Se Young Chun

Nonrigid PET motion compensation in the lower abdomen using simultaneous tagged‐MRI and PET imaging

PURPOSE We propose a novel approach for PET respiratory motion correction using tagged-MRI and simultaneous PET-MRI acquisitions. METHODS We use a tagged-MRI acquisition followed by motion tracking in the phase domain to estimate the nonrigid deformation of biological tissues during breathing. In order to accurately estimate motion even in the presence of noise and susceptibility artifacts, we regularize the traditional HARP tracking strategy using a quadratic roughness penalty on neighboring displacement vectors (R-HARP). We then incorporate the motion fields estimated with R-HARP in the system matrix of an MLEM PET reconstruction algorithm formulated both for sinogram and list-mode data representations. This approach allows reconstruction of all detected coincidences in a single image while modeling the effect of motion both in the emission and the attenuation maps. At present, tagged-MRI does not allow estimation of motion in the lungs and our approach is therefore limited to motion correction in soft tissues. Since it is difficult to assess the accuracy of motion correction approaches in vivo, we evaluated the proposed approach in numerical simulations of simultaneous PET-MRI acquisitions using the NCAT phantom. We also assessed its practical feasibility in PET-MRI acquisitions of a small deformable phantom that mimics the complex deformation pattern of a lung that we imaged on a combined PET-MRI brain scanner. RESULTS Simulations showed that the R-HARP tracking strategy accurately estimated realistic respiratory motion fields for different levels of noise in the tagged-MRI simulation. In simulations of tumors exhibiting increased uptake, contrast estimation was 20% more accurate with motion correction than without. Signal-to-noise ratio (SNR) was more than 100% greater when performing motion-corrected reconstruction which included all counts, compared to when reconstructing only coincidences detected in the first of eight gated frames. These results were confirmed in our proof-of-principle PET-MRI acquisitions, indicating that our motion correction strategy is accurate, practically feasible, and is therefore ready to be tested in vivo. CONCLUSIONS This work shows that PET motion correction using motion fields measured with tagged-MRI in simultaneous PET-MRI acquisitions can be made practical for clinical application and that doing so has the potential to remove motion blur in whole-body PET studies of the torso.

A Simple Regularizer for B-spline Nonrigid Image Registration That Encourages Local Invertibility

Nonrigid image registration is an important task for many medical imaging applications. In particular, for radiation oncology it is desirable to track respiratory motion for thoracic cancer treatment. B-splines are convenient for modeling nonrigid deformations, but ensuring invertibility can be a challenge. This paper describes sufficient conditions for local invertibility of deformations based on B-spline bases. These sufficient conditions can be used with constrained optimization to enforce local invertibility. We also incorporate these conditions into nonrigid image registration methods based on a simple penalty approach that encourages diffeomorphic deformations. Traditional Jacobian penalty methods penalize negative Jacobian determinant values only at grid points. In contrast, our new method enforces a sufficient condition for invertibility directly on the deformation coefficients to encourage invertibility globally over a 3-D continuous domain. The proposed penalty approach requires substantially less compute time than Jacobian penalties per iteration.

Noise Properties of Motion-Compensated Tomographic Image Reconstruction Methods

Motion-compensated image reconstruction (MCIR) methods incorporate motion models to improve image quality in the presence of motion. MCIR methods differ in terms of how they use motion information and they have been well studied separately. However, there have been less theoretical comparisions of different MCIR methods. This paper compares the theoretical noise properties of three popular MCIR methods assuming known nonrigid motion. We show the relationship among three MCIR methods-motion-compensated temporal regularization (MTR), the parametric motion model (PMM), and post-reconstruction motion correction (PMC)-for penalized weighted least square cases. These analyses show that PMM and MTR are matrix-weighted sums of all registered image frames, while PMC is a scalar-weighted sum. We further investigate the noise properties of MCIR methods with Poisson models and quadratic regularizers by deriving accurate and fast variance prediction formulas using an “analytical approach.” These theoretical noise analyses show that the variances of PMM and MTR are lower than or comparable to the variance of PMC due to the statistical weighting. These analyses also facilitate comparisons of the noise properties of different MCIR methods, including the effects of different quadratic regularizers, the influence of the motion through its Jacobian determinant, and the effect of assuming that total activity is preserved. Two-dimensional positron emission tomography simulations demonstrate the theoretical results.

