arXiv subjects

Gregery T. Buzzard

Publications and source records attributed to Gregery T. Buzzard.

At least 37 records · Page 2Linked to original sources

arXiv2023

Generative Plug and Play: Posterior Sampling for Inverse Problems

Over the past decade, Plug-and-Play (PnP) has become a popular method for reconstructing images using a modular framework consisting of a forward and prior model. The great strength of PnP is that an image denoiser can be used as a prior model while the forward model can be implemented using more traditional physics-based approaches. However, a limitation of PnP is that it reconstructs only a single deterministic image. In this paper, we introduce Generative Plug-and-Play (GPnP), a generalization of PnP to sample from the posterior distribution. As with PnP, GPnP has a modular framework using a physics-based forward model and an image denoising prior model. However, in GPnP these models are extended to become proximal generators, which sample from associated distributions. GPnP applies these proximal generators in alternation to produce samples from the posterior. We present experimental simulations using the well-known BM3D denoiser. Our results demonstrate that the GPnP method is robust, easy to implement, and produces intuitively reasonable samples from the posterior for sparse interpolation and tomographic reconstruction. Code to accompany this paper is available at https://github.com/gbuzzard/generative-pnp-allerton .

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arXiv2023

Dynamic DH-MBIR for Phase-Error Estimation from Streaming Digital-Holography Data

Directed energy applications require the estimation of digital-holographic (DH) phase errors due to atmospheric turbulence in order to accurately focus the outgoing beam. These phase error estimates must be computed with very low latency to keep pace with changing atmospheric parameters, which requires that phase errors be estimated in a single shot of DH data. The digital holography model-based iterative reconstruction (DH-MBIR) algorithm is capable of accurately estimating phase errors in a single shot using the expectation maximization (EM) algorithm. However, existing implementations of DH-MBIR require hundreds of iterations, which is not practical for real-time applications. In this paper, we present the Dynamic DH-MBIR (DDH-MBIR) algorithm for estimating isoplanatic phase errors from streaming single-shot data with extremely low latency. The Dynamic DH-MBIR algorithm reduces the computation and latency by orders of magnitude relative to conventional DH-MBIR, making real-time throughput and latency feasible in applications. Using simulated data that models frozen flow of atmospheric turbulence, we show that our algorithm can achieve a consistently high Strehl ratio with realistic simulation parameters using only 1 iteration per timestep.

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arXiv2023

An Edge Alignment-based Orientation Selection Method for Neutron Tomography

Neutron computed tomography (nCT) is a 3D characterization technique used to image the internal morphology or chemical composition of samples in biology and materials sciences. A typical workflow involves placing the sample in the path of a neutron beam, acquiring projection data at a predefined set of orientations, and processing the resulting data using an analytic reconstruction algorithm. Typical nCT scans require hours to days to complete and are then processed using conventional filtered back-projection (FBP), which performs poorly with sparse views or noisy data. Hence, the main methods in order to reduce overall acquisition time are the use of an improved sampling strategy combined with the use of advanced reconstruction methods such as model-based iterative reconstruction (MBIR). In this paper, we propose an adaptive orientation selection method in which an MBIR reconstruction on previously-acquired measurements is used to define an objective function on orientations that balances a data-fitting term promoting edge alignment and a regularization term promoting orientation diversity. Using simulated and experimental data, we demonstrate that our method produces high-quality reconstructions using significantly fewer total measurements than the conventional approach.

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arXiv2023

X-ray Spectral Estimation using Dictionary Learning

As computational tools for X-ray computed tomography (CT) become more quantitatively accurate, knowledge of the source-detector spectral response is critical for quantitative system-independent reconstruction and material characterization capabilities. Directly measuring the spectral response of a CT system is hard, which motivates spectral estimation using transmission data obtained from a collection of known homogeneous objects. However, the associated inverse problem is ill-conditioned, making accurate estimation of the spectrum challenging, particularly in the absence of a close initial guess. In this paper, we describe a dictionary-based spectral estimation method that yields accurate results without the need for any initial estimate of the spectral response. Our method utilizes a MAP estimation framework that combines a physics-based forward model along with an $L_0$ sparsity constraint and a simplex constraint on the dictionary coefficients. Our method uses a greedy support selection method and a new pair-wise iterated coordinate descent method to compute the above estimate. We demonstrate that our dictionary-based method outperforms a state-of-the-art method as shown in a cross-validation experiment on four real datasets collected at beamline 8.3.2 of the Advanced Light Source (ALS).

