Towards SAR Tomographic Inversion via Sparse Bayesian Learning

Existing SAR tomography (TomoSAR) algorithms are mostly based on an inversion of the SAR imaging model, which are often computationally expensive. Previous study showed perspective of using data-driven methods like KPCA to decompose the signal and reduce the computational complexity. This paper gives a preliminary demonstration of a new data-driven method based on sparse Bayesian learning. Experiments on simulated data show that the proposed method significantly outperforms KPCA methods in estimating the steering vectors of the scatterers. This gives a perspective of data-drive approach or combining it with model-driven approach for high precision tomographic inversion of large areas.Comment: accepted in preliminary version for EUSAR2020 conferenc

Unitary Approximate Message Passing for Sparse Bayesian Learning and Bilinear Recovery

Over the past several years, the approximate message passing (AMP) algorithm has been applied to a broad range of problems, including compressed sensing (CS), robust regression, Bayesian estimation, etc. AMP was originally developed for compressed sensing based on the loopy belief propagation (BP). Compared to convex optimization based algorithms, AMP has low complexity and its performance can be rigorously characterized by a scalar state evolution (SE) in the case of a large independent and identically distributed (i.i.d.) (sub-) Gaussian matrix. AMP was then extended to solve general estimation problems with a generalized linear observation model. However, AMP performs poorly on a generic matrix such as non-zero mean, rank-deficient, correlated, or ill-conditioned matrix, resulting in divergence and degraded performance. It was discovered later that applying AMP to a unitary transform of the original model can remarkably enhance the robustness to difficult matrices. This variant is named unitary AMP (UAMP), or formally called UTAMP. In this thesis, leveraging UAMP, we propose UAMP-SBL for sparse signal recovery and Bi-UAMP for bilinear recovery, both of which inherit the low complexity and robustness of UAMP. Sparse Bayesian learning (SBL) is a powerful tool for recovering a sparse signal from noisy measurements, which finds numerous applications in various areas. As a traditional implementation of SBL, e.g., Tipping’s method, involves matrix inversion in each iteration, the computational complexity can be prohibitive for large scale problems. To circumvent this, AMP and its variants have been used as low-complexity solutions. Unfortunately, they will diverge for ‘difficult’ measurement matrices as previously mentioned. In this thesis, leveraging UAMP, a novel SBL algorithm called UAMP-SBL is proposed where UAMP is incorporated into the structured variational message passing (SVMP) to handle the most computationally intensive part of message computations. It is shown that, compared to state-of-the-art AMP based SBL algorithms, the proposed UAMP-SBL is more robust and efficient, leading to remarkably better performance. The bilinear recovery problem has many applications such as dictionary learning, selfcalibration, compressed sensing with matrix uncertainty, etc. Compared to existing nonmessage passing alternates, several AMP based algorithms have been developed to solve bilinear problems. By using UAMP, a more robust and faster approximate inference algorithm for bilinear recovery is proposed in this thesis, which is called Bi-UAMP. With the lifting approach, the original bilinear problem is reformulated as a linear one. Then, variational inference (VI), expectation propagation (EP) and BP are combined with UAMP to implement the approximate inference algorithm Bi-UAMP, where UAMP is adopted for the most computationally intensive part. It is shown that, compared to state-of-the-art bilinear recovery algorithms, the proposed Bi-UAMP is much more robust and faster, and delivers significantly better performance. Recently, UAMP has also been employed for many other applications such as inverse synthetic aperture radar (ISAR) imaging, low-complexity direction of arrival (DOA) estimation, iterative detection for orthogonal time frequency space modulation (OTFS), channel estimation for RIS-Aided MIMO communications, etc. Promising performance was achieved in all of the applications, and more applications of UAMP are expected in the future

Sparse Bases and Bayesian Inference of Electromagnetic Scattering

Many approaches in CEM rely on the decomposition of complex radiation and scattering behavior with a set of basis vectors. Accurate estimation of the quantities of interest can be synthesized through a weighted sum of these vectors. In addition to basis decompositions, sparse signal processing techniques developed in the CS community can be leveraged when only a small subset of the basis vectors are required to sufficiently represent the quantity of interest. We investigate several concepts in which novel bases are applied to common electromagnetic problems and leverage the sparsity property to improve performance and/or reduce computational burden. The first concept explores the use of multiple types of scattering primitives to reconstruct scattering patterns of electrically large targets. Using a combination of isotropic point scatterers and wedge diffraction primitives as our bases, a 40% reduction in reconstruction error can be achieved. Next, a sparse basis is used to improve DOA estimation. We implement the BSBL technique to determine the angle of arrival of multiple incident signals with only a single snapshot of data from an arbitrary arrangement of non-isotropic antennas. This is an improvement over the current state-of-the-art, where restrictions on the antenna type, configuration, and a priori knowledge of the number of signals are often assumed. Lastly, we investigate the feasibility of a basis set to reconstruct the scattering patterns of electrically small targets. The basis is derived from the TCM and can capture non-localized scattering behavior. Preliminary results indicate that this basis may be used in an interpolation and extrapolation scheme to generate scattering patterns over multiple frequencies

