123 research outputs found
Designing a high-performance boundary element library with OpenCL and Numba
The Bempp boundary element library is a well known library for the simulation of a range of electrostatic, acoustic and electromagnetic problems in homogeneous bounded and unbounded domains. It originally started as a traditional C++ library with a Python interface. Over the last two years we have completely redesigned Bempp as a native Python library, called Bempp-cl, that provides computational backends for OpenCL (using PyOpenCL) and Numba. The OpenCL backend implements kernels for GPUs and CPUs with SIMD optimization. In this paper, we discuss the design of Bempp-cl, provide performance comparisons on different compute devices, and discuss the advantages and disadvantages of OpenCL as compared to Numba
On Learning the Invisible in Photoacoustic Tomography with Flat Directionally Sensitive Detector
In photoacoustic tomography (PAT) with flat sensor, we routinely encounter
two types of limited data. The first is due to using a finite sensor and is
especially perceptible if the region of interest is large relatively to the
sensor or located farther away from the sensor. In this paper, we focus on the
second type caused by a varying sensitivity of the sensor to the incoming
wavefront direction which can be modelled as binary i.e. by a cone of
sensitivity. Such visibility conditions result, in Fourier domain, in a
restriction of both the image and the data to a bowtie, akin to the one
corresponding to the range of the forward operator. The visible ranges, in
image and data domains, are related by the wavefront direction mapping. We
adapt the wedge restricted Curvelet decomposition, we previously proposed for
the representation of the full PAT data, to separate the visible and invisible
wavefronts in the image. We optimally combine fast approximate operators with
tailored deep neural network architectures into efficient learned
reconstruction methods which perform reconstruction of the visible coefficients
and the invisible coefficients are learned from a training set of similar data.Comment: Submitted to SIAM Journal on Imaging Science
Product algebras for Galerkin discretisations of boundary integral operators and their applications
Operator products occur naturally in a range of regularized boundary integral equation formulations. However, while a Galerkin discretisation only depends on the domain space and the test (or dual) space of the operator, products require a notion of the range. In the boundary element software package Bempp we have implemented a complete operator algebra that depends on knowledge of the domain, range and test space. The aim was to develop a way of working with Galerkin operators in boundary element software that is as close to working with the strong form on paper as possible while hiding the complexities of Galerkin discretisations. In this paper, we demonstrate the implementation of this operator algebra and show, using various Laplace and Helmholtz example problems, how it significantly simplifies the definition and solution of a wide range of typical boundary integral equation problems
On the Adjoint Operator in Photoacoustic Tomography
Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from
coupled physics" technique, in which the image contrast is due to optical
absorption, but the information is carried to the surface of the tissue as
ultrasound pulses. Many algorithms and formulae for PAT image reconstruction
have been proposed for the case when a complete data set is available. In many
practical imaging scenarios, however, it is not possible to obtain the full
data, or the data may be sub-sampled for faster data acquisition. In such
cases, image reconstruction algorithms that can incorporate prior knowledge to
ameliorate the loss of data are required. Hence, recently there has been an
increased interest in using variational image reconstruction. A crucial
ingredient for the application of these techniques is the adjoint of the PAT
forward operator, which is described in this article from physical, theoretical
and numerical perspectives. First, a simple mathematical derivation of the
adjoint of the PAT forward operator in the continuous framework is presented.
Then, an efficient numerical implementation of the adjoint using a k-space time
domain wave propagation model is described and illustrated in the context of
variational PAT image reconstruction, on both 2D and 3D examples including
inhomogeneous sound speed. The principal advantage of this analytical adjoint
over an algebraic adjoint (obtained by taking the direct adjoint of the
particular numerical forward scheme used) is that it can be implemented using
currently available fast wave propagation solvers.Comment: submitted to "Inverse Problems
Product algebras for Galerkin discretisations of boundary integral operators and their applications
Operator products occur naturally in a range of regularised boundary integral equation formulations. However, while a Galerkin discretisation only depends on the domain space and the test (or dual) space of the operator, products require a notion of the range. In the boundary element software package Bempp, we have implemented a complete operator algebra that depends on knowledge of the domain, range, and test space. The aim was to develop a way of working with Galerkin operators in boundary element software that is as close to working with the strong form on paper as possible, while hiding the complexities of Galerkin discretisations. In this article, we demonstrate the implementation of this operator algebra and show, using various Laplace and Helmholtz example problems, how it significantly simplifies the definition and solution of a wide range of typical boundary integral equation problems
Learned Interferometric Imaging for the SPIDER Instrument
The Segmented Planar Imaging Detector for Electro-Optical Reconnaissance
(SPIDER) is an optical interferometric imaging device that aims to offer an
alternative to the large space telescope designs of today with reduced size,
weight and power consumption. This is achieved through interferometric imaging.
State-of-the-art methods for reconstructing images from interferometric
measurements adopt proximal optimization techniques, which are computationally
expensive and require handcrafted priors. In this work we present two
data-driven approaches for reconstructing images from measurements made by the
SPIDER instrument. These approaches use deep learning to learn prior
information from training data, increasing the reconstruction quality, and
significantly reducing the computation time required to recover images by
orders of magnitude. Reconstruction time is reduced to
milliseconds, opening up the possibility of real-time imaging with SPIDER for
the first time. Furthermore, we show that these methods can also be applied in
domains where training data is scarce, such as astronomical imaging, by
leveraging transfer learning from domains where plenty of training data are
available.Comment: 21 pages, 14 figure
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