Bessel function of order zero and sizes, shapes, and permittivities of the inhomogeneities is obtained and the theoretical reason of the limitation identified. A modified version of DSM is then proposed in order to improve the imaging method. The theoretical results are supported by numerical results using synthetic data.

In many applications, such as Eddy-Current Testing (ECT), we are often interested in the joint model choice and parameter estimation. Nested Sampling (NS) is one of the possible methods. The key step that reflects the efficiency of the NS algorithm is how to get samples with hard constraint on the likelihood value. This contribution is based on the classical idea where the new sample is drawn within a hyper-ellipsoid, the latter being located from Gaussian approximation. This sampling strategy can automatically guarantee the hard constraint on the likelihood. Meanwhile, it shows the best sampling efficiency for models which have Gaussian-like likelihood distributions. We apply this method in ECT. The simulation results show that this method has high model choice ability and good parameter estimation accuracy, and low computational cost meanwhile.

In the framework of inverse scattering techniques for microwave imaging, this paper proposes an approach based on the integration between a multiscaling procedure and the level-set-based optimization in order to properly deal with the shape reconstruction of multiple and disconnected homogeneous scatterers. The effectiveness and robustness of the proposed approach is assessed against both synthetic and experimental data. A selected set of results concerned with complex shapes is presented and discussed.

Electromagnetic three-component magnetic probes at diffusion frequencies are now available for use in slim mineral-exploration boreholes. When a source is operated at or below the surface of the Earth in the vicinity of a conductive orebody, these probes provide, after appropriate processing, the secondary vector magnetic field attributed to this body. Proper inversion of the resulting datasets requires as a first step a clear understanding of the electromagnetic interaction of model signals with model bodies. In this paper, the response of a conductive ellipsoid buried at shallow depth in a half-space Earth is investigate by a novel hybrid approach combining the localized nonlinear approximation and the low frequency scattering theory. The ellipsoidal shape indeed fits a large class of scatterers and yet is amenable to analytical calculations in the intricate world of ellipsoidal harmonics, while the localized nonlinear approximation is known to provide fairly accurate results at least for low contrasts of conductivity between a scattering body and its host medium. In addition, weak coupling of the body to the interface is assumed. The primary field accounts for the presence of the interface, but multiple reflection of the secondary field on this interface is neglected. After analyzing the theoretical bases of the approach, numerical simulations in several geometrical and electrical configurations illustrate how estimators of the secondary magnetic field along a nearby borehole behave with respect to a general-purpose method-of-moments (MoM) code. Perspectives of the investigation and extensions, in particular, to two-body systems, strong coupling to the interface, and high contrast cases, are discussed.