CIF: Small: Computationally Efficient Analytic Reconstructions via Embeddings and Sparsity for Non-Linear Dynamic Imaging Problems

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With the development of low cost, high endurance uninhabited vehicles, it is now possible to acquire imaging data persistently over long periods of time and space using multiple distributed sensors. Such persistent multi-pass sensing systems have several advantages over single-pass systems including the ability to monitor a dynamic medium, wider spatial coverage, increased resolution and the ability to acquire three or higher dimensional information. While such persistent systems have the potential to revolutionize sensing and imaging across many domains of applications, one of the fundamental bottlenecks for the deployment of these systems is the challenges in image formation: First, the reconstructions of 3D deformations, velocity fields and imaging in unknown complex environments are highly non-linear large scale inverse problems. Secondly, such systems can acquire hundreds of terabytes of data daily and forming a standard image using even a single-pass data cannot currently be done in real-time.This project develops a unified mathematical framework and new classes of novel, computationally efficient analytic image reconstruction methods to address these large scale, computationally demanding, non-linear inverse problems. Central to our development is the synergistic combination of inverse scattering theory, sparse signal recovery methods and microlocal analysis. Our research involves the following topics: (i) Development of accurate forward models for 3D deformation-rate imaging, velocity imaging and imaging in unknown heterogenous environments using multiple sensors. (ii) Reformulation of the resulting nonlinear problems as linear problems by embedding them into larger dimensional spaces coupled with sparsity constraints. (iii) Design of analytic, computationally efficient methods for inversion by synergistically combining ideas from microlocal analysis and sparse signal recovery methods.