A Multi-Grid Iterative Method for Photoacoustic Tomography

Inspired by the recent advances on minimizing nonsmooth or bound-constrained convex functions on models using varying degrees of fidelity, we propose a line search multigrid (MG) method for full-wave iterative image reconstruction in photoacoustic tomography (PAT) in heterogeneous media. To compute the search direction at each iteration, we decide between the gradient at the target level, or alternatively an approximate error correction at a coarser level, relying on some predefined criteria. To incorporate absorption and dispersion, we derive the analytical adjoint directly from the first-order acoustic wave system. The effectiveness of the proposed method is tested on a total-variation penalized Iterative Shrinkage Thresholding algorithm (ISTA) and its accelerated variant (FISTA), which have been used in many studies of image reconstruction in PAT. The results show the great potential of the proposed method in improving speed of iterative image reconstruction

A finite element analysis of crack propagation problems with applications to seismology

Imperial Users onl

Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast

Ultrasound Tomography has seen a revival of interest in the past decade, especially for breast imaging, due to improvements in both ultrasound and computing hardware. In particular, three-dimensional ultrasound tomography, a fully tomographic method in which the medium to be imaged is surrounded by ultrasound transducers, has become feasible. In this paper, a comprehensive derivation and study of a robust framework for large-scale bent-ray ultrasound tomography in 3D for a hemispherical detector array is presented. Two ray-tracing approaches are derived and compared. More significantly, the problem of linking the rays between emitters and receivers, which is challenging in 3D due to the high number of degrees of freedom for the trajectory of rays, is analysed both as a minimisation and as a root-finding problem. The ray-linking problem is parameterised for a convex detection surface and three robust, accurate, and efficient ray-linking algorithms are formulated and demonstrated. To stabilise these methods, novel adaptive-smoothing approaches are proposed that control the conditioning of the update matrices to ensure accurate linking. The nonlinear UST problem of estimating the sound speed was recast as a series of linearised subproblems, each solved using the above algorithms and within a steepest descent scheme. The whole imaging algorithm was demonstrated to be robust and accurate on realistic data simulated using a full-wave acoustic model and an anatomical breast phantom, and incorporating the errors due to time-of-flight picking that would be present with measured data. This method can used to provide a low-artefact, quantitatively accurate, 3D sound speed maps. In addition to being useful in their own right, such 3D sound speed maps can be used to initialise full-wave inversion methods, or as an input to photoacoustic tomography reconstructions

State-dependent Kalman filters for robust engine control

Vehicle emissions variations impose significant challenges to the automotive industry. In these simulation studies, nonlinear estimation techniques based on state-dependent and extended Kalman filtering are developed for spark ignition engines to enhance robustness of the feedforward fuel controllers to changes in nominal system parameters and measurement errors. A model-based approach is used to derive the optimal filters. Numerical simulations indicate the superiority of estimation-based approaches to enhance robustness of in-cylinder air estimation which directly contributes to the precision of engine exhaust air-fuel ratio and, consequently the consistency of the tailpipe emissions. The results obtained are for an aggressive driving profile and are presented and discusse

Hessian-inversion-free ray-born inversion for quantitative ultrasound tomography

This study proposes a Hessian-inversion-free ray-born inversion approach for biomedical ultrasound tomography. The proposed approach is a more efficient version of the ray-born inversion approach proposed in [1]. Using these approaches, the propagation of acoustic waves are modelled using a ray approximation to heterogeneous Green's function. The inverse problem is solved in the frequency domain by iteratively linearisation and minimisation of the objective function from low to high frequencies. In [1], the linear subproblem associated with each frequency interval is solved by an implicit and iterative inversion of the Hessian matrix (inner iterations). Instead, this study applies a preconditioning approach on each linear subproblem so that the Hessian matrix becomes diagonalised, and can thus be inverted in a single step. Using the proposed preconditioning approach, the computational cost of solving each linear subproblem of the proposed ray-Born inversion approach becomes almost the same as solving one linear subproblem associated with a radon-type time-of-flight-based approach using bent rays. More importantly, the smoothness assumptions made for diagonalising the Hessian matrix make the image reconstruction more stable than the inversion approach in [1] to noise

On inclusion of source in the system of first-order linear acoustic wave equations

Simulating propagation of acoustic waves via solving a system of three-coupled first-order linear differential equations using a k-space pseudo-spectral method is popular for biomedical applications, firstly because of availability of an open-source toolbox for implementation of this numerical approach, and secondly because of its efficiency. The k-space pseudo-spectral method is efficient, because it allows coarser computational grids and larger time steps than finite difference and finite element methods for the same accuracy. The goal of this study is to compare this numerical wave solver with an analytical solution to the wave equation using the Green's function for computing propagation of acoustic waves in homogeneous media. This comparison is done in the frequency domain. Using the k-Wave solver, a match to the Green's function is obtained after modifying the approach taken for including mass source in the linearised equation of continuity (conservation of mass) in the associated system of wave equations.Comment: List of changes: 1) In version 1, there was a mistake in displaying figures 3(d), 3(e), 3(f), 6(d), 6(e) and 6(f). Those figures are corrected. 2) The word "acoustic" was added to the titl