<pre>Coherent lidar uses a chirped laser pulse for 3D imaging of distant targets.However, existing coherent lidar image reconstruction methods do not account for the system's aperture, resulting in sub-optimal resolution.Moreover, these methods use majorization-minimization for computational efficiency, but do so without a theoretical treatment of convergence.<br> <br>In this work, we present Coherent Lidar Aperture Modeled Plug-and-Play (CLAMP) for multi-look coherent lidar image reconstruction.CLAMP uses multi-agent consensus equilibrium (a form of PnP) to combine a neural network denoiser with an accurate physics-based forward model.CLAMP introduces an FFT-based method to account for the effects of the aperture and uses majorization of the forward model for computational efficiency.We also formalize the use of majorization-minimization in consensus optimization problems and prove convergence to the exact consensus equilibrium solution.Finally, we apply CLAMP to synthetic and measured data to demonstrate its effectiveness in producing high-resolution, speckle-free, 3D imagery.</pre><p></p>

Our knowledge of elastic wave propagation in general heterogeneous media with complex geological structures comes principally from numerical simulations. In this dissertation, I demonstrate through rigorous theoretical analyses and comprehensive numerical experiments that the Fourier method is a suitable method of choice for large scale 3D seismic modeling and imaging problems, due to its high accuracy and computational efficiency. The most attractive feature of the Fourier method is its ability to produce highly accurate solutions on relatively coarser grids, compared with other numerical methods for solving wave equations. To further advance the Fourier method, I identify two aspects of the method to focus on in this work, i.e., its implementation on modern clusters of computers and efficient high-order time stepping schemes. I propose two new parallel algorithms to improve the efficiency of the Fourier method on distributed memory systems using MPI. The first algorithm employs non-blocking all-to-all communications to optimize the conventional parallel Fourier modeling workflows by overlapping communication with computation. With a carefully designed communication-computation overlapping mechanism, a large amount of communication overhead can be concealed when implementing different kinds of wave equations. The second algorithm combines the advantages of both the Fourier method and the finite difference method by using convolutional high-order finite difference operators to evaluate the spatial derivatives in the decomposed direction. The high-order convolutional finite difference method guarantees a satisfactory accuracy and provides the flexibility of using non-blocking point-to-point communications for efficient interprocessor data exchange and the possibility of overlapping communication and computation. As a result, this hybrid method achieves an optimized balance between numerical accuracy and computational efficiency. To improve the overall accuracy of time domain Fourier simulations, I propose a family of new high-order time stepping schemes, based on a novel algorithm for designing time integration operators, to reduce temporal derivative discretization errors in a cost-effective fashion. I explore the pseudo-analytical method and propose high-order formulations to further improve its accuracy and ability to deal with spatial heterogeneities. I also extend the pseudo-analytical method to solve the variable-density acoustic and elastic wave equations. I thoroughly examine the finite difference method by conducting complete numerical dispersion and stability analyses. I comprehensively compare the finite difference method with the Fourier method and provide a series of detailed benchmarking tests of these two methods under a number of different simulation configurations. The Fourier method outperforms the finite difference method, in terms of both accuracy and efficiency, for both the theoretical studies and the numerical experiments, which provides solid evidence that the Fourier method is a superior scheme for large scale seismic modeling and imaging problems. / text

<p dir="ltr">There is a growing need to reconstruct high quality tomographic images from sparse view measurements to accommodate time and space constraints as well as patient well-being in medical CT. Analytical methods perform poorly with sub-Nyquist acquisition rates. In extreme cases with 4 or fewer views, effective reconstruction approaches must be able to incorporate side information to constrain the solution space of an otherwise under-determined problem. This thesis presents two sparse view tomography problems that are solved using techniques that exploit. knowledge of the structural and physical properties of the scanned objects.</p><p dir="ltr"><br></p><p dir="ltr">First, we reconstruct four view CT datasets obtained from an in-situ imaging system used to observe Kolsky bar impact experiments. Test subjects are typically 3D-printed out ofhomogeneous materials into shapes with circular cross sections. Two advanced prior modelsare formulated to incorporate these assumptions in a modular fashion into the iterativeradiographic inversion framework. The first is a Multi-Slice Fusion and the latter is TotalVariation regularization that operates in cylindrical coordinates.</p><p dir="ltr"><br></p><p dir="ltr">In the second problem, artificial neural networks (NN) are used to directly invert a temporal sequence of four radiographic images of discontinuities propagating through an imploding steel shell. The NN is fed the radiographic features that are robust to scatter and is trained using density simulations synthesized as solutions to hydrodynamic equations of state. The proposed reconstruction pipeline learns and enforces physics-based assumptions of hydrodynamics and shock physics to constrain the final reconstruction to a space ofphysically admissible solutions.</p>