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arXiv2023

Ringing Artifact Reduction Method for Ultrasound Reconstruction Using Multi-Agent Consensus Equilibrium

Non-destructive characterization of multi-layered structures that can be accessed from only a single side is important for applications such as well-bore integrity inspection. Existing methods related to Synthetic Aperture Focusing Technique (SAFT) rapidly produce acceptable results but with significant artifacts. Recently, ultrasound model-based iterative reconstruction (UMBIR) approaches have shown significant improvements over SAFT. However, even these methods produce ringing artifacts due to the high fractional-bandwidth of the excitation signal. In this paper, we propose a ringing artifact reduction method for ultrasound image reconstruction that uses a multi-agent consensus equilibrium (RARE-MACE) framework. Our approach integrates a physics-based forward model that accounts for the propagation of a collimated ultrasonic beam in multi-layered media, a spatially varying image prior, and a denoiser designed to suppress the ringing artifacts that are characteristic of reconstructions from high-fractional bandwidth ultrasound sensor data. We test our method on simulated and experimental measurements and show substantial improvements in image quality compared to SAFT and UMBIR.

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arXiv2022

Model-based Reconstruction for Multi-Frequency Collimated Beam Ultrasound Systems

Collimated beam ultrasound systems are a technology for imaging inside multi-layered structures such as geothermal wells. These systems work by using a collimated narrow-band ultrasound transmitter that can penetrate through multiple layers of heterogeneous material. A series of measurements can then be made at multiple transmit frequencies. However, commonly used reconstruction algorithms such as Synthetic Aperture Focusing Technique (SAFT) tend to produce poor quality reconstructions for these systems both because they do not model collimated beam systems and they do not jointly reconstruct the multiple frequencies. In this paper, we propose a multi-frequency ultrasound model-based iterative reconstruction (UMBIR) algorithm designed for multi-frequency collimated beam ultrasound systems. The combined system targets reflective imaging of heterogeneous, multi-layered structures. For each transmitted frequency band, we introduce a physics-based forward model to accurately account for the propagation of the collimated narrow-band ultrasonic beam through the multi-layered media. We then show how the joint multi-frequency UMBIR reconstruction can be computed by modeling the direct arrival signals, detector noise, and incorporating a spatially varying image prior. Results using both simulated and experimental data indicate that multi-frequency UMBIR reconstruction yields much higher reconstruction quality than either single frequency UMBIR or SAFT.

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arXiv2022

Multi-Pose Fusion for Sparse-View CT Reconstruction Using Consensus Equilibrium

CT imaging works by reconstructing an object of interest from a collection of projections. Traditional methods such as filtered-back projection (FBP) work on projection images acquired around a fixed rotation axis. However, for some CT problems, it is desirable to perform a joint reconstruction from projection data acquired from multiple rotation axes. In this paper, we present Multi-Pose Fusion, a novel algorithm that performs a joint tomographic reconstruction from CT scans acquired from multiple poses of a single object, where each pose has a distinct rotation axis. Our approach uses multi-agent consensus equilibrium (MACE), an extension of plug-and-play, as a framework for integrating projection data from different poses. We apply our method on simulated data and demonstrate that Multi-Pose Fusion can achieve a better reconstruction result than single pose reconstruction.

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arXiv2022

Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging

Plug-and-Play Priors (PnP) is one of the most widely-used frameworks for solving computational imaging problems through the integration of physical models and learned models. PnP leverages high-fidelity physical sensor models and powerful machine learning methods for prior modeling of data to provide state-of-the-art reconstruction algorithms. PnP algorithms alternate between minimizing a data-fidelity term to promote data consistency and imposing a learned regularizer in the form of an image denoiser. Recent highly-successful applications of PnP algorithms include bio-microscopy, computerized tomography, magnetic resonance imaging, and joint ptycho-tomography. This article presents a unified and principled review of PnP by tracing its roots, describing its major variations, summarizing main results, and discussing applications in computational imaging. We also point the way towards further developments by discussing recent results on equilibrium equations that formulate the problem associated with PnP algorithms.

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arXiv2021

Sparse-View CT Reconstruction using Recurrent Stacked Back Projection

Sparse-view CT reconstruction is important in a wide range of applications due to limitations on cost, acquisition time, or dosage. However, traditional direct reconstruction methods such as filtered back-projection (FBP) lead to low-quality reconstructions in the sub-Nyquist regime. In contrast, deep neural networks (DNNs) can produce high-quality reconstructions from sparse and noisy data, e.g. through post-processing of FBP reconstructions, as can model-based iterative reconstruction (MBIR), albeit at a higher computational cost. In this paper, we introduce a direct-reconstruction DNN method called Recurrent Stacked Back Projection (RSBP) that uses sequentially-acquired backprojections of individual views as input to a recurrent convolutional LSTM network. The SBP structure maintains all information in the sinogram, while the recurrent processing exploits the correlations between adjacent views and produces an updated reconstruction after each new view. We train our network on simulated data and test on both simulated and real data and demonstrate that RSBP outperforms both DNN post-processing of FBP images and basic MBIR, with a lower computational cost than MBIR.

