Browsing by Subject "Artificial neural network"

Spectral CT using a photon counting x-ray detector (PCXD) shows great potential for measuring material composition based on energy dependent x-ray attenuation. Spectral CT is especially suited for imaging with K-edge contrast agents to address the otherwise limited contrast in soft tissues. We have developed a micro-CT system based on a PCXD. This system enables full spectrum CT in which the energy thresholds of the PCXD are swept to sample the full energy spectrum for each detector element and projection angle. Measurements provided by the PCXD, however, are distorted due to undesirable physical eects in the detector and are very noisy due to photon starvation. In this work, we proposed two methods based on machine learning to address the spectral distortion issue and to improve the material decomposition. This rst approach is to model distortions using an articial neural network (ANN) and compensate for the distortion in a statistical reconstruction. The second approach is to directly correct for the distortion in the projections. Both technique can be done as a calibration process where the neural network can be trained using 3D printed phantoms data to learn the distortion model or the correction model of the spectral distortion. This replaces the need for synchrotron measurements required in conventional technique to derive the distortion model parametrically which could be costly and time consuming. The results demonstrate experimental feasibility and potential advantages of ANN-based distortion modeling and correction for more accurate K-edge imaging with a PCXD. Given the computational eciency with which the ANN can be applied to projection data, the proposed scheme can be readily integrated into existing CT reconstruction pipelines.

Artificial neural networks fundamentally shift the paradigm of computational imaging. Powerful neural processing is not only taking place of the conventional algorithms, but also embracing radical and physically plausible forward models that better sample the high dimensional light field. Physical designs of sampling in turn tailor simulation and neural algorithms for optimal inverse estimation. Sampling, simulation and neural algorithms as three essential components compose a novel imaging paradigm -- artificial neural imaging, in which they interact and improve themselves in an upward spiral.

Here we present three concrete examples of artificial neural imaging and the important roles physical designs play. In all-in-focus imaging, we see autofocus, sampling and fusion algorithms are redefined for optimizing the image quality of a camera with limited depth of field. Image-based neural autofocus acts 5-10x faster than traditional algorithms. The focus control based on the rule or reinforcement learning dynamically estimates the environment and optimizes the focus trajectory. Along with the neural fusion algorithm, the pipeline outperforms traditional focal stacking approaches in static and dynamic scenes. In scatter ptychography, we show imaging the secondary scatters reflected by a remote target under coherent illumination can create a synthetic aperture on the scatterer. The reconstruction of the object through phase retrieval algorithms can drastically exceed the resolution of directly viewing the target. In the lab experiment we demonstrate 32x resolution improvement relative to direct imaging using error-reduction and plug-and-play algorithms. In array camera imaging, we demonstrate heterogeneous multiaperture designs that have better sampling structures and physics-aware transformers for feature-based data fusion. The proposed transformer incorporates the physical information of the camera array as its receptive fields, demonstrating the superior ability of image compositing on array cameras with diverse resolutions, focal lengths, focal planes, color spaces, and exposures. We also demonstrate a scalable pipeline of data synthesis through computer graphics software that empowers the transformers.

The examples above justify artificial neural imaging and the physical designs interweaved. We expect better designs in sampling, simulation, neural algorithms and eventually better estimation of the light field.

This thesis presents a method for solving partial differential equations (PDEs) using articial neural networks. The method uses a constrained backpropagation (CPROP) approach for preserving prior knowledge during incremental training for solving nonlinear elliptic and parabolic PDEs adaptively, in non-stationary environments. Compared to previous methods that use penalty functions or Lagrange multipliers,

CPROP reduces the dimensionality of the optimization problem by using direct elimination, while satisfying the equality constraints associated with the boundary and initial conditions exactly, at every iteration of the algorithm. The effectiveness of this method is demonstrated through several examples, including nonlinear elliptic

and parabolic PDEs with changing parameters and non-homogeneous terms. The computational complexity analysis shows that CPROP compares favorably to existing methods of solution, and that it leads to considerable computational savings when subject to non-stationary environments.

The CPROP based approach is extended to a constrained integration (CINT) method for solving initial boundary value partial differential equations (PDEs). The CINT method combines classical Galerkin methods with CPROP in order to constrain the ANN to approximately satisfy the boundary condition at each stage of integration. The advantage of the CINT method is that it is readily applicable to PDEs in irregular domains and requires no special modification for domains with complex geometries. Furthermore, the CINT method provides a semi-analytical solution that is infinitely differentiable. The CINT method is demonstrated on two hyperbolic and one parabolic initial boundary value problems (IBVPs). These IBVPs are widely used and have known analytical solutions. When compared with Matlab's nite element (FE) method, the CINT method is shown to achieve significant improvements both in terms of computational time and accuracy. The CINT method is applied to a distributed optimal control (DOC) problem of computing optimal state and control trajectories for a multiscale dynamical system comprised of many interacting dynamical systems, or agents. A generalized reduced gradient (GRG) approach is presented in which the agent dynamics are described by a small system of stochastic dierential equations (SDEs). A set of optimality conditions is derived using calculus of variations, and used to compute the optimal macroscopic state and microscopic control laws. An indirect GRG approach is used to solve the optimality conditions numerically for large systems of agents. By assuming a parametric control law obtained from the superposition of linear basis functions, the agent control laws can be determined via set-point regulation, such

that the macroscopic behavior of the agents is optimized over time, based on multiple, interactive navigation objectives.

Lastly, the CINT method is used to identify optimal root profiles in water limited ecosystems. Knowledge of root depths and distributions is vital in order to accurately model and predict hydrological ecosystem dynamics. Therefore, there is interest in accurately predicting distributions for various vegetation types, soils, and climates. Numerical experiments were were performed that identify root profiles that maximize transpiration over a 10 year period across a transect of the Kalahari. Storm types were varied to show the dependence of the optimal profile on storm frequency and intensity. It is shown that more deeply distributed roots are optimal for regions where

storms are more intense and less frequent, and shallower roots are advantageous in regions where storms are less intense and more frequent.