Lars Ruthotto

Motion Correction in Dual Gated Cardiac PET Using Mass-Preserving Image Registration

Respiratory and cardiac motion leads to image degradation in positron emission tomography (PET) studies of the human heart. In this paper we present a novel approach to motion correction based on dual gating and mass-preserving hyperelastic image registration. Thereby, we account for intensity modulations caused by the highly nonrigid cardiac motion. This leads to accurate and realistic motion estimates which are quantitatively validated on software phantom data and carried over to clinically relevant data using a hardware phantom. For patient data, the proposed method is first evaluated in a high statistic (20 min scans) dual gating study of 21 patients. It is shown that the proposed approach properly corrects PET images for dual-cardiac as well as respiratory-motion. In a second study the list mode data of the same patients is cropped to a scan time reasonable for clinical practice (3 min). This low statistic study not only shows the clinical applicability of our method but also demonstrates its robustness against noise obtained by hyperelastic regularization.

Diffeomorphic susceptibility artifact correction of diffusion-weighted magnetic resonance images

Diffusion-weighted magnetic resonance imaging is a key investigation technique in modern neuroscience. In clinical settings, diffusion-weighted imaging and its extension to diffusion tensor imaging (DTI) are usually performed applying the technique of echo-planar imaging (EPI). EPI is the commonly available ultrafast acquisition technique for single-shot acquisition with spatial encoding in a Cartesian system. A drawback of these sequences is their high sensitivity against small perturbations of the magnetic field, caused, e.g., by differences in magnetic susceptibility of soft tissue, bone and air. The resulting magnetic field inhomogeneities thus cause geometrical distortions and intensity modulations in diffusion-weighted images. This complicates the fusion with anatomical T1- or T2-weighted MR images obtained with conventional spin- or gradient-echo images and negligible distortion. In order to limit the degradation of diffusion-weighted MR data, we present here a variational approach based on a reference scan pair with reversed polarity of the phase- and frequency-encoding gradients and hence reversed distortion. The key novelty is a tailored nonlinear regularization functional to obtain smooth and diffeomorphic transformations. We incorporate the physical distortion model into a variational image registration framework and derive an accurate and fast correction algorithm. We evaluate the applicability of our approach to distorted DTI brain scans of six healthy volunteers. For all datasets, the automatic correction algorithm considerably reduced the image degradation. We show that, after correction, fusion with T1- or T2-weighted images can be obtained by a simple rigid registration. Furthermore, we demonstrate the improvement due to the novel regularization scheme. Most importantly, we show that it provides meaningful, i.e. diffeomorphic, geometric transformations, independent of the actual choice of the regularization parameters.

A Hyperelastic Regularization Energy for Image Registration

Image registration is one of the most challenging problems in image processing, where ill-posedness arises due to noisy data as well as nonuniqueness, and hence the choice of regularization is crucial. This paper presents hyperelasticity as a regularizer and introduces a new and stable numerical implementation. On one hand, hyperelastic registration is an appropriate model for large and highly nonlinear deformations, for which a linear elastic model needs to fail. On the other hand, the hyperelastic regularizer yields very regular and diffeomorphic transformations. While hyperelasticity might be considered as just an additional outstanding regularization option for some applications, it becomes inevitable for applications involving higher order distance measures like mass-preserving registration. The paper gives a short introduction to image registration and hyperelasticity. The hyperelastic image registration problem is phrased in a variational setting, and an existence proof is provided. The focus of th...

Stable architectures for deep neural networks

Deep neural networks have become invaluable tools for supervised machine learning, e.g., classification of text or images. While often offering superior results over traditional techniques and successfully expressing complicated patterns in data, deep architectures are known to be challenging to design and train such that they generalize well to new data. Important issues with deep architectures are numerical instabilities in derivative-based learning algorithms commonly called exploding or vanishing gradients. In this paper we propose new forward propagation techniques inspired by systems of Ordinary Differential Equations (ODE) that overcome this challenge and lead to well-posed learning problems for arbitrarily deep networks. The backbone of our approach is our interpretation of deep learning as a parameter estimation problem of nonlinear dynamical systems. Given this formulation, we analyze stability and well-posedness of deep learning and use this new understanding to develop new network architectures. We relate the exploding and vanishing gradient phenomenon to the stability of the discrete ODE and present several strategies for stabilizing deep learning for very deep networks. While our new architectures restrict the solution space, several numerical experiments show their competitiveness with state-of-the-art networks.

High-resolution diffusion kurtosis imaging at 3T enabled by advanced post-processing.

Diffusion Kurtosis Imaging (DKI) is more sensitive to microstructural differences and can be related to more specific micro-scale metrics (e.g., intra-axonal volume fraction) than diffusion tensor imaging (DTI), offering exceptional potential for clinical diagnosis and research into the white and gray matter. Currently DKI is acquired only at low spatial resolution (2–3 mm isotropic), because of the lower signal-to-noise ratio (SNR) and higher artifact level associated with the technically more demanding DKI. Higher spatial resolution of about 1 mm is required for the characterization of fine white matter pathways or cortical microstructure. We used restricted-field-of-view (rFoV) imaging in combination with advanced post-processing methods to enable unprecedented high-quality, high-resolution DKI (1.2 mm isotropic) on a clinical 3T scanner. Post-processing was advanced by developing a novel method for Retrospective Eddy current and Motion ArtifacT Correction in High-resolution, multi-shell diffusion data (REMATCH). Furthermore, we applied a powerful edge preserving denoising method, denoted as multi-shell orientation-position-adaptive smoothing (msPOAS). We demonstrated the feasibility of high-quality, high-resolution DKI and its potential for delineating highly myelinated fiber pathways in the motor cortex. REMATCH performs robustly even at the low SNR level of high-resolution DKI, where standard EC and motion correction failed (i.e., produced incorrectly aligned images) and thus biased the diffusion model fit. We showed that the combination of REMATCH and msPOAS increased the contrast between gray and white matter in mean kurtosis (MK) maps by about 35% and at the same time preserves the original distribution of MK values, whereas standard Gaussian smoothing strongly biases the distribution.

