<p></p><p>One-sided ultrasonic non-destructive evaluation (UNDE) is extensively used to characterize structures that need to be inspected and maintained from defects and flaws that could affect the performance of power plants, such as nuclear power plants. Most UNDE systems send acoustic pulses into the structure of interest, measure the received waveform and use an algorithm to reconstruct the quantity of interest. The most widely used algorithm in UNDE systems is the synthetic aperture focusing technique (SAFT) because it produces acceptable results in real time. A few regularized inversion techniques with linear models have been proposed which can improve on SAFT, but they tend to make simplifying assumptions that show artifacts and do not address how to obtain reconstructions from large real data sets. In this thesis, we present two studies. The first study covers the model-based iterative reconstruction (MBIR) technique which is used to resolve some of the issues in SAFT and the current linear regularized inversion techniques, and the second study covers the direct deep learning (DDL) technique which is used to further resolve issues related to non-linear interactions between the ultrasound signal and the specimen.</p> <p>In the first study, we propose a model-based iterative reconstruction (MBIR) algorithm designed for scanning UNDE systems. MBIR reconstructs the image by optimizing a cost function that contains two terms: the forward model that models the measurements and the prior model that models the object. To further reduce some of the artifacts in the results, we enhance the forward model of MBIR to account for the direct arrival artifacts and the isotropic artifacts. The direct arrival signals are the signals received directly from the transmitter without being reflected. These signals contain no useful information about the specimen and produce high amplitude artifacts in regions close to the transducers. We resolve this issue by modeling these direct arrival signals in the forward model to reduce their artifacts while maintaining information from reflections of other objects. Next, the isotropic artifacts appear when the transmitted signal is assumed to propagate in all directions equally. Therefore, we modify our forward model to resolve this issue by modeling the anisotropic propagation. Next, because of the significant attenuation of the transmitted signal as it propagates through deeper regions, the reconstruction of deeper regions tends to be much dimmer than closer regions. Therefore, we combine the forward model with a spatially variant prior model to account for the attenuation by reducing the regularization as the pixel gets deeper. Next, for scanning large structures, multiple scans are required to cover the whole field of view. Typically, these scans are performed in raster order which makes adjacent scans share some useful correlations. Reconstructing each scan individually and performing a conventional stitching method is not an efficient way because this could produce stitching artifacts and ignore extra information from adjacent scans. We present an algorithm to jointly reconstruct measurements from large data sets that reduces the stitching artifacts and exploits useful information from adjacent scans. Next, using simulated and extensive experimental data, we show MBIR results and demonstrate how we can improve over SAFT as well as existing regularized inversion techniques. However, even with this improvement, MBIR still results in some artifacts caused by the inherent non-linearity of the interaction between the ultrasound signal and the specimen.</p> <p>In the second study, we propose DDL, a non-iterative model-based reconstruction method for inverting measurements that are based on non-linear forward models for ultrasound imaging. Our approach involves obtaining an approximate estimate of the reconstruction using a simple linear back-projection and training a deep neural network to refine this to the actual reconstruction. While the technique we are proposing can show significant enhancement compared to the current techniques with simulated data, one issue appears with the performance of this technique when applied to experimental data. The issue is a modeling mismatch between the simulated training data and the real data. We propose an effective solution that can reduce the effect of this modeling mismatch by adding noise to the simulation input of the training set before simulation. This solution trains the neural network on the general features of the system rather than specific features of the simulator and can act as a regularization to the neural network. Another issue appears similar to the issue in MBIR caused by the attenuation of deeper reflections. Therefore, we propose a spatially variant amplification technique applied to the back-projection to amplify deeper regions. Next, to reconstruct from a large field of view that requires multiple scans, we propose a joint deep neural network technique to jointly reconstruct an image from these multiple scans. Finally, we apply DDL to simulated and experimental ultrasound data to demonstrate significant improvements in image quality compared to the delay-and-sum approach and the linear model-based reconstruction approach.</p><br><p></p>

