MACE CT Reconstruction for Modular Material Decomposition from Energy Resolving Photon-Counting Data

X-ray computed tomography (CT) based on photon counting detectors (PCD) extends standard CT by counting detected photons in multiple energy bins. PCD data can be used to increase the contrast-to-noise ratio (CNR), increase spatial resolution, reduce radiation dose, reduce injected contrast dose, and compute a material decomposition using a specified set of basis materials. Current commercial and prototype clinical photon counting CT systems utilize PCD-CT reconstruction methods that either reconstruct from each spectral bin separately, or first create an estimate of a material sinogram using a specified set of basis materials and then reconstruct from these material sinograms. However, existing methods are not able to utilize simultaneously and in a modular fashion both the measured spectral information and advanced prior models in order to produce a material decomposition. We describe an efficient, modular framework for PCD-based CT reconstruction and material decomposition using on Multi-Agent Consensus Equilibrium (MACE). Our method employs a detector proximal map or agent that uses PCD measurements to update an estimate of the pathlength sinogram. We also create a prior agent in the form of a sinogram denoiser that enforces both physical and empirical knowledge about the material-decomposed sinogram. The sinogram reconstruction is computed using the MACE algorithm, which finds an equilibrium solution between the two agents, and the final image is reconstructed from the estimated sinogram. Importantly, the modularity of our method allows the two agents to be designed, implemented, and optimized independently. Our results on simulated data show a substantial (450%) CNR boost vs conventional maximum likelihood reconstruction when applied to a phantom used to evaluate low contrast detectability.

Texture Matching GAN for CT Image Enhancement

Deep neural networks (DNN) are commonly used to denoise and sharpen X-ray computed tomography (CT) images with the goal of reducing patient X-ray dosage while maintaining reconstruction quality. However, naive application of DNN-based methods can result in image texture that is undesirable in clinical applications. Alternatively, generative adversarial network (GAN) based methods can produce appropriate texture, but naive application of GANs can introduce inaccurate or even unreal image detail. In this paper, we propose a texture matching generative adversarial network (TMGAN) that enhances CT images while generating an image texture that can be matched to a target texture. We use parallel generators to separate anatomical features from the generated texture, which allows the GAN to be trained to match the desired texture without directly affecting the underlying CT image. We demonstrate that TMGAN generates enhanced image quality while also producing image texture that is desirable for clinical application.

Design of Novel Loss Functions for Deep Learning in X-ray CT

Deep learning (DL) shows promise of advantages over conventional signal processing techniques in a variety of imaging applications. The networks' being trained from examples of data rather than explicitly designed allows them to learn signal and noise characteristics to most effectively construct a mapping from corrupted data to higher quality representations. In inverse problems, one has options of applying DL in the domain of the originally captured data, in the transformed domain of the desired final representation, or both. X-ray computed tomography (CT), one of the most valuable tools in medical diagnostics, is already being improved by DL methods. Whether for removal of common quantum noise resulting from the Poisson-distributed photon counts, or for reduction of the ill effects of metal implants on image quality, researchers have begun employing DL widely in CT. The selection of training data is driven quite directly by the corruption on which the focus lies. However, the way in which differences between the target signal and measured data is penalized in training generally follows conventional, pointwise loss functions. This work introduces a creative technique for favoring reconstruction characteristics that are not well described by norms such as mean-squared or mean-absolute error. Particularly in a field such as X-ray CT, where radiologists' subjective preferences in image characteristics are key to acceptance, it may be desirable to penalize differences in DL more creatively. This penalty may be applied in the data domain, here the CT sinogram, or in the reconstructed image. We design loss functions for both shaping and selectively preserving frequency content of the signal.

Statistically Adaptive Filtering for Low Signal Correction in X-ray Computed Tomography

Low x-ray dose is desirable in x-ray computed tomographic (CT) imaging due to health concerns. But low dose comes with a cost of low signal artifacts such as streaks and low frequency bias in the reconstruction. As a result, low signal correction is needed to help reduce artifacts while retaining relevant anatomical structures. Low signal can be encountered in cases where sufficient number of photons do not reach the detector to have confidence in the recorded data. % NOTE: SNR is ratio of powers, not std. dev. X-ray photons, assumed to have Poisson distribution, have signal to noise ratio proportional to the dose, with poorer SNR in low signal areas. Electronic noise added by the data acquisition system further reduces the signal quality. In this paper we will demonstrate a technique to combat low signal artifacts through adaptive filtration. It entails statistics-based filtering on the uncorrected data, correcting the lower signal areas more aggressively than the high signal ones. We look at local averages to decide how aggressive the filtering should be, and local standard deviation to decide how much detail preservation to apply. Implementation consists of a pre-correction step i.e. local linear minimum mean-squared error correction, followed by a variance stabilizing transform, and finally adaptive bilateral filtering. The coefficients of the bilateral filter are computed using local statistics. Results show that improvements were made in terms of low frequency bias, streaks, local average and standard deviation, modulation transfer function and noise power spectrum.

MBIR Training for a 2.5D DL network in X-ray CT

In computed tomographic imaging, model based iterative reconstruction methods have generally shown better image quality than the more traditional, faster filtered backprojection technique. The cost we have to pay is that MBIR is computationally expensive. In this work we train a 2.5D deep learning (DL) network to mimic MBIR quality image. The network is realized by a modified Unet, and trained using clinical FBP and MBIR image pairs. We achieve the quality of MBIR images faster and with a much smaller computation cost. Visually and in terms of noise power spectrum (NPS), DL-MBIR images have texture similar to that of MBIR, with reduced noise power. Image profile plots, NPS plots, standard deviation, etc. suggest that the DL-MBIR images result from a successful emulation of an MBIR operator.

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 .

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.

Projected Multi-Agent Consensus Equilibrium (PMACE) for Distributed Reconstruction with Application to Ptychography

Multi-Agent Consensus Equilibrium (MACE) formulates an inverse imaging problem as a balance among multiple update agents such as data-fitting terms and denoisers. However, each such agent operates on a separate copy of the full image, leading to redundant memory use and slow convergence when each agent affects only a small subset of the full image. In this paper, we extend MACE to Projected Multi-Agent Consensus Equilibrium (PMACE), in which each agent updates only a projected component of the full image, thus greatly reducing memory use for some applications.We describe PMACE in terms of an equilibrium problem and an equivalent fixed point problem and show that in most cases the PMACE equilibrium is not the solution of an optimization problem. To demonstrate the value of PMACE, we apply it to the problem of ptychography, in which a sample is reconstructed from the diffraction patterns resulting from coherent X-ray illumination at multiple overlapping spots. In our PMACE formulation, each spot corresponds to a separate data-fitting agent, with the final solution found as an equilibrium among all the agents. Our results demonstrate that the PMACE reconstruction algorithm generates more accurate reconstructions at a lower computational cost than existing ptychography algorithms when the spots are sparsely sampled.

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.

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).