Correction for Collimator-Detector Response in SPECT Using Point Spread Function Template

Compensating for the collimator-detector response (CDR) in SPECT is important for accurate quantification. The CDR consists of both a geometric response and a septal penetration and collimator scatter response. The geometric response can be modeled analytically and is often used for modeling the whole CDR if the geometric response dominates. However, for radionuclides that emit medium or high-energy photons such as I-131, the septal penetration and collimator scatter response is significant and its modeling in the CDR correction is important for accurate quantification. There are two main methods for modeling the depth-dependent CDR so as to include both the geometric response and the septal penetration and collimator scatter response. One is to fit a Gaussian plus exponential function that is rotationally invariant to the measured point source response at several source-detector distances. However, a rotationally-invariant exponential function cannot represent the star-shaped septal penetration tails in detail. Another is to perform Monte-Carlo (MC) simulations to generate the depth-dependent point spread functions (PSFs) for all necessary distances. However, MC simulations, which require careful modeling of the SPECT detector components, can be challenging and accurate results may not be available for all of the different SPECT scanners in clinics. In this paper, we propose an alternative approach to CDR modeling. We use a Gaussian function plus a 2-D B-spline PSF template and fit the model to measurements of an I-131 point source at several distances. The proposed PSF-template-based approach is nearly non-parametric, captures the characteristics of the septal penetration tails, and minimizes the difference between the fitted and measured CDR at the distances of interest. The new model is applied to I-131 SPECT reconstructions of experimental phantom measurements, a patient study, and a MC patient simulation study employing the XCAT phantom. The proposed model yields up to a 16.5 and 10.8% higher recovery coefficient compared to the results with the conventional Gaussian model and the Gaussian plus exponential model, respectively.

Spatial Resolution Properties of Motion-Compensated Tomographic Image Reconstruction Methods

Many motion-compensated image reconstruction (MCIR) methods have been proposed to correct for subject motion in medical imaging. MCIR methods incorporate motion models to improve image quality by reducing motion artifacts and noise. This paper analyzes the spatial resolution properties of MCIR methods and shows that nonrigid local motion can lead to nonuniform and anisotropic spatial resolution for conventional quadratic regularizers. This undesirable property is akin to the known effects of interactions between heteroscedastic log-likelihoods (e.g., Poisson likelihood) and quadratic regularizers. This effect may lead to quantification errors in small or narrow structures (such as small lesions or rings) of reconstructed images. This paper proposes novel spatial regularization design methods for three different MCIR methods that account for known nonrigid motion. We develop MCIR regularization designs that provide approximately uniform and isotropic spatial resolution and that match a user-specified target spatial resolution. Two-dimensional PET simulations demonstrate the performance and benefits of the proposed spatial regularization design methods.

Joint image reconstruction and nonrigid motion estimation with a simple penalty that encourages local invertibility

Motion artifacts are a significant issue in medical image reconstruction. There are many methods for incorporating motion information into image reconstruction. However, there are fewer studies that focus on deformation regularization in motioncompensated image reconstruction. The usual choice for deformation regularization has been penalty functions based on the assumption that tissues are elastic. In the image registration field, there have been some methods proposed that impose deformation invertibility using constraints or regularization, assuming that organ motions are invertible transformations. However, most of these methods require very high memory or computation complexity, making them poorly suited for dealing with multiple images simultaneously in motion-compensated image reconstruction. Recently we proposed an image registration method that uses a simple penalty function based on a sufficient condition for the local invertibility of deformations.1 That approach encourages local invertibility in a fast and memory-efficient way. This paper investigates the use of that regularization method for the more challenging problem of joint image reconstruction and nonrigid motion estimation. A 2D PET simulation (based on realistic motion from real patient CT data) demonstrates the benefits of such motion regularization for joint image reconstruction/registration.

Alternating Direction Method of Multiplier for Tomography With Nonlocal Regularizers

The ordered subset expectation maximization (OSEM) algorithm approximates the gradient of a likelihood function using a subset of projections instead of using all projections so that fast image reconstruction is possible for emission and transmission tomography such as SPECT, PET, and CT. However, OSEM does not significantly accelerate reconstruction with computationally expensive regularizers such as patch-based nonlocal (NL) regularizers, because the regularizer gradient is evaluated for every subset. We propose to use variable splitting to separate the likelihood term and the regularizer term for penalized emission tomographic image reconstruction problem and to optimize it using the alternating direction method of multiplier (ADMM). We also propose a fast algorithm to optimize the ADMM parameter based on convergence rate analysis. This new scheme enables more sub-iterations related to the likelihood term. We evaluated our ADMM for 3-D SPECT image reconstruction with a patch-based NL regularizer that uses the Fair potential function. Our proposed ADMM improved the speed of convergence substantially compared to other existing methods such as gradient descent, EM, and OSEM using De Pierros approach, and the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm.