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arXiv2021

Projected Multi-Agent Consensus Equilibrium for Ptychographic Image Reconstruction

Ptychography is a computational imaging technique using multiple, overlapping, coherently illuminated snapshots to achieve nanometer resolution by solving a nonlinear phase-field recovery problem. Ptychography is vital for imaging of manufactured nanomaterials, but existing algorithms have computational shortcomings that limit large-scale application. In this paper, we present the Projected Multi-Agent Consensus Equilibrium (PMACE) approach for solving the ptychography inversion problem. This approach extends earlier work on MACE, which formulates an inversion problem as an equilibrium among multiple agents, each acting independently to update a full reconstruction. In PMACE, each agent acts on a portion (projection) corresponding to one of the snapshots, and these updates to projections are then combined to give an update to the full reconstruction. The resulting algorithm is easily parallelized, with convergence properties inherited from convergence results associated with MACE. We apply our method on simulated data and demonstrate that it outperforms competing algorithms in both reconstruction quality and convergence speed.

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arXiv2021

Convergence of Griddy Gibbs Sampling and other perturbed Markov chains

The Griddy Gibbs sampling was proposed by Ritter and Tanner (1992) as a computationally efficient approximation of the well-known Gibbs sampling method. The algorithm is simple and effective and has been used successfully to address problems in various fields of applied science. However, the approximate nature of the algorithm has prevented it from being widely used: the Markov chains generated by the Griddy Gibbs sampling method are not reversible in general, so the existence and uniqueness of its invariant measure is not guaranteed. Even when such an invariant measure uniquely exists, there was no estimate of the distance between it and the probability distribution of interest, hence no means to ensure the validity of the algorithm as a means to sample from the true distribution. In this paper, we show, subject to some fairly natural conditions, that the Griddy Gibbs method has a unique, invariant measure. Moreover, we provide $L^p$ estimates on the distance between this invariant measure and the corresponding measure obtained from Gibbs sampling. These results provide a theoretical foundation for the use of the Griddy Gibbs sampling method. We also address a more general result about the sensitivity of invariant measures under small perturbations on the transition probability. That is, if we replace the transition probability $P$ of any Monte Carlo Markov chain by another transition probability $Q$ where $Q$ is close to $P$, we can still estimate the distance between the two invariant measures. The distinguishing feature between our approach and previous work on convergence of perturbed Markov chain is that by considering the invariant measures as fixed points of linear operators on function spaces, we don't need to impose any further conditions on the rate of convergence of the Markov chain.

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arXiv2021

Multi-Slice Fusion for Sparse-View and Limited-Angle 4D CT Reconstruction

Inverse problems spanning four or more dimensions such as space, time and other independent parameters have become increasingly important. State-of-the-art 4D reconstruction methods use model based iterative reconstruction (MBIR), but depend critically on the quality of the prior modeling. Recently, plug-and-play (PnP) methods have been shown to be an effective way to incorporate advanced prior models using state-of-the-art denoising algorithms. However, state-of-the-art denoisers such as BM4D and deep convolutional neural networks (CNNs) are primarily available for 2D or 3D images and extending them to higher dimensions is difficult due to algorithmic complexity and the increased difficulty of effective training. In this paper, we present multi-slice fusion, a novel algorithm for 4D reconstruction, based on the fusion of multiple low-dimensional denoisers. Our approach uses multi-agent consensus equilibrium (MACE), an extension of plug-and-play, as a framework for integrating the multiple lower-dimensional models. We apply our method to 4D cone-beam X-ray CT reconstruction for non destructive evaluation (NDE) of samples that are dynamically moving during acquisition. We implement multi-slice fusion on distributed, heterogeneous clusters in order to reconstruct large 4D volumes in reasonable time and demonstrate the inherent parallelizable nature of the algorithm. We present simulated and real experimental results on sparse-view and limited-angle CT data to demonstrate that multi-slice fusion can substantially improve the quality of reconstructions relative to traditional methods, while also being practical to implement and train.

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arXiv2019

Plug and play methods for magnetic resonance imaging (long version)

Magnetic Resonance Imaging (MRI) is a non-invasive diagnostic tool that provides excellent soft-tissue contrast without the use of ionizing radiation. Compared to other clinical imaging modalities (e.g., CT or ultrasound), however, the data acquisition process for MRI is inherently slow, which motivates undersampling and thus drives the need for accurate, efficient reconstruction methods from undersampled datasets. In this article, we describe the use of "plug-and-play" (PnP) algorithms for MRI image recovery. We first describe the linearly approximated inverse problem encountered in MRI. Then we review several PnP methods, where the unifying commonality is to iteratively call a denoising subroutine as one step of a larger optimization-inspired algorithm. Next, we describe how the result of the PnP method can be interpreted as a solution to an equilibrium equation, allowing convergence analysis from the equilibrium perspective. Finally, we present illustrative examples of PnP methods applied to MRI image recovery.

