arXiv subjects

Matthew Tivnan

Publications and source records attributed to Matthew Tivnan.

30 records · Page 2Linked to original sources

arXiv2024

Conditional Score-Based Diffusion Model for Cortical Thickness Trajectory Prediction

Alzheimer's Disease (AD) is a neurodegenerative condition characterized by diverse progression rates among individuals, with changes in cortical thickness (CTh) closely linked to its progression. Accurately forecasting CTh trajectories can significantly enhance early diagnosis and intervention strategies, providing timely care. However, the longitudinal data essential for these studies often suffer from temporal sparsity and incompleteness, presenting substantial challenges in modeling the disease's progression accurately. Existing methods are limited, focusing primarily on datasets without missing entries or requiring predefined assumptions about CTh progression. To overcome these obstacles, we propose a conditional score-based diffusion model specifically designed to generate CTh trajectories with the given baseline information, such as age, sex, and initial diagnosis. Our conditional diffusion model utilizes all available data during the training phase to make predictions based solely on baseline information during inference without needing prior history about CTh progression. The prediction accuracy of the proposed CTh prediction pipeline using a conditional score-based model was compared for sub-groups consisting of cognitively normal, mild cognitive impairment, and AD subjects. The Bland-Altman analysis shows our diffusion-based prediction model has a near-zero bias with narrow 95% confidential interval compared to the ground-truth CTh in 6-36 months. In addition, our conditional diffusion model has a stochastic generative nature, therefore, we demonstrated an uncertainty analysis of patient-specific CTh prediction through multiple realizations.

eess.IV↗

arXiv2023

How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control

Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions, important questions remain on the reliability and trustworthiness of these sampling procedures for their responsible use in critical scenarios. Conformal prediction is a modern tool to construct finite-sample, distribution-free uncertainty guarantees for any black-box predictor. In this work, we focus on image-to-image regression tasks and we present a generalization of the Risk-Controlling Prediction Sets (RCPS) procedure, that we term $K$-RCPS, which allows to $(i)$ provide entrywise calibrated intervals for future samples of any diffusion model, and $(ii)$ control a certain notion of risk with respect to a ground truth image with minimal mean interval length. Differently from existing conformal risk control procedures, ours relies on a novel convex optimization approach that allows for multidimensional risk control while provably minimizing the mean interval length. We illustrate our approach on two real-world image denoising problems: on natural images of faces as well as on computed tomography (CT) scans of the abdomen, demonstrating state of the art performance.

stat.ML↗

arXiv2023

A Joint Processing Strategy for Image Quality Improvement in 3D Digital Subtraction Angiography

Three-dimensional digital subtraction angiography (3D-DSA) is a widely adopted technique for clinical evaluation of contrast-enhanced vasculatures. The distribution of a contrast agent such as iodine is often estimated via temporal subtraction. Advancements in spectral imaging technologies such as photon counting detectors offer new opportunities to improve DSA image quality. In this work, we propose a novel joint processing strategy to achieve an iodine image using two-bin spectral measurements from a photon counting detector acquired both the pre- and post-contrast injection. Simulation studies were performed using a digital phantom with iodine-enhanced vessels. The proposed method was compared with temporal subtraction and conventional spectral imaging using just the post-contrast measurements. Imaging performance was evaluated in terms of noise-resolution tradeoffs. Preliminary findings have shown measurably improved image quality given by joint processing, reducing noise by 40% and 70% compared to temporal subtraction and conventional spectral imaging, respectively.

physics.med-ph↗

arXiv2023

Fourier Diffusion Models: A Method to Control MTF and NPS in Score-Based Stochastic Image Generation

Score-based stochastic denoising models have recently been demonstrated as powerful machine learning tools for conditional and unconditional image generation. The existing methods are based on a forward stochastic process wherein the training images are scaled to zero over time and white noise is gradually added such that the final time step is approximately zero-mean identity-covariance Gaussian noise. A neural network is then trained to approximate the time-dependent score function, or the gradient of the logarithm of the probability density, for that time step. Using this score estimator, it is possible to run an approximation of the time-reversed stochastic process to sample new images from the training data distribution. These score-based generative models have been shown to out-perform generative adversarial neural networks using standard benchmarks and metrics. However, one issue with this approach is that it requires a large number of forward passes of the neural network. Additionally, the images at intermediate time steps are not useful, since the signal-to-noise ratio is low. In this work we present a new method called Fourier Diffusion Models which replaces the scalar operations of the forward process with shift-invariant convolutions and the additive white noise with additive stationary noise. This allows for control of MTF and NPS at intermediate time steps. Additionally, the forward process can be crafted to converge to the same MTF and NPS as the measured images. This way, we can model continuous probability flow from true images to measurements. In this way, the sample time can be used to control the tradeoffs between measurement uncertainty and generative uncertainty of posterior estimates. We compare Fourier diffusion models to existing scalar diffusion models and show that they achieve a higher level of performance and allow for a smaller number of time steps.