Post-reconstruction non-local means filtering methods using CT side information for quantitative SPECT

Quantitative SPECT techniques are important for many applications including internal emitter therapy dosimetry where accurate estimation of total target activity and activity distribution within targets are both potentially important for dose–response evaluations. We investigated non-local means (NLM) post-reconstruction filtering for accurate I-131 SPECT estimation of both total target activity and the 3D activity distribution. We first investigated activity estimation versus number of ordered-subsets expectation–maximization (OSEM) iterations. We performed simulations using the XCAT phantom with tumors containing a uniform and a non-uniform activity distribution, and measured the recovery coefficient (RC) and the root mean squared error (RMSE) to quantify total target activity and activity distribution, respectively. We observed that using more OSEM iterations is essential for accurate estimation of RC, but may or may not improve RMSE. We then investigated various post-reconstruction filtering methods to suppress noise at high iteration while preserving image details so that both RC and RMSE can be improved. Recently, NLM filtering methods have shown promising results for noise reduction. Moreover, NLM methods using high-quality side information can improve image quality further. We investigated several NLM methods with and without CT side information for I-131 SPECT imaging and compared them to conventional Gaussian filtering and to unfiltered methods. We studied four different ways of incorporating CT information in the NLM methods: two known (NLM CT-B and NLM CT-M) and two newly considered (NLM CT-S and NLM CT-H). We also evaluated the robustness of NLM filtering using CT information to erroneous CT. NLM CT-S and NLM CT-H yielded comparable RC values to unfiltered images while substantially reducing RMSE. NLM CT-S achieved −2.7 to 2.6% increase of RC compared to no filtering and NLM CT-H yielded up to 6% decrease in RC while other methods yielded lower RCs than them: Gaussian filtering (up to 11.8% decrease in RC), NLM method without CT (up to 9.5% decrease in RC), and NLM CT-M and NLM CT-B (up to 19.4% decrease in RC). NLM CT-S and NLM CT-H achieved 8.2 to 33.9% and −0.9 to 36% decreased RMSE on tumors compared to no filtering respectively while other methods yielded less reduced or increased RMSE: Gaussian filtering (up to 7.9% increase in RMSE), NLM method without CT (up to 18.3% increase in RMSE), and NLM CT-M and NLM CT-B (up to 31.5% increase in RMSE). NLM CT-S and NLM CT-H also yielded images with tumor shapes that better-matched the true shapes than other methods. All NLM methods using CT information were robust to small misregistration between SPECT and CT, but NLM CT-S and NLM CT-H were more sensitive than NLM CT-M and NLM CT-B to missing CT information.

Non-local means methods using CT side information for I-131 SPECT image reconstruction

Recently, non-local means (NLM) methods for both image denoising and inverse problems have shown promising results in image processing and medical imaging. Moreover, some researchers have also shown that using additional information with low noise and/or high resolution for these problems can improve the image quality further. We investigated several NLM methods including NLM filters and NLM regularizers with and without CT side information for 1-131 SPECT image reconstruction. We compared two different ways to incorporate CT side information in the NLM filtering methods. We also propose a new way of incorporating side information in the NLM reconstruction method. XCAT simulation results with two uniform tumors (72 cc, 11 cc) show that the NLM filtering method with CT side information decreased the root mean square error (RMSE) up to 18.6% as compared to unregularized method. Our proposed NLM-based regularizers in iterative image reconstructions with CT side information also yielded up to 29.2% better RMSE and up to 18.1 % better recovery coefficient than unregularized reconstruction.

Regularized methods for topology-preserving smooth nonrigid image registration using B-spline basis

B-splines are a convenient tool for nonrigid registration, but ensuring invertibility can be challenge. This paper describes a new penalty method that is devised to enforce a sufficient condition for local invertibility and smoothness of nth order B-spline based deformations. Traditional direct Jacobian penalty methods penalize negative Jacobian determinant values only at grid points. In contrast, our new penalty method enforces the sufficient condition for invertibility directly on the B-spline coefficients by using a modified quadratic penalty function so that it enforces invertibility globally over a 3D continuous domain. This approach also saves computation time and memory compared to using Jacobian determinant values. We apply this method to 3D CT images of a thorax at inhale and exhale.