Expansion of the nodal-adjoint method for simple and efficient computation of the 2d tomographic imaging jacobian matrix

This paper focuses on the construction of the Jacobian matrix required in tomographic reconstruction algorithms. In microwave tomography, computing the forward solutions during the iterative reconstruction process impacts the accuracy and computational efficiency. Towards this end, we have applied the discrete dipole approximation for the forward solutions with significant time savings. However, while we have discovered that the imaging problem configuration can dramatically impact the computation time required for the forward solver, it can be equally beneficial in constructing the Jacobian matrix calculated in iterative image reconstruction algorithms. Key to this implementation, we propose to use the same simulation grid for both the forward and imaging domain discretizations for the discrete dipole approximation solutions and report in detail the theoretical aspects for this localization. In this way, the computational cost of the nodal adjoint method decreases by several orders of magnitude. Our investigations show that this expansion is a significant enhancement compared to previous implementations and results in a rapid calculation of the Jacobian matrix with a high level of accuracy. The discrete dipole approximation and the newly efficient Jacobian matrices are effectively implemented to produce quantitative images of the simplified breast phantom from the microwave imaging system

Frequency domain high density diffuse optical tomography for functional brain imaging

Measurements of dynamic near-infrared (NIR) light attenuation across the human head together with model-based image reconstruction algorithms allow the recovery of three-dimensional spatial brain activation maps. Previous studies using high-density diffuse optical tomography (HD-DOT) systems have reported improved image quality over sparse arrays. Modulated NIR light, known as Frequency Domain (FD) NIR, enables measurements of phase shift along with amplitude attenuation. It is hypothesised that the utilization of these two sets of complementary data (phase and amplitude) for brain activity detection will result in an improvement in reconstructed image quality within HD-DOT. However, parameter recovery in DOT is a computationally expensive algorithm, especially when FD-HD measurements are required over a large and complex volume, as in the case of brain functional imaging. Therefore, computational tools for the light propagation modelling, known as the forward model, and the parameter recovery, known as the inverse problem, have been developed, in order to enable FD-HD-DOT. The forward model, within a diffusion approximation-based finite-element modelling framework, is accelerated by employing parallelization. A 10-fold speed increase when GPU architectures are available is achieved while maintaining high accuracy. For a very high-resolution finite-element model of the adult human head with ∼600,000 nodes, light propagation can be calculated at ∼0.25s per excitation source. Additionally, a framework for the sparse formulation of the inverse model, incorporating parallel computing, is proposed, achieving a 10-fold speed increase and a 100-fold memory efficiency, whilst maintaining reconstruction quality. Finally, to evaluate image reconstruction with and without the additional phase information, point spread functions have been simulated across a whole-scalp field of view in 24 subject-specific anatomical models using an experimentally derived noise model. The addition of phase information has shown to improve the image quality by reducing localization error by up to 59%, effective resolution by up to 21%, and depth penetration up to 5mm, as compared to using the intensity attenuation measurements alone. In addition, experimental data collected during a retinotopic experiment reveal that the phase data contains unique information about brain activity and enables images to be resolved for deeper brain regions

Solution of the inverse scattering problem by T-matrix completion. II. Simulations

This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory and here we present simulations for inverse scattering of scalar waves. The underlying mathematical model is the scalar wave equation and the object function that is reconstructed is the medium susceptibility. The simulations are relevant to ultrasound tomographic imaging and seismic tomography. It is shown that DCTMC is a viable method for solving strongly nonlinear inverse problems with large data sets. It provides not only the overall shape of the object but the quantitative contrast, which can correspond, for instance, to the variable speed of sound in the imaged medium.Comment: This is Part II of a paper series. Part I contains theory and is available at arXiv:1401.3319 [math-ph]. Accepted in this form to Phys. Rev.

Computational Methods and Graphical Processing Units for Real-time Control of Tomographic Adaptive Optics on Extremely Large Telescopes.

Ground based optical telescopes suffer from limited imaging resolution as a result of the effects of atmospheric turbulence on the incoming light. Adaptive optics technology has so far been very successful in correcting these effects, providing nearly diffraction limited images. Extremely Large Telescopes will require more complex Adaptive Optics configurations that introduce the need for new mathematical models and optimal solvers. In addition, the amount of data to be processed in real time is also greatly increased, making the use of conventional computational methods and hardware inefficient, which motivates the study of advanced computational algorithms, and implementations on parallel processors. Graphical Processing Units (GPUs) are massively parallel processors that have so far demonstrated a very high increase in speed compared to CPUs and other devices, and they have a high potential to meet the real-time restrictions of adaptive optics systems. This thesis focuses on the study and evaluation of existing proposed computational algorithms with respect to computational performance, and their implementation on GPUs. Two basic methods, one direct and one iterative are implemented and tested and the results presented provide an evaluation of the basic concept upon which other algorithms are based, and demonstrate the benefits of using GPUs for adaptive optics

Quasi-Newton inversion of seismic first arrivals using source finite bandwidth assumption: Application to subsurface characterization of landslides

International audienceCharacterizing the internal structure of landslides is of first importance to assess the hazard. Many geophysical techniques have been used in the recent years to image these structures, and among them is seismic tomography. The objective of this work is to present a high resolution seismic inversion algorithm of first arrival times that minimizes the use of subjective regularization operators. A Quasi-Newton P-wave tomography inversion algorithm has been developed. It is based on a finite frequency assumption for highly heterogeneous media which considers an objective inversion regularization (based on the wave propagation principle) and uses the entire source frequency spectrum to improve the tomography resolution. The Fresnel wavepaths calculated for different source frequencies are used to retropropagate the traveltime residuals, assuming that in highly heterogeneous media, the first arrivals are only affected by velocity anomalies present in the first Fresnel zone. The performance of the algorithm is first evaluated on a synthetic dataset, and further applied on a real dataset acquired at the Super-Sauze landslide which is characterized by a complex bedrock geometry, a layering of different materials and important changes in soil porosity (e.g. surface fissures). The seismic P-wave velocity and the wave attenuation are calculated, and the two tomographies are compared to previous studies on the site

