Sean Rose

Noise properties of CT images reconstructed by use of constrained total-variation, data-discrepancy minimization

PURPOSE The authors develop and investigate iterative image reconstruction algorithms based on data-discrepancy minimization with a total-variation (TV) constraint. The various algorithms are derived with different data-discrepancy measures reflecting the maximum likelihood (ML) principle. Simulations demonstrate the iterative algorithms and the resulting image statistical properties for low-dose CT data acquired with sparse projection view angle sampling. Of particular interest is to quantify improvement of image statistical properties by use of the ML data fidelity term. METHODS An incremental algorithm framework is developed for this purpose. The instances of the incremental algorithms are derived for solving optimization problems including a data fidelity objective function combined with a constraint on the image TV. For the data fidelity term the authors, compare application of the maximum likelihood principle, in the form of weighted least-squares (WLSQ) and Poisson-likelihood (PL), with the use of unweighted least-squares (LSQ). RESULTS The incremental algorithms are applied to projection data generated by a simulation modeling the breast computed tomography (bCT) imaging application. The only source of data inconsistency in the bCT projections is due to noise, and a Poisson distribution is assumed for the transmitted x-ray photon intensity. In the simulations involving the incremental algorithms an ensemble of images, reconstructed from 1000 noise realizations of the x-ray transmission data, is used to estimate the image statistical properties. The WLSQ and PL incremental algorithms are seen to reduce image variance as compared to that of LSQ without sacrificing image bias. The difference is also seen at few iterations--short of numerical convergence of the corresponding optimization problems. CONCLUSIONS The proposed incremental algorithms prove effective and efficient for iterative image reconstruction in low-dose CT applications particularly with sparse-view projection data.

Investigation of optimization-based reconstruction with an image-total-variation constraint in PET.

In this work, we investigate PET-image reconstruction by using optimization-based algorithms. The work is motivated by the observation that advanced algorithms may be exploited potentially for improving PET-reconstruction quality in current applications and for enabling innovative, advanced PET-scan configurations. may be used for enabling the design of innovative PET systems. Specifically, we investigate image reconstruction from data, collected with PET-scan configuration with sparsely-populated detectors, by formulating it as an image-total-variation (TV)-constrained, Kullback-Leibler (KL)-data-divergence minimization, and then by solving the minimization with a primal-dual optimization algorithm developed by Chambolle and Pock. We carry out IEC-phantom data studies to demonstrate the potential of the reconstruction design and algorithm in enabling PET imaging configurations with reduced number of detectors.

Investigating simulation‐based metrics for characterizing linear iterative reconstruction in digital breast tomosynthesis

Purpose Simulation‐based image quality metrics are adapted and investigated for characterizing the parameter dependences of linear iterative image reconstruction for DBT. Methods Three metrics based on a 2D DBT simulation are investigated: (1) a root‐mean‐square‐error (RMSE) between the test phantom and reconstructed image, (2) a gradient RMSE where the comparison is made after taking a spatial gradient of both image and phantom, and (3) a region‐of‐interest (ROI) Hotelling observer (HO) for signal‐known‐exactly/background‐known‐exactly (SKE/BKE) and signal‐known‐exactly/background‐known‐statistically (SKE/BKS) detection tasks. Two simulation studies are performed using the aforementioned metrics, varying voxel aspect ratio, and regularization strength for two types of Tikhonov‐regularized least‐squares optimization. The RMSE metrics are applied to a 2D test phantom with resolution bar patterns at varying angles, and the ROI‐HO metric is applied to two tasks relevant to DBT: lesion detection, modeled by use of a large, low‐contrast signal, and microcalcification detection, modeled by use of a small, high‐contrast signal. The RMSE metric trends are compared with visual assessment of the reconstructed bar‐pattern phantom. The ROI‐HO metric trends are compared with 3D reconstructed images from ACR phantom data acquired with a Hologic Selenia Dimensions DBT system. Results Sensitivity of the image RMSE to mean pixel value is found to limit its applicability to the assessment of DBT image reconstruction. The image gradient RMSE is insensitive to mean pixel value and appears to track better with subjective visualization of the reconstructed bar‐pattern phantom. The ROI‐HO metric shows an increasing trend with regularization strength for both forms of Tikhonov‐regularized least‐squares; however, this metric saturates at intermediate regularization strength indicating a point of diminishing returns for signal detection. Visualization with the reconstructed ACR phantom images appear to show a similar dependence with regularization strength. Conclusions From the limited studies presented it appears that image gradient RMSE trends correspond with visual assessment better than image RMSE for DBT image reconstruction. The ROI‐HO metric for both detection tasks also appears to reflect visual trends in the ACR phantom reconstructions as a function of regularization strength. We point out, however, that the true utility of these metrics can only be assessed after amassing more data.

TV-constrained incremental algorithms for low-intensity CT image reconstruction

Low-dose X-ray computed tomography (CT) has garnered much recent interest as it provides a method to lower patient dose and simultaneously reduce scan time. In non-medical applications the possibility of preventing sample damage makes low-dose CT desirable. Reconstruction in low-dose CT poses a significant challenge due to the high level of noise in the data. Here we propose an iterative method for reconstruction which minimizes the transmission Poisson likelihood subject to a total-variation constraint. This formulation accommodates efficient methods of parameter selection because the choice of TV constraint can be guided by an image reconstructed by filtered backprojection (FBP). We apply our algorithm to low-dose synchrotron X-ray CT data from the Advanced Photon Source (APS) at Argonne National Labs (ANL) to demonstrate its potential utility. We find that the algorithm provides a means of edge-preserving regularization with the potential to generate useful images at low iteration number in low-dose CT.