A variational approach for the correction of field-inhomogeneities in EPI sequences

A wide range of medical applications in clinic and research exploit images acquired by fast magnetic resonance imaging (MRI) sequences such as echo-planar imaging (EPI), e.g. functional MRI (fMRI) and diffusion tensor MRI (DT-MRI). Since the underlying assumption of homogeneous static fields fails to hold in practical applications, images acquired by those sequences suffer from distortions in both geometry and intensity. In the present paper we propose a new variational image registration approach to correct those EPI distortions. To this end we acquire two reference EPI images without diffusion sensitizing and with inverted phase encoding gradients in order to calculate a rectified image. The idea is to apply a specialized registration scheme which compensates for the characteristical direction dependent image distortions. In addition the proposed scheme automatically corrects for intensity distortions. This is done by evoking a problem dependent distance measure incorporated into a variational setting. We adjust not only the image volumes but also the phase encoding direction after correcting for patients head-movements between the acquisitions. Finally, we present first successful results of the new algorithm for the registration of DT-MRI datasets.

Hyperelastic susceptibility artifact correction of DTI in SPM

Echo Planar Imaging (EPI) is a MRI acquisition technique that is the backbone of widely used investigation techniques in neuroscience like, e.g., Diffusion Tensor Imaging (DTI). While EPI offers considerable reduction of the acquisition time one major drawback is its high sensitivity to susceptibility artifacts. Susceptibility differences between soft tissue, bone and air cause geometrical distortions and intensity modulations of the EPI data. These susceptibility artifacts severely complicate the fusion of micro-structural information acquired with EPI and conventionally acquired structural information. In this paper, we introduce a new tool for hyperelastic susceptibility correction of DTI data (HySCO) that is integrated into the Statistical Parametric Mapping (SPM) software as a toolbox. Our new correction pipeline is based on two datasets acquired with reversed phase encoding gradients. For the correction, we integrated the variational image registration approach by Ruthotto et al. 2007 into the SPM batch mode. We briefly review the model, discuss involved parameter settings and exemplarily demonstrate the effectiveness of HySCO on a human brain DTI dataset.

Motion correction of cardiac PET using mass-preserving registration

Cardiac motion leads to image quality degradation in positron emission tomography (PET). In the literature gated listmode acquisition along with motion estimation techniques, such as optical flow or image registration, proved successful for respiratory motion correction. Cardiac gated PET images, however, are affected by the partial volume effect (PVE) which is expressed in strongly varying local intensities. This fact complicates the motion estimation process. To overcome this problem, the mass-preserving nature of PET images is identified and included into the image registration problem. We show that our mass-preserving registration approach allows cardiac motion correction with high accuracy due to realistic motion estimates. In addition, neglecting the mass-preserving property of PET is proven to entail unrealistic results.

jInv--a Flexible Julia Package for PDE Parameter Estimation

Estimating parameters of Partial Differential Equations (PDEs) from noisy and indirect measurements often requires solving ill-posed inverse problems. These so called parameter estimation or inverse medium problems arise in a variety of applications such as geophysical, medical imaging, and nondestructive testing. Their solution is computationally intense since the underlying PDEs need to be solved numerous times until the reconstruction of the parameters is sufficiently accurate. Typically, the computational demand grows significantly when more measurements are available, which poses severe challenges to inversion algorithms as measurement devices become more powerful. In this paper we present jInv, a flexible framework and open source software that provides parallel algorithms for solving parameter estimation problems with many measurements. Being written in the expressive programming language Julia, jInv is portable, easy to understand and extend, cross-platform tested, and well-documented. It provides novel parallelization schemes that exploit the inherent structure of many parameter estimation problems and can be used to solve multiphysics inversion problems as is demonstrated using numerical experiments motivated by geophysical imaging.

A Lagrangian Gauss--Newton--Krylov Solver for Mass- and Intensity-Preserving Diffeomorphic Image Registration

We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized. Our solver supports both stationary and non-stationary (i.e., transient or time-dependent) velocity fields. As transformation models, we consider both the transport equation (assuming intensities are preserved during the deformation) and the continuity equation (assuming mass-preservation). We consider the reduced form of the optimal control problem and solve the resulting unconstrained optimization problem using a discretize-then-optimize approach. A key contribution is the elimination of the PDE constraint using a Lagrangian hyperbolic PDE solver. Lagrangian methods rely on the concept of characteristic curves. We approximate these curves using a fourth-order Runge-Kutta method. We also present an efficient algorithm for computing the derivatives of the final state of the system with respect to the velocity field. This allows us to use fast Gauss-Newton based methods. We present quickly converging iterative linear solvers using spectral preconditioners that render the overall optimization efficient and scalable. Our method is embedded into the image registration framework FAIR and, thus, supports the most commonly used similarity measures and regularization functionals. We demonstrate the potential of our new approach using several synthetic and real world test problems with up to 14.7 million degrees of freedom.