physics.med-ph↗

arXiv2021

High-Sensitivity Iodine Imaging by Combining Spectral CT Technologies

Spectral CT offers enhanced material discrimination over single-energy systems and enables quantitative estimation of basis material density images. Water/iodine decomposition in contrast-enhanced CT is one of the most widespread applications of this technology in the clinic. However, low concentrations of iodine can be difficult to estimate accurately, limiting potential clinical applications and/or raising injected contrast agent requirements. We seek high-sensitivity spectral CT system designs which minimize noise in water/iodine density estimates. In this work, we present a model-driven framework for spectral CT system design optimization to maximize material separability. We apply this tool to optimize the sensitivity spectra on a spectral CT test bench using a hybrid design which combines source kVp control and k-edge filtration. Following design optimization, we scanned a water/iodine phantom with the hybrid spectral CT system and performed dose-normalized comparisons to two single-technique designs which use only kVp control or only kedge filtration. The material decomposition results show that the hybrid system reduces both standard deviation and crossmaterial noise correlations compared to the designs where the constituent technologies are used individually.

physics.med-ph↗

arXiv2020

Manifold Reconstruction of Differences: A Model-Based Iterative Statistical Estimation Algorithm with a Data-Driven Prior

Manifold learning using deep neural networks been shown to be an effective tool for building sophisticated prior image models that can be applied to noise reduction in low-dose CT. We propose a new iterative CT reconstruction algorithm, called Manifold Reconstruction of Differences (MRoD), which combines physical and statistical models with a data-driven prior based on manifold learning. The MRoD algorithm involves estimating a manifold component, approximating common features among all patients, and the difference component which has the freedom to fit the measured data. By applying a sparsity-promoting penalty to the difference image rather than a hard constraint to the manifold, the MRoD algorithm is able to reconstruct features which are not present in the training data. The difference component itself may be independently useful. While the manifold captures typical patient features (e.g. healthy anatomy), the difference image highlights patient-specific elements (e.g. pathology). In this work, we present a description of an optimization framework which combines trained manifold-based modules with physical modules. We present a simulation study using anthropomorphic lung data showing that the MRoD algorithm can both isolate differences between a particular patient and the typical distribution, but also provide significant noise reduction with less bias than a typical penalized likelihood estimator in composite manifold plus difference reconstructions.

physics.med-ph↗

arXiv2020

Design of Spatial-Spectral Filters for CT Material Decomposition

Spectral CT has shown promise for high-sensitivity quantitative imaging and material decomposition. This work presents a new device called a spatial-spectral filter (SSF) which consists of a tiled array of filter materials positioned near the x-ray source that is used to modulate the spectral shape of the x-ray beam. The filter is moved to obtain projection data that is sparse in each spectral channel. To process this sparse data, we employ a direct model-based material decomposition (MBMD)to reconstruct basis material density images directly from the SSF CT data. To evaluate different possible SSF designs, we define a new Fisher-information-based predictive image quality metric called separability index which characterizes the ability of a spectral CT system to distinguish between the signals from two or more materials. This predictive metric is used to define a system design optimization framework. We have applied this framework to find optimized combinations of filter materials, filter tile widths, and source settings for SSF CT. We conducted simulation-based design optimization study and separability-optimized filter designs are presented for water/iodine imaging and water/iodine/gadolinium/gold imaging for different patient sizes. Finally, we present MBMD results using simulated SSFCT data using the optimized designs to demonstrate the ability to reconstruct basis material density images and to show the benefits of the optimized designs.

physics.med-ph↗

arXiv2020

Multi-Contrast CT Imaging with a Prototype Spatial-Spectral Filter

Spectral CT has great potential for a variety of clinical applications due to the improved material discrimination with respect to conventional CT. Many clinical and preclinical spectral CT systems have two spectral channels for dual-energy CT using strategies such as split-filtration, dual-layer detectors, or kVp-switching. However, there are emerging clinical imaging applications which would require three or more spectral sensitivity channels, for example, multiple exogenous contrast agents in a single scan. Spatial-spectral filters are a new spectral CT technology which use x-ray beam modulation to offer greater spectral diversity. The device consists of an array of k-edge filters which divide the x-ray beam into spectrally varied beamlets. This design allows for an arbitrary number of spectral channels; however, traditional two-step reconstruction-decomposition schemes are typically not effective because the measured data for any individual spectral channel is sparse in the projection domain. Instead, we use a one-step model-based material decomposition algorithm to iteratively estimate material density images directly from spectral CT data. In this work, we present a prototype spatial-spectral filter integrated with an x-ray CT test-bench. The filter is composed of an array of tin, erbium, tantalum, and lead filter tiles which spatially modulate the system spectral sensitivity pattern. After the system was characterized and modeled, we conducted a spectral CT scan of a multi-contrast-enhanced phantom containing water, iodine, and gadolinium solutions. We present the resulting spectral CT data as well as the material density images estimated by model-based material decomposition...