An Iterative Receiver for OFDM With Sparsity-Based Parametric Channel Estimation

In this work we design a receiver that iteratively passes soft information between the channel estimation and data decoding stages. The receiver incorporates sparsity-based parametric channel estimation. State-of-the-art sparsity-based iterative receivers simplify the channel estimation problem by restricting the multipath delays to a grid. Our receiver does not impose such a restriction. As a result it does not suffer from the leakage effect, which destroys sparsity. Communication at near capacity rates in high SNR requires a large modulation order. Due to the close proximity of modulation symbols in such systems, the grid-based approximation is of insufficient accuracy. We show numerically that a state-of-the-art iterative receiver with grid-based sparse channel estimation exhibits a bit-error-rate floor in the high SNR regime. On the contrary, our receiver performs very close to the perfect channel state information bound for all SNR values. We also demonstrate both theoretically and numerically that parametric channel estimation works well in dense channels, i.e., when the number of multipath components is large and each individual component cannot be resolved.Comment: Major revision, accepted for IEEE Transactions on Signal Processin

From representation learning to thematic classification - Application to hierarchical analysis of hyperspectral images

Numerous frameworks have been developed in order to analyze the increasing amount of available image data. Among those methods, supervised classification has received considerable attention leading to the development of state-of-the-art classification methods. These methods aim at inferring the class of each observation given a specific class nomenclature by exploiting a set of labeled observations. Thanks to extensive research efforts of the community, classification methods have become very efficient. Nevertheless, the results of a classification remains a highlevel interpretation of the scene since it only gives a single class to summarize all information in a given pixel. Contrary to classification methods, representation learning methods are model-based approaches designed especially to handle high-dimensional data and extract meaningful latent variables. By using physic-based models, these methods allow the user to extract very meaningful variables and get a very detailed interpretation of the considered image. The main objective of this thesis is to develop a unified framework for classification and representation learning. These two methods provide complementary approaches allowing to address the problem using a hierarchical modeling approach. The representation learning approach is used to build a low-level model of the data whereas classification is used to incorporate supervised information and may be seen as a high-level interpretation of the data. Two different paradigms, namely Bayesian models and optimization approaches, are explored to set up this hierarchical model. The proposed models are then tested in the specific context of hyperspectral imaging where the representation learning task is specified as a spectral unmixing proble

Bayesian Variational Regularisation for Dark Matter Reconstruction with Uncertainty Quantification

Despite the great wealth of cosmological knowledge accumulated since the early 20th century, the nature of dark-matter, which accounts for ~85% of the matter content of the universe, remains illusive. Unfortunately, though dark-matter is scientifically interesting, with implications for our fundamental understanding of the Universe, it cannot be directly observed. Instead, dark-matter may be inferred from e.g. the optical distortion (lensing) of distant galaxies which, at linear order, manifests as a perturbation to the apparent magnitude (convergence) and ellipticity (shearing). Ensemble observations of the shear are collected and leveraged to construct estimates of the convergence, which can directly be related to the universal dark-matter distribution. Imminent stage IV surveys are forecast to accrue an unprecedented quantity of cosmological information; a discriminative partition of which is accessible through the convergence, and is disproportionately concentrated at high angular resolutions, where the echoes of cosmological evolution under gravity are most apparent. Capitalising on advances in probability concentration theory, this thesis merges the paradigms of Bayesian inference and optimisation to develop hybrid convergence inference techniques which are scalable, statistically principled, and operate over the Euclidean plane, celestial sphere, and 3-dimensional ball. Such techniques can quantify the plausibility of inferences at one-millionth the computational overhead of competing sampling methods. These Bayesian techniques are applied to the hotly debated Abell-520 merging cluster, concluding that observational catalogues contain insufficient information to determine the existence of dark-matter self-interactions. Further, these techniques were applied to all public lensing catalogues, recovering the then largest global dark-matter mass-map. The primary methodological contributions of this thesis depend only on posterior log-concavity, paving the way towards a, potentially revolutionary, complete hybridisation with artificial intelligence techniques. These next-generation techniques are the first to operate over the full 3-dimensional ball, laying the foundations for statistically principled universal dark-matter cartography, and the cosmological insights such advances may provide