Algorithm enabled TOF-PET imaging with reduced scan time

Time-of-flight (TOF) positron emission tomography (PET) has gained remarkable development recently due to the advances in scintillator, silicon photomultipliers (SiPM), and fast electronics. However, current clinical reconstruction algorithms in TOF-PET are still based on ordered-subset-expectation-maximization (OSEM) and its variants, which may face challenges in non-conventional imaging applications, such as fast imaging within short scan time. In this work, we propose an image-TV constrained optimization problem, and tailor a primal- dual algorithm for solving the problem and reconstructing images. We collect list-mode data of a Jaszczak phantom with a prototype digital TOF-PET scanner. We focus on investigating image reconstruction from data collected within reduced scan time, and thus of lower count levels. Results of the study indicate that our proposed algorithm can 1) yield image reconstruction with suppressed noise, extended axial volume coverage, and improved spatial resolution over that obtained in conventional reconstructions, and 2) yield reconstructions with potential clinical utility from data collected within shorter scan time.

Parameter selection with the Hotelling observer in linear iterative image reconstruction for breast tomosynthesis

In this work we investigate an efficient implementation of a region-of-interest (ROI) based Hotelling observer (HO) in the context of parameter optimization for detection of a rod signal at two orientations in linear iterative image reconstruction for DBT. Our preliminary results suggest that ROI-HO performance trends may be efficiently estimated by modeling only the 2D plane perpendicular to the detector and containing the X-ray source trajectory. In addition, the ROI-HO is seen to exhibit orientation dependent trends in detectability as a function of the regularization strength employed in reconstruction. To further investigate the ROI-HO performance in larger 3D system models, we present and validate an iterative methodology for calculating the ROI-HO. Lastly, we present a real data study investigating the correspondence between ROI-HO performance trends and signal conspicuity. Conspicuity of signals in real data reconstructions is seen to track well with trends in ROI-HO detectability. In particular, we observe orientation dependent conspicuity matching the orientation dependent detectability of the ROI-HO.

A Convex Reconstruction Model for X-Ray Tomographic Imaging With Uncertain Flat-Fields

Classical methods for X-ray computed tomography are based on the assumption that the X-ray source intensity is known, but in practice, the intensity is measured and hence uncertain. Under normal operating conditions, when the exposure time is sufficiently high, this kind of uncertainty typically has a negligible effect on the reconstruction quality. However, in time- or dose-limited applications such as dynamic CT, this uncertainty may cause severe and systematic artifacts known as ring artifacts. By carefully modeling the measurement process and by taking uncertainties into account, we derive a new convex model that leads to improved reconstructions despite poor quality measurements. We demonstrate the effectiveness of the methodology based on simulated and real datasets.

The randomized Kaczmarz method with mismatched adjoint

This paper investigates the randomized version of the Kaczmarz method to solve linear systems in the case where the adjoint of the system matrix is not exact—a situation we refer to as “mismatched adjoint”. We show that the method may still converge both in the over- and underdetermined consistent case under appropriate conditions, and we calculate the expected asymptotic rate of linear convergence. Moreover, we analyze the inconsistent case and obtain results for the method with mismatched adjoint as for the standard method. Finally, we derive a method to compute optimized probabilities for the choice of the rows and illustrate our findings with numerical examples.

Orientation dependent detectability of fiber-like signals in linear iterative image reconstruction for breast tomosynthesis.

We characterize the detectability of fiber-like signals in digital breast tomosynthesis (DBT) for linear iterative image reconstruction (IIR) algorithms. The detectability is investigated as a function of signal orientation and IIR regularization strength. The detectability is computed with a region-of-interest (ROI) Hotelling observer (HO) and applied to two linear IIR algorithms. Trends in detectability are compared with conspicuity of signals reconstructed in both simulation and real data studies. A common trend is observed with both algorithms in which signals oriented parallel to the detector and the plane containing the source-trajectory have lower detectability than their orthogonal counterparts at low regularization strengths. The orientation dependence is gradually reduced with increasing regularization strength. These trends in detectability are seen to match well with trends in the conspicuity of reconstructed signals in both simulation and real data studies.

Choosing anisotropic voxel dimensions in optimization-based image reconstruction for limited angle CT

Resolution of reconstructions in limited angle X-ray computed tomography (CT) is inherently anisotropic due to the limited angular range of acquired projections. This justifies the use of anisotropic voxels in limited angle image reconstruction. For analytic reconstruction algorithms, this only changes the intervals at which the reconstruction is sampled, but for optimization-based image reconstruction, changing the voxel dimensions redefines the reconstruction optimization problem and can have pronounced effects on the reconstructed image. In this work we investigate the choice of anisotropic voxel dimensions in optimization-based image reconstruction for limited angle CT. In particular, a 2D simulation study is performed to assess the optimal choice of pixel dimension in the longitudinal direction - the direction of lowest resolution. It is demonstrated that as this pixel dimension is decreased, deterioration of system matrix conditioning can lead to severe distortion in reconstructions performed with low regularization strength. This conditioning issue occurs at approximately the point where the number of pixels is equal to the number of measurements. While the distortion can be mitigated by increasing regularization, our results suggest that there are structures which are only resolvable by using even smaller voxel sizes.