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arXiv2019

Distributed Iterative CT Reconstruction using Multi-Agent Consensus Equilibrium

Model-Based Image Reconstruction (MBIR) methods significantly enhance the quality of computed tomographic (CT) reconstructions relative to analytical techniques, but are limited by high computational cost. In this paper, we propose a multi-agent consensus equilibrium (MACE) algorithm for distributing both the computation and memory of MBIR reconstruction across a large number of parallel nodes. In MACE, each node stores only a sparse subset of views and a small portion of the system matrix, and each parallel node performs a local sparse-view reconstruction, which based on repeated feedback from other nodes, converges to the global optimum. Our distributed approach can also incorporate advanced denoisers as priors to enhance reconstruction quality. In this case, we obtain a parallel solution to the serial framework of Plug-n-play (PnP) priors, which we call MACE-PnP. In order to make MACE practical, we introduce a partial update method that eliminates nested iterations and prove that it converges to the same global solution. Finally, we validate our approach on a distributed memory system with real CT data. We also demonstrate an implementation of our approach on a massive supercomputer that can perform large-scale reconstruction in real-time.

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arXiv2019

Safe Approximate Dynamic Programming Via Kernelized Lipschitz Estimation

We develop a method for obtaining safe initial policies for reinforcement learning via approximate dynamic programming (ADP) techniques for uncertain systems evolving with discrete-time dynamics. We employ kernelized Lipschitz estimation and semidefinite programming for computing admissible initial control policies with provably high probability. Such admissible controllers enable safe initialization and constraint enforcement while providing exponential stability of the equilibrium of the closed-loop system.

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arXiv2019

4D X-Ray CT Reconstruction using Multi-Slice Fusion

There is an increasing need to reconstruct objects in four or more dimensions corresponding to space, time and other independent parameters. The best 4D reconstruction algorithms use regularized iterative reconstruction approaches such as model based iterative reconstruction (MBIR), which depends critically on the quality of the prior modeling. Recently, Plug-and-Play methods have been shown to be an effective way to incorporate advanced prior models using state-of-the-art denoising algorithms designed to remove additive white Gaussian noise (AWGN). However, state-of-the-art denoising algorithms such as BM4D and deep convolutional neural networks (CNNs) are primarily available for 2D and sometimes 3D images. In particular, CNNs are difficult and computationally expensive to implement in four or more dimensions, and training may be impossible if there is no associated high-dimensional training data. In this paper, we present Multi-Slice Fusion, a novel algorithm for 4D and higher-dimensional reconstruction, based on the fusion of multiple low-dimensional denoisers. Our approach uses multi-agent consensus equilibrium (MACE), an extension of Plug-and-Play, as a framework for integrating the multiple lower-dimensional prior models. We apply our method to the problem of 4D cone-beam X-ray CT reconstruction for Non Destructive Evaluation (NDE) of moving parts. This is done by solving the MACE equations using lower-dimensional CNN denoisers implemented in parallel on a heterogeneous cluster. Results on experimental CT data demonstrate that Multi-Slice Fusion can substantially improve the quality of reconstructions relative to traditional 4D priors, while also being practical to implement and train.

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arXiv2018

Deep neural networks for non-linear model-based ultrasound reconstruction

Ultrasound reflection tomography is widely used to image large complex specimens that are only accessible from a single side, such as well systems and nuclear power plant containment walls. Typical methods for inverting the measurement rely on delay-and-sum algorithms that rapidly produce reconstructions but with significant artifacts. Recently, model-based reconstruction approaches using a linear forward model have been shown to significantly improve image quality compared to the conventional approach. However, even these techniques result in artifacts for complex objects because of the inherent non-linearity of the ultrasound forward model. In this paper, we propose 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. We apply our method to simulated ultrasound data and demonstrate dramatic improvements in image quality compared to the delay-and-sum approach and the linear model-based reconstruction approach.

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arXiv2018

Deep Back Projection for Sparse-View CT Reconstruction

Filtered back projection (FBP) is a classical method for image reconstruction from sinogram CT data. FBP is computationally efficient but produces lower quality reconstructions than more sophisticated iterative methods, particularly when the number of views is lower than the number required by the Nyquist rate. In this paper, we use a deep convolutional neural network (CNN) to produce high-quality reconstructions directly from sinogram data. A primary novelty of our approach is that we first back project each view separately to form a stack of back projections and then feed this stack as input into the convolutional neural network. These single-view back projections convert the encoding of sinogram data into the appropriate spatial location, which can then be leveraged by the spatial invariance of the CNN to learn the reconstruction effectively. We demonstrate the benefit of our CNN based back projection on simulated sparse-view CT data over classical FBP.

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