Lorentz TEM observations of magnetic nanoparticles contain information on the magnetic and electrostatic potentials of the sample. These potentials can be extracted from the electron wave phase shift by separating electrostatic and magnetic phase shifts, followed by 3D tomographic reconstructions. In past, Vector Field Electron Tomography (VFET) was utilized to perform the reconstruction. However, VFET is based on a conventional tomography method called filtered back-projection (FBP). Consequently, the VFET approach tends to produce inconsistencies that are prominent along the edges of the sample. We propose a model-based iterative reconstruction (MBIR) approach to improve the reconstruction of magnetic vector potential, A(r). In the case of scalar tomography, the MBIR method is known to yield better reconstructions than the conventional FBP approach, due to the fact that MBIR can incorporate prior knowledge about the system to be reconstructed. For the same reason, we seek to use the MBIR approach to optimize vector field tomographic reconstructions via incorporation of prior knowledge. We combine a forward model for image formation in TEM experiments with a prior model to formulate the tomographic problem as a maximum a posteriori probability estimation problem (MAP). The MAP cost function is minimized iteratively to deduce the vector potential. A detailed study of reconstructions from simulated as well as experimental data sets is provided to establish the superiority of the MBIR approach over the VFET approach.

<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>

<p dir="ltr">X-ray computed tomography (CT) is one of the most widely used imaging modalities for medical diagnosis. Improving the quality of clinical CT images while keeping the X-ray dosage of patients low has been an active area of research. Recently, there have been two major technological advances in the commercial CT systems. The first is the use of Deep Neural Networks (DNN) to denoise and sharpen CT images, and the second is use of photon counting detectors (PCD) which provide higher spectral and spatial resolution compared to the conventional energy-integrating detectors. While both techniques have potential to improve the quality of CT images significantly, there are still challenges to improve the quality further.</p><p dir="ltr"><br></p><p dir="ltr">A denoising or sharpening algorithm for CT images must retain a favorable texture which is critically important for radiologists. However, commonly used methodologies in DNN training produce over-smooth images lacking texture. The lack of texture is a systematic error leading to a biased estimator.</p><p><br></p><p dir="ltr">In the first portion of this thesis, we propose three algorithms to reduce the bias, thereby to retain the favorable texture. The first method proposes a novel approach to designing a loss function that penalizes bias in the image more while training a DNN, producing more texture and detail in results. Our experiments verify that the proposed loss function outperforms the commonly used mean squared error loss function. The second algorithm proposes a novel approach to designing training pairs for a DNN-based sharpener. While conventional sharpeners employ noise-free ground truth producing over-smooth images, the proposed Noise Preserving Sharpening Filter (NPSF) adds appropriately scaled noise to both the input and the ground truth to keep the noise texture in the sharpened result similar to that of the input. Our evaluations show that the NPSF can sharpen noisy images while producing desired noise level and texture. The above two algorithms merely control the amount of texture retained and are not designed to produce texture that matches to a target texture. A Generative Adversarial Network (GAN) can produce the target texture. However, naive application of GANs can introduce inaccurate or even unreal image detail. Therefore, we propose a Texture Matching GAN (TMGAN) that uses parallel generators to separate anatomical features from the generated texture, which allows the GAN to be trained to match the target texture without directly affecting the underlying CT image. We demonstrate that TMGAN generates enhanced image quality while also producing texture that is desirable for clinical application.</p><p><br></p><p dir="ltr">In the second portion of this research, we propose a novel algorithm for the optimal statistical processing of photon-counting detector data for CT reconstruction. Current reconstruction and material decomposition algorithms for photon counting CT are not able to utilize simultaneously both the measured spectral information and advanced prior models. We propose a modular framework based on Multi-Agent Consensus Equilibrium (MACE) to obtain material decomposition and reconstructions using the PCD data. Our method employs a detector agent that uses PCD measurements to update an estimate along with a prior agent that enforces both physical and empirical knowledge about the material-decomposed sinograms. Importantly, the modular framework allows the two agents to be designed and optimized independently. Our evaluations on simulated data show promising results.</p>

Cryo-electron microscopy (cryo-EM) has been established as the leading imaging technique for structural studies from small proteins to whole cells at a molecular level. The great advances in cryo-EM have led to the ability to provide unique insights into a wide variety of biological processes in a close to native, hydrated state at near-atomic resolutions. The developments of computational approaches have significantly contributed to the exciting achievements of cryo-EM. This dissertation emphasizes new approaches to address image processing problems in cryo-EM, including tilt series alignment evaluation, simultaneous determination of sample thickness, tilt, and electron mean free path based on Beer-Lambert law, Model-Based Iterative Reconstruction (MBIR) on tomographic data, minimization of objective lens astigmatism in instrument alignment and defocus and magnification dependent astigmatism of TEM images. The final goal of these methodological developments is to improve the 3D reconstruction of cryo-EM and visualize more detailed characterization.