physics.med-ph↗

arXiv2020

Optimized Spatial-Spectral CT for Multi-Material Decomposition

Spectral CT is an emerging modality that uses a data acquisition scheme with varied spectral responses to provide enhanced material discrimination in addition to the structural information of conventional CT. Existing clinical and preclinical designs with this capability include kV-switching, split-filtration, and dual-layer detector systems to provide two spectral channels of projection data. In this work, we examine an alternate design based on a spatial-spectral filter. This source-side filter is made up a linear array of materials that divide the incident x-ray beam into spectrally varied beamlets. This design allows for any number of spectral channels; however, each individual channel is sparse in the projection domain. Model-based iterative reconstruction methods can accommodate such sparse spatial-spectral sampling patterns and allow for the incorporation of advanced regularization. With the goal of an optimized physical design, we characterize the effects of design parameters including filter tile order and filter tile width and their impact on material decomposition performance. We present results of numerical simulations that characterize the impact of each design parameter using a realistic CT geometry and noise model to demonstrate feasibility. Results for filter tile order show little change indicating that filter order is a low-priority design consideration. We observe improved performance for narrower filter widths; however, the performance drop-off is relatively flat indicating that wider filter widths are also feasible designs.

physics.med-ph↗

arXiv2020

Combining Spectral CT Acquisition Methods for High-Sensitivity Material Decomposition

Quantitative estimation of contrast agent concentration is made possible by spectral CT and material decomposition. There are several approaches to modulate the sensitivity of the imaging system to obtain the different spectral channels required for decomposition. Spectral CT technologies that enable this varied sensitivity include source kV-switching, dual-layer detectors, and source-side filtering (e.g., tiled spatial-spectral filters). In this work, we use an advanced physical model to simulate these three spectral CT strategies as well as hybrid acquisitions using all combinations of two or three strategies. We apply model-based material decomposition to a water-iodine phantom with iodine concentrations from 0.1 to 5.0 mg/mL. We present bias-noise plots for the different combinations of spectral techniques and show that combined approaches permit diversity in spectral sensitivity and improve low concentration imaging performance relative to the those strategies applied individually. Better ability to estimate low concentrations of contrast agent has the potential to reduce risks associated with contrast administration (by lowering dosage) or to extend imaging applications into targets with much lower uptake.

physics.med-ph↗

arXiv2020

A Preconditioned Algorithm for Model-Based Iterative CT Reconstruction and Material Decomposition from Spectral CT Data

Model-based material decomposition is a statisticaliterative reconstruction framework where basis material densityimages are estimated directly from spectral CT data. This methoduses a physical model for polyenergetic x-ray transmission andattenuation and therefore it does not typically suffer frombeam-hardening artifacts. However, this estimation is a poorly-conditioned inverse problem due to the strong anticorrelationbetween basis materials. In this work we propose an precondi-tioned optimization algorithm for a nonlinear penalized weightedleast-squares objective function.

physics.med-ph↗

arXiv2020

Physical Modeling and Performance of Spatial-Spectral Filters for CT Material Decomposition

Material decomposition for imaging multiple contrast agents in a single acquisition has been made possible by spectral CT: a modality which incorporates multiple photon energy spectral sensitivities into a single data collection. This work presents an investigation of a new approach to spectral CT which does not rely on energy-discriminating detectors or multiple x-ray sources. Instead, a tiled pattern of K-edge filters are placed in front of the x-ray to create spatially encoded spectra data. For improved sampling, the spatial-spectral filter is moved continuously with respect to the source. A model-based material decomposition algorithm is adopted to directly reconstruct multiple material densities from projection data that is sparse in each spectral channel. Physical effects associated with the x-ray focal spot size and motion blur for the moving filter are expected to impact overall performance. In this work, those physical effects are modeled and a performance analysis is conducted. Specifically, experiments are presented with simulated focal spot widths between 0.2 mm and 4.0 mm. Additionally, filter motion blur is simulated for a linear translation speeds between 50 mm/s and 450 mm/s. The performance differential between a 0.2 mm and a 1.0 mm focal spot is less than 15% suggesting feasibility of the approach with realistic x-ray tubes. Moreover, for reasonable filter actuation speeds, higher speeds are shown to decrease error (due to improved sampling) despite motion-based spectral blur.

physics.med-ph↗