Bayesian Compressive Sensing With Variational Inference and Wavelet Tree Structure for Solving Inverse Scattering Problems

The inverse scattering problems (ISPs) refer to reconstructing properties of unknown scatterers from measured scattered fields, and their solving process is inherently complex and fraught with various difficulties. In response to these challenges, a solver operating in a Bayesian compressive sensing (BCS) manner is proposed, which uses variational inference, wavelet tree structure, and an improved linear relationship. Specifically, the BCS enables sparsity regularization; the improved linear relationship possessing cross-validation information (CVI) is designed to reduce error propagation and enable the solver to work in an iterative manner; the utilization of a wavelet tree structure based on discrete wavelet transform (DWT) can implement sparse coding and provide more prior information; variational inference is exploited to estimate parameters and hyperparameters in the BCS manner. Theoretical analysis and representative numerical results from synthetic and experimental data demonstrate that the proposed solver showcases superior performance when compared with other competitive solvers based on a BCS manner or contrast source inversion (CSI), especially in reconstructing complex configurations characterized by nonsparse and nonweak scatterers.