28 research outputs found
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
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
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
A continuous adjoint for photo-acoustic tomography of the brain
We present an optimization framework for photo-acoustic tomography of brain
based on a system of coupled equations that describe the propagation of sound
waves in linear isotropic inhomogeneous and lossy elastic media with the
absorption and physical dispersion following a frequency power law using
fractional Laplacian operators. The adjoint of the associated continuous
forward operator is derived, and a numerical framework for computing this
adjoint based on a k- space pseudospectral method is presented. We analytically
show that the derived continuous adjoint matches the adjoint of an associated
discretised operator. We include this adjoint in a first-order positivity
constrained optimization algorithm that is regularized by total variation
minimization, and show that the iterates monotonically converge to a minimizer
of an objective function, even in the presence of some error in estimating the
physical parameters of the medium.Comment: 28 pages, 24 figure (eps
Ray-based inversion accounting for scattering for biomedical ultrasound computed tomography
An efficient and accurate image reconstruction algorithm for ultrasound
tomography (UST) is described and demonstrated, which can recover accurate
sound speed distribution from acoustic time series measurements made in soft
tissue. The approach is based on a second-order iterative minimisation of the
difference between the measurements and a model based on a ray-approximation to
the heterogeneous Green's function. It overcomes the computational burden of
full-wave solvers while avoiding the drawbacks of time-of-flight methods.
Through the use of a second-order iterative minimisation scheme, applied
stepwise from low to high frequencies, the effects of scattering are
incorporated into the inversion
Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast
Ultrasound tomography (UST) 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 UST, a fully tomographic method in which the medium to be imaged is surrounded by ultrasound transducers, has become feasible. This has led to renewed attention on UST image reconstruction algorithms. In this paper, a comprehensive derivation and study of a robust framework for large-scale bent-ray UST in 3D for a hemispherical detector array is presented. Two ray
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Automated four-dimensional long term imaging enables single cell tracking within organotypic brain slices to study neurodevelopment and degeneration.
Current approaches for dynamic profiling of single cells rely on dissociated cultures, which lack important biological features existing in tissues. Organotypic slice cultures preserve aspects of structural and synaptic organisation within the brain and are amenable to microscopy, but established techniques are not well adapted for high throughput or longitudinal single cell analysis. Here we developed a custom-built, automated confocal imaging platform, with improved organotypic slice culture and maintenance. The approach enables fully automated image acquisition and four-dimensional tracking of morphological changes within individual cells in organotypic cultures from rodent and human primary tissues for at least 3 weeks. To validate this system, we analysed neurons expressing a disease-associated version of huntingtin (HTT586Q138-EGFP), and observed that they displayed hallmarks of Huntington's disease and died sooner than controls. By facilitating longitudinal single-cell analyses of neuronal physiology, our system bridges scales necessary to attain statistical power to detect developmental and disease phenotypes
DIRECT QUANTITATIVE PHOTOACOUSTIC TOMOGRAPHY FOR REALISTIC ACOUSTIC MEDIA
Quantitative photo-acoustic tomography (QPAT) seeks to reconstruct a
distribution of optical attenuation coefficients inside a sample from a set of
time series of pressure data that is measured outside the sample. The associated
inverse problems involve two steps, namely acoustic and optical, which can
be solved separately or as a direct composite problem. We adopt the latter
approach for realistic acoustic media that possess heterogeneous and often not
accurately known distributions for sound speed and ambient density, as well
as an attenuation following a frequency power law that is evident in tissue
media. We use a diffusion approximation (DA) model for the optical portion
of the problem. We solve the corresponding composite inverse problem using
three total variation (TV) regularised optimisation approaches. Accordingly,
we develop two Krylov-subspace inexact-Newton algorithms that utilise the
Jacobian matrix in a matrix-free manner in order to handle the computational
cost. Additionally, we use a gradient-based algorithm that computes a search
direction using the L-BFGS method, and applies a TV regularisation based
on the alternating direction method of multipliers (ADMM) as a benchmark,
because this method is popular for QPAT and direct QPAT. The results indicate
the superiority of the developed inexact Newton algorithms over gradientbased quasi-Newton approaches for a comparable computational complexity