Convolutional Dictionary Regularizers for Tomographic Inversion

There has been a growing interest in the use of data-driven regularizers to solve inverse problems associated with computational imaging systems. The convolutional sparse representation model has recently gained attention, driven by the development of fast algorithms for solving the dictionary learning and sparse coding problems for sufficiently large images and data sets. Nevertheless, this model has seen very limited application to tomographic reconstruction problems. In this paper, we present a model-based tomographic reconstruction algorithm using a learnt convolutional dictionary as a regularizer. The key contribution is the use of a data-dependent weighting scheme for the l1 regularization to construct an effective denoising method that is integrated into the inversion using the Plug-and-Play reconstruction framework. Using simulated data sets we demonstrate that our approach can improve performance over traditional regularizers based on a Markov random field model and a patch-based sparse representation model for sparse and limited-view tomographic data sets

Plug-and-play priors for model based reconstruction

Abstract-Model-based reconstruction is a powerful framework for solving a variety of inverse problems in imaging. In recent years, enormous progress has been made in the problem of denoising, a special case of an inverse problem where the forward model is an identity operator. Similarly, great progress has been made in improving model-based inversion when the forward model corresponds to complex physical measurements in applications such as X-ray CT, electron-microscopy, MRI, and ultrasound, to name just a few. However, combining state-of-theart denoising algorithms (i.e., prior models) with state-of-the-art inversion methods (i.e., forward models) has been a challenge for many reasons. In this paper, we propose a flexible framework that allows state-of-the-art forward models of imaging systems to be matched with state-of-the-art priors or denoising models. This framework, which we term as Plug-and-Play priors, has the advantage that it dramatically simplifies software integration, and moreover, it allows state-of-the-art denoising methods that have no known formulation as an optimization problem to be used. We demonstrate with some simple examples how Plug-and-Play priors can be used to mix and match a wide variety of existing denoising models with a tomographic forward model, thus greatly expanding the range of possible problem solutions

Deep learning based workflow for accelerated industrial X-ray Computed Tomography

X-ray computed tomography (XCT) is an important tool for high-resolution non-destructive characterization of additively-manufactured metal components. XCT reconstructions of metal components may have beam hardening artifacts such as cupping and streaking which makes reliable detection of flaws and defects challenging. Furthermore, traditional workflows based on using analytic reconstruction algorithms require a large number of projections for accurate characterization - leading to longer measurement times and hindering the adoption of XCT for in-line inspections. In this paper, we introduce a new workflow based on the use of two neural networks to obtain high-quality accelerated reconstructions from sparse-view XCT scans of single material metal parts. The first network, implemented using fully-connected layers, helps reduce the impact of BH in the projection data without the need of any calibration or knowledge of the component material. The second network, a convolutional neural network, maps a low-quality analytic 3D reconstruction to a high-quality reconstruction. Using experimental data, we demonstrate that our method robustly generalizes across several alloys, and for a range of sparsity levels without any need for retraining the networks thereby enabling accurate and fast industrial XCT inspections

Autonomous Polycrystalline Material Decomposition for Hyperspectral Neutron Tomography

Hyperspectral neutron tomography is an effective method for analyzing crystalline material samples with complex compositions in a non-destructive manner. Since the counts in the hyperspectral neutron radiographs directly depend on the neutron cross-sections, materials may exhibit contrasting neutron responses across wavelengths. Therefore, it is possible to extract the unique signatures associated with each material and use them to separate the crystalline phases simultaneously. We introduce an autonomous material decomposition (AMD) algorithm to automatically characterize and localize polycrystalline structures using Bragg edges with contrasting neutron responses from hyperspectral data. The algorithm estimates the linear attenuation coefficient spectra from the measured radiographs and then uses these spectra to perform polycrystalline material decomposition and reconstructs 3D material volumes to localize materials in the spatial domain. Our results demonstrate that the method can accurately estimate both the linear attenuation coefficient spectra and associated reconstructions on both simulated and experimental neutron data

Model-based iterative reconstruction for micro-scale and nano-scale imaging

Transmission electron microscopes (TEM) and synchrotron X-ray (SX) sources are widely being used to characterize materials at the nano-scale and micron-scale in two/three dimensions. While there has been significant progress in enhancing the hardware in these instruments to improve image quality, the algorithms used for image reconstruction have not fully exploited the statistical information in the data and the properties of the material being imaged to enhance the quality of the images. Model-based iterative reconstruction (MBIR) is an emerging theme for image reconstruction that combines a probabilistic model for the measurement system (forward model) with a probabilistic model for the image (prior model) to formulate the reconstruction as a high-dimensional estimation problem. In this dissertation, we propose MBIR algorithms for different imaging modalities used in a TEM and in SX imaging. First, we propose an MBIR algorithm for high angle annular dark field - scanning TEM (HAADF-STEM) tomography. Next, we present an MBIR algorithm for handling anomalous measurements encountered in bright field - electron tomography (BF-ET) of crystalline samples. Results on simulated as well as real data show significant improvements over the typical reconstruction approaches used for HAADFSTEM tomography and BF-ET. Furthermore, the proposed MBIR for BF-ET is also useful for SX tomography as it can handle anomalous measurements from saturated detector pixels. Finally, we propose a flexible optimization framework, termed Plug-and-Play priors, that allows state-of-the-art forward models of imaging systems to be matched with state-of-the-art denoising algorithms for MBIR. We will demonstrate how the Plug-and-Play priors can be used to mix and match a wide variety of denoising algorithms based on advanced image models with forward models encountered in TEM tomography, SX tomography and in sparse image reconstruction from STEM data, thus greatly expanding the range of possible problem solutions

Plug-and-Play Priors for Model Based Reconstruction

Model-based reconstruction is a powerful framework for solving a variety of inverse problems in imaging. The method works by combining a forward model of the imaging system with a prior model of the image itself, and the reconstruction is then computed by minimizing a functional consisting of the sum of two terms corresponding to the forward and prior models. In recent years, enormous progress has been made in the problem of denoising, a special case of an inverse problem where the forward model is an identity operator. A wide range of methods including nonlocal means, dictionary-based methods, 3D block matching, TV minimization and kernel-based filtering have proven that it is possible to recover high fidelity images even after a great deal of noise has been added. Similarly, great progress has been made in improving model-based inversion when the forward model corresponds to complex physical measurements in applications such as X-ray CT, electronmicroscopy, MRI, and ultrasound, to name just a few. However, combining state-of-the-art denoising algorithms (i.e., prior models) with state-of-the-art inversion methods (i.e., forward models) has been a challenge for many reasons. In this report, we propose a flexible framework that allows state-of-the-art forward models of imaging systems to be matched with state-of-the-art prior or denoising models. This framework, which we term as Plug-and-Play priors, has the advantage that it dramatically simplifies software integration, and moreover, it allows state-of-the-art denoising methods that have no known formulation as an optimization problem to be used. We demonstrate with some simple examples how Plug-and-Play priors can be used to mix and match a wide variety of existing denoising models with a tomographic forward model, thus greatly expanding the range of possible problem solutions