Overview of inverse problems in acoustic and seismic signal processing

Abstract

An overview of inverse problems in acoustic and seismic signal processing is presented. The main goal of seismic inversion is to determine earth properties from seismic reflections or signals. Acoustic inversion includes ultrasonic imaging, acoustic tomography, acoustic oceanography, and propagation medium modeling. System identification, parameter estimation, image reconstruction from incomplete data, and blind deconvolution are all inverse problems. Most practical inverse problems are underdetermined and their solutions are not unique. The nonuniqueness is addressed by maximum entropy, minimum relative entropy methods, and Bayesian methods. Bayes method determines maximum a posteriori (MAP) probability density estimates of the model. Many inverse problems are numerically unstable. Various regularization methods are used to alleviate numerical instability. Classical least-squares inversion, singular value decomposition, and recent developments of blind deconvolution are reviewed. [Work supported by ONR.]