Incorporating Fresnel-Propagation into Electron Holographic Tomography: A possible way towards three-dimensional atomic resolution

Tomographic electron holography combines tomography, the reconstruction of three-dimensionally resolved data from multiple measurements with different specimen orientations, with electron holography, an interferometrical method for measuring the complex wave function inside a transmission electron microscope (TEM). Due to multiple scattering and free wave propagation conventional, ray projection based, tomography does perform badly when approaching atomic resolution. This is remedied by incorporating propagation effects into the projection while maintaining linearity in the object potential. Using the Rytov approach an approximation is derived, where the logarithm of the complex wave is linear in the potential. The ray projection becomes a convolution with a Fresnel propagation kernel, which is considerably more computationally expensive. A framework for such calculations has been implemented in Python. So has a multislice electron scattering algorithm, optimised for large fields of view and high numbers of atoms for simulations of scattering at nanoparticles. The Rytov approximation gives a remarkable increase in resolution and signal quality over the conventional approach in the tested system of a tungsten disulfide nanotube. The response to noise seems to be similar as in conventional tomography, so rather benign. This comes at the downside of much longer calculation time per iteration.Tomographische Elektronenholographie kombiniert Tomographie, die Rekonstruktion dreidimensional aufgelößter Daten aus einem Satz von mehreren Messungen bei verschiedenen Objektorientierungen, mit Elektronenholographie, eine interferrometrische Messung der komplexen Elektronenwelle im Transmissionselektronenmikroskop (TEM). Wegen Mehrfachstreuung und Propagationseffekten erzeugt konventionelle, auf einer Strahlprojektion basierende, Tomography ernste Probleme bei Hochauflösung hin zu atomarer Auflösung. Diese sollen durch ein Modell, welches Fresnel-Propagation beinhaltet, aber weiterhin linear im Potential des Objektes ist, vermindert werden. Mit dem Rytov-Ansatz wird eine Näherung abgeleitet, wobei der Logarithmus der komplexen Welle linear im Potential ist. Die Strahlen-Projektion ist dann eine Faltung mit dem Fresnel-Propagations-Faltungskernel welche rechentechnisch wesentlich aufwendiger ist. Ein Programm-Paket für solche Rechnungen wurde in Python implementiert. Weiterhin wurde ein Multislice Algorithmus für große Gesichtsfelder und Objekte mit vielen Atomen wie Nanopartikel optimiert. Die Rytov-Näherung verbessert sowohl die Auflösung als auch die Signalqualität immens gegenüber konventioneller Tomographie, zumindest in dem getesteten System eines Wolframdisulfid-Nanoröhrchens. Das Rauschverhalten scheint ähnlich der konventionallen Tomographie zu sein, also eher gutmütig. Im Gegenzug braucht die Tomographie basierend auf der Rytov-Näherung wesentlich mehr Rechenzeit pro Iteration

Time-resolved laser speckle contrast imaging (TR-LSCI) of cerebral blood flow

To address many of the deficiencies in optical neuroimaging technologies such as poor spatial resolution, time-consuming reconstruction, low penetration depth, and contact-based measurement, a novel, noncontact, time-resolved laser speckle contrast imaging (TR-LSCI) technique has been developed for continuous, fast, and high-resolution 2D mapping of cerebral blood flow (CBF) at different depths of the head. TR-LSCI illuminates the head with picosecond-pulsed, coherent, widefield near-infrared light and synchronizes a newly developed, high-resolution, gated single-photon avalanche diode camera (SwissSPAD2) to capture CBF maps at different depths. By selectively collecting diffuse photons with longer pathlengths through the head, TR-LSCI reduces partial volume artifacts from the overlying tissues, thus improving the accuracy of CBF measurement in the deep brain. CBF map reconstruction was dramatically expedited by incorporating highly parallelized computation. The performance of TR-LSCI was evaluated using head-simulating phantoms with known properties and in-vivo rodents with varied hemodynamic challenges to the brain. Results from these pilot studies demonstrated that TR-LSCI enabled mapping CBF variations at different depths with a sampling rate of up to 1 Hz and spatial resolutions ranging from tens of micrometers on the head surface to 1-2 millimeters in the deep brain. With additional improvements and validation in larger populations against established methods, we anticipate offering a noncontact, fast, high-resolution, portable, and affordable brain imager for fundamental neuroscience research in animals and for translational studies in humans.Comment: 22 pages, 7 figures, 4 table

Microwave Sensing and Imaging

In recent years, microwave sensing and imaging have acquired an ever-growing importance in several applicative fields, such as non-destructive evaluations in industry and civil engineering, subsurface prospection, security, and biomedical imaging. Indeed, microwave techniques allow, in principle, for information to be obtained directly regarding the physical parameters of the inspected targets (dielectric properties, shape, etc.) by using safe electromagnetic radiations and cost-effective systems. Consequently, a great deal of research activity has recently been devoted to the development of efficient/reliable measurement systems, which are effective data processing algorithms that can be used to solve the underlying electromagnetic inverse scattering problem, and efficient forward solvers to model electromagnetic interactions. Within this framework, this Special Issue aims to provide some insights into recent microwave sensing and imaging systems and techniques