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Simon Arridge: Nonlinear Inverse Problems with Learning

Time: Thu 2024-06-13 13.30 - 14.30

Location: Digital Futures Hub, Osquars Backe 5, floor 2

Participating: Simon Arridge (University College London)

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Several problems in imaging are based on recovering coefficients of a PDE, resulting in a non-linear inverse problem that is typically solved by an iterative algorithm with the gradient obtained by an adjoint state method. When the forward problem is time-varying this corresponds to the method of time-reversal which convolves a forward and time-reversed field with the derivative of the spatial operator (sometimes called the “imaging condition”). Applications include full-waveform imaging (FWI) in Ultrasound Computed Tomography, PhotoAcoustic Tomography (PAT) and time-resolved Diffuse Optical Tomography (tDOT). Within Learned Physics approaches time reversal corresponds to the Neural ODE method for learning the time-derivative of an ODE parameterised by a neural network. By combining the trained network with symbolic regression an interpretable model can be discovered. In this talk I will discuss application of these methods for solving some forward and inverse problems in imaging.