Model based learning for accelerated, limited-view 3D photoacoustic tomography

Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed-up. In this work we present a deep neural network that is specifically designed to provide high resolution 3D images from restricted photoacoustic measurements. The network is designed to represent an iterative scheme and incorporates gradient information of the data fit to compensate for limited view artefacts. Due to the high complexity of the photoacoustic forward operator, we separate training and computation of the gradient information. A suitable prior for the desired image structures is learned as part of the training. The resulting network is trained and tested on a set of segmented vessels from lung CT scans and then applied to in-vivo photoacoustic measurement data

An introduction to structural optimization problems

The object of the research described in this thesis is to examine the possibilities of developing analytical and computational procedures for a class of structural optimization problems in the presence of behaviour and side constraints. These are essentially optimal control problems based on the maximum principle of Pontryagin and dynamic programming formalism of Bellman. They are characterised by inequality constraints on the state and control variables giving rise to systems of highly complex differential equations which present formidable difficulties both in the construction of the appropriate boundary conditions and subsequent development of solution procedures for these boundary value problems. Therefore an alternative approach is used whereby the problem is discretised leading to a non-linear programming approximation. The associated non-linear programs are characterised by non-analytic "black box" type representations for the behaviour constraints. The solutions are based on a "steepest descent–alternate step" mode of travel in design space. [Continues.

A Variational Level Set Approach for Surface Area Minimization of Triply Periodic Surfaces

In this paper, we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a theoretical characterization of and a numerical algorithm for computing these surfaces. We use our theoretical and computational formulation to study the optimality of the Schwartz P, Schwartz D, and Schoen G surfaces when the volume fractions of the two phases are equal and explore the properties of optimal structures when the volume fractions of the two phases not equal. Due to the computational cost of the fully, three-dimensional shape optimization problem, we implement our numerical simulations using a parallel level set method software package.Comment: 28 pages, 16 figures, 3 table