Unified Supervised-Unsupervised (SUPER) Learning for X-ray CT Image Reconstruction

Traditional model-based image reconstruction (MBIR) methods combine forward and noise models with simple object priors. Recent machine learning methods for image reconstruction typically involve supervised learning or unsupervised learning, both of which have their advantages and disadvantages. In this work, we propose a unified supervised-unsupervised (SUPER) learning framework for X-ray computed tomography (CT) image reconstruction. The proposed learning formulation combines both unsupervised learning-based priors (or even simple analytical priors) together with (supervised) deep network-based priors in a unified MBIR framework based on a fixed point iteration analysis. The proposed training algorithm is also an approximate scheme for a bilevel supervised training optimization problem, wherein the network-based regularizer in the lower-level MBIR problem is optimized using an upper-level reconstruction loss. The training problem is optimized by alternating between updating the network weights and iteratively updating the reconstructions based on those weights. We demonstrate the learned SUPER models' efficacy for low-dose CT image reconstruction, for which we use the NIH AAPM Mayo Clinic Low Dose CT Grand Challenge dataset for training and testing. In our experiments, we studied different combinations of supervised deep network priors and unsupervised learning-based or analytical priors. Both numerical and visual results show the superiority of the proposed unified SUPER methods over standalone supervised learning-based methods, iterative MBIR methods, and variations of SUPER obtained via ablation studies. We also show that the proposed algorithm converges rapidly in practice.Comment: 15 pages, 16 figures, submitted journal pape

Basis Vector Model Method for Proton Stopping Power Estimation using Dual-Energy Computed Tomography

Accurate estimation of the proton stopping power ratio (SPR) is important for treatment planning and dose prediction for proton beam therapy. The state-of-the-art clinical practice for estimating patient-specific SPR distributions is the stoichiometric calibration method using single-energy computed tomography (SECT) images, which in principle may introduce large intrinsic uncertainties into estimation results. One major factor that limits the performance of SECT-based methods is the Hounsfield unit (HU) degeneracy in the presence of tissue composition variations. Dual-energy computed tomography (DECT) has shown the potential of reducing uncertainties in proton SPR prediction via scanning the patient with two different source energy spectra. Numerous methods have been studied to estimate the SPR by dual-energy CT DECT techniques using either image-domain or sinogram-domain decomposition approaches. In this work, we implement and evaluate a novel DECT approach for proton SPR mapping, which integrates image reconstruction and material characterization using a joint statistical image reconstruction (JSIR) method based on a linear basis vector model (BVM). This method reconstructs two images of material parameters simultaneously from the DECT measurement data and then uses them to predict the electron densities and the mean excitation energies, which are required by the Bethe equation for computing proton SPR. The proposed JSIR-BVM method is first compared with image-domain and sinogram-domain decomposition approaches based on three available SPR models including the BVM in a well controlled simulation framework that is representative of major uncertainty sources existing in practice. The intrinsic SPR modeling accuracy of the three DECT-SPR models is validated via theoretical computed radiological quantities for various reference human tissues. The achievable performances of the investigated methods in the presence of image formation uncertainties are evaluated using synthetic DECT transmission sinograms of virtual cylindrical phantoms and virtual patients, which consist of reference human tissues with known densities and compositions. The JSIR-BVM method is then experimentally commissioned using the DECT measurement data acquired on a Philips Brilliance Big Bore CT scanner at 90 kVp and 140 kVp for two phantoms of different sizes, each of which contains 12 different soft and bony tissue surrogates. An image-domain decomposition method that utilizes the two HU images reconstructed via the scanner\u27s software is implemented for comparison The JSIR-BVM method outperforms the other investigated methods in both the simulation and experimental settings. Although all investigated DECT-SPR models support low intrinsic modeling errors (i.e., less than 0.2% RMS errors for reference human tissues), the achievable accuracy of the image- and sinogram-domain methods is limited by the image formation uncertainties introduced by the reconstruction and decomposition processes. In contrast, by taking advantage of an accurate polychromatic CT data model and a joint DECT statistical reconstruction algorithm, the JSIR-BVM method accounts for both systematic bias and random noise in the acquired DECT measurement data. Therefore, the JSIR-BVM method achieves much better accuracy and precision on proton SPR estimation compared to the image- and sinogram-domain methods for various materials and object sizes, with an overall RMS-of-mean error of 0.4% and a maximum absolute-mean error of 0.7% for test samples in the experimental setting. The JSIR-BVM method also reduces the pixel-wise random variation by 4-fold to 6-fold within homogeneous regions compared to the image- and sinogram-domain methods while exhibiting relatively higher spatial resolution. The results suggest that the JSIR-BVM method has the potential for better SPR prediction in clinical settings

Multi-dimensional extension of the alternating minimization algorithm in x-ray computed tomography

X-ray computed tomography (CT) is an important and effective tool in medical and industrial imaging applications. The state-of-the-art methods to reconstruct CT images have had great development but also face challenges. This dissertation derives novel algorithms to reduce bias and metal artifacts in a wide variety of imaging modalities and increase performance in low-dose scenarios. The most widely available CT systems still use the single-energy CT (SECT), which is good at showing the anatomic structure of the patient body. However, in SECT image reconstruction, energy-related information is lost. In applications like radiation treatment planning and dose prediction, accurate energy-related information is needed. Spectral CT has shown the potential to extract energy-related information. Dual-energy CT (DECT) is the first successful implementation of spectral CT. By using two different spectra, the energy-related information can be exported by reconstructing basis-material images. A sinogram-based decomposition method has shown good performance in clinical applications. However, when the x-ray dose level is low, the sinogram-based decomposition methods generate biased estimates. The bias increases rapidly when the dose level decreases. The bias comes from the ill-posed statistical model in the sinogram-decomposition method. To eliminate the bias in low-dose cases, a joint statistical image reconstruction (JSIR) method using the dual-energy alternating minimization (DEAM) algorithm is proposed. By correcting the ill-posed statistical model, a relative error as high as 15% in the sinogram-based decomposition method can be reduced to less than 1% with DEAM, which is an approximately unbiased estimation. Photon counting CT (PCCT) is an emerging CT technique that also can resolve the energy information. By using photon-counting detectors (PCD), PCCT keeps track of the energy of every photon received. Though PCDs have an entirely different physical performance from the energy-integrating detectors used in DECT, the problem of biased estimation with the sinogram-decomposition method remains. Based on DEAM, a multi-energy alternating minimization (MEAM) algorithm for PCCT is proposed. In the simulation experiments, MEAM can effectively reduce bias by more than 90%. Metal artifacts have been a concern since x-ray CT came into medical imaging. When there exist dense or metal materials in the scanned object, the image quality may suffer severe artifacts. The auxiliary sinogram alternating minimization (ASAM) algorithm is proposed to take advantages of two major categories of methods to deal with metal artifacts: the pre-processing method and statistical image reconstruction. With a phantom experiment, it has been shown that ASAM has better metal-artifact reduction performance compared with the current methods. A significant challenge in security imaging is that due to the large geometry and power consumption, low photon statistics are detected. The detected photons suffer high noise and heavy artifacts. Image-domain regularized iterative reconstruction algorithms can reduce the noise but also result in biased reconstruction. A wavelet-domain penalty is introduced which does not bring in bias and can effectively eliminate steaking artifacts. By combining the image-domain and wavelet-domain penalty, the image quality can be further improved. When the wavelet penalty is used, a concern is that no empirical way, like in the image-domain penalty, is available to determine the penalty weight. Laplace variational automatic relevance determination (Lap-VARD) method is proposed to reconstruct the image and optimal penalty weight choice at the same time