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.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85951/1/Fessler21.pd

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.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85929/1/Fessler237.pd

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.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85874/1/Fessler232.pd

Sufficient Condition for Local Invertibility of Spatio-Temporal 4D B-Spline Deformations

Recent advances in medical imaging technologies have made 4D image sequences available in clinical routine. As a consequence, image registration techniques are evolving from alignment of pairs of static volumetric images to spatio-temporal registration of dynamic (4D) images. Since the elastic image registration problem is ill-posed, additional prior information or constraints are usually required to regularize the problem. This work proposes to enforce local invertibility (diffeomorphism) of 4D deformations. A novel sufficient condition for local invertibility over continuous space and time is proposed and a practical regularization prior is designed from the theory. The method has been applied to an image registration (motion tracking) of a dynamic 4D CT image sequence. Results show that using proposed regularizer leads to deformations that are more plausible for respiratory motion than the standard approach without additional temporal regularization.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85901/1/Fessler246.pd

A Simple Penalty that Encourages Local Invertibility and Considers Sliding Effects for Respiratory Motion

Nonrigid image registration is a key tool in medical imaging. Because of high degrees of freedom in nonrigid transforms, there have been many efforts to regularize the deformation based on some reasonable assumptions. Especially, motion invertibility and local tissue rigidity have been investigated as reasonable priors in image registration. There have been several papers on exploiting each constraint separately. These constraints are reasonable in respiratory motion estimation because breathing motion is invertible and there are some rigid structures such as bones. Using both constraints seems very attractive in respiratory motion registration since using invertibility prior alone usually causes bone warping in ribs. Using rigidity prior seems natural and straightforward. However, the “sliding effect” near the interface between rib cage and diaphragm makes problem harder because it is not locally invertible. In this area, invertibility and rigidity priors have opposite forces. Recently, we proposed a simple piecewise quadratic penalty that encourages the local invertibility of motions. In this work we relax this penalty function by using a Geman-type function that allows the deformation to be piecewise smooth instead of globally smooth. This allows the deformation to be discontinuous in the area of the interface between rib cage and diaphragm. With some small sacrifice of regularity, we could achieve more realistic discontinuous motion near diaphragm, better data fitting error as well as less bone warping. We applied this Geman-type function penalty only to the x- and y-direction partial derivatives of the z-direction deformation to address the sliding effect. 192 × 128 × 128 3D CT inhale and exhale images of a real patient were used to show the benefits of this new penalty method.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85922/1/Fessler238.pd

Optimization Transfer Approach to Joint Registration / Reconstruction for Motion-Compensated Image Reconstruction

Motion artifacts in image reconstruction problems can be reduced by performing image motion estimation and image reconstruction jointly using a penalized-likelihood cost function. However, updating the motion parameters by conventional gradient-based iterations can be computationally demanding due to the system model required in inverse problems. This paper describes an optimization transfer approach that leads to minimization steps for the motion parameters that have comparable complexity to those needed in image registration problems. This approach can simplify the implementation of motion-compensated image reconstruction (MCIR) methods when the motion parameters are estimated jointly with the reconstructed image.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85845/1/Fessler247.pd

Fast 4D elastic group-wise image registration. Convolutional interpolation revisited

Background and Objective:This paper proposes a new and highly efficient implementation of 3D+t groupwise registration based on the free-form deformation paradigm. Methods:Deformation is posed as a cascade of 1D convolutions, achieving great reduction in execution time for evaluation of transformations and gradients. Results:The proposed method has been applied to 4D cardiac MRI and 4D thoracic CT monomodal datasets. Results show an average runtime reduction above 90%, both in CPU and GPU executions, compared with the classical tensor product formulation. Conclusions:Our implementation, although fully developed for the metric sum of squared differences, can be extended to other metrics and its adaptation to multiresolution strategies is straightforward. Therefore, it can be extremely useful to speed up image registration procedures in different applications where high dimensional data are involved.MEC-TEC2017-82408-

Scalable Machine Learning Methods for Massive Biomedical Data Analysis.

Modern data acquisition techniques have enabled biomedical researchers to collect and analyze datasets of substantial size and complexity. The massive size of these datasets allows us to comprehensively study the biological system of interest at an unprecedented level of detail, which may lead to the discovery of clinically relevant biomarkers. Nonetheless, the dimensionality of these datasets presents critical computational and statistical challenges, as traditional statistical methods break down when the number of predictors dominates the number of observations, a setting frequently encountered in biomedical data analysis. This difficulty is compounded by the fact that biological data tend to be noisy and often possess complex correlation patterns among the predictors. The central goal of this dissertation is to develop a computationally tractable machine learning framework that allows us to extract scientifically meaningful information from these massive and highly complex biomedical datasets. We motivate the scope of our study by considering two important problems with clinical relevance: (1) uncertainty analysis for biomedical image registration, and (2) psychiatric disease prediction based on functional connectomes, which are high dimensional correlation maps generated from resting state functional MRI.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111354/1/takanori_1.pd