Group sparse reconstruction using intensity-based clustering.

Compressed sensing has been of great interest to speed up the acquisition of MR images. The k-t group sparse (k-t GS) method has recently been introduced for dynamic MR images to exploit not just the sparsity, as in compressed sensing, but also the spatial group structure in the sparse representation. k-t GS achieves higher acceleration factors compared to the conventional compressed sensing method. However, it assumes a spatial structure in the sparse representation and it requires a time consuming hard-thresholding reconstruction scheme. In this work, we propose to modify k-t GS by incorporating prior information about the sorted intensity of the signal in the sparse representation, for a more general and robust group assignment. This approach is referred to as group sparse reconstruction using intensity-based clustering. The feasibility of the proposed method is demonstrated for static 3D hyperpolarized lung images and applications with both dynamic and intensity changes, such as 2D cine and perfusion cardiac MRI, with retrospective undersampling. For all reported acceleration factors the proposed method outperforms the original compressed sensing method. Improved reconstruction over k-t GS method is demonstrated when k-t GS assumptions are not satisfied. The proposed method was also applied to cardiac cine images with a prospective sevenfold acceleration, outperforming the standard compressed sensing reconstruction.

k-t Group sparse: a method for accelerating dynamic MRI.

Compressed sensing (CS) is a data-reduction technique that has been applied to speed up the acquisition in MRI. However, the use of this technique in dynamic MR applications has been limited in terms of the maximum achievable reduction factor. In general, noise-like artefacts and bad temporal fidelity are visible in standard CS MRI reconstructions when high reduction factors are used. To increase the maximum achievable reduction factor, additional or prior information can be incorporated in the CS reconstruction. Here, a novel CS reconstruction method is proposed that exploits the structure within the sparse representation of a signal by enforcing the support components to be in the form of groups. These groups act like a constraint in the reconstruction. The information about the support region can be easily obtained from training data in dynamic MRI acquisitions. The proposed approach was tested in two-dimensional cardiac cine MRI with both downsampled and undersampled data. Results show that higher acceleration factors (up to 9-fold), with improved spatial and temporal quality, can be obtained with the proposed approach in comparison to the standard CS reconstructions.

A computationally efficient OMP-based compressed sensing reconstruction for dynamic MRI.

Compressed sensing (CS) methods in MRI are computationally intensive. Thus, designing novel CS algorithms that can perform faster reconstructions is crucial for everyday applications. We propose a computationally efficient orthogonal matching pursuit (OMP)-based reconstruction, specifically suited to cardiac MR data. According to the energy distribution of a y-f space obtained from a sliding window reconstruction, we label the y-f space as static or dynamic. For static y-f space images, a computationally efficient masked OMP reconstruction is performed, whereas for dynamic y-f space images, standard OMP reconstruction is used. The proposed method was tested on a dynamic numerical phantom and two cardiac MR datasets. Depending on the field of view composition of the imaging data, compared to the standard OMP method, reconstruction speedup factors ranging from 1.5 to 2.5 are achieved.

Whole-heart imaging using undersampled radial phase encoding (RPE) and iterative sensitivity encoding (SENSE) reconstruction.

Whole-heart isotropic nonangulated cardiac magnetic resonance (CMR) is becoming an important protocol in simplifying MRI, since it reduces the need of cumbersome planning of angulations. However the acquisition times of whole-heart MRI are prohibitive due to the large fields of view (FOVs) and the high spatial resolution required for depicting small structures and vessels. To address this problem, we propose a three-dimensional (3D) acquisition scheme that combines Cartesian sampling in the readout direction with an undersampled radial scheme in the phase-encoding plane. Different undersampling patterns were investigated in combination with an iterative sensitivity encoding (SENSE) reconstruction and a 32-channel cardiac coil. Noise amplification maps were calculated to compare the performance of the different patterns using iterative SENSE reconstruction. The radial phase-encoding (RPE) scheme was implemented on a clinical MR scanner and tested on phantoms and healthy volunteers. The proposed method exhibits better image quality even for high acceleration factors (up to 12) in comparison to Cartesian acquisitions.

Quantification of the shape of fiber tracts.

The fiber tracts generated using diffusion MRI are usually simply displayed and assessed visually for a specific clinical or medical research purpose. This paper proposes computational techniques that can be used to study the shape of the tracts and make interindividual comparisons. These methods make use of fundamental geometric invariants, such as curvatures and torsions, or Fourier descriptors, together with the link of a pair of curves. Intersubject comparisons only require that the starting and ending points of the tracts can be defined and do not require point-by-point correspondences such as obtained using image registration. Principal component analysis-based shape analysis is also investigated. The invariants are tested on simulations and in vivo datasets, and the scale dependence and noise sensitivity of the measures are assessed. The potential for these techniques to be used in neuroscience research and clinical applications is demonstrated.

Matrix description of general motion correction applied to multishot images.

Motion of an object degrades MR images, as the acquisition is time-dependent, and thus k-space is inconsistently sampled. This causes ghosts. Current motion correction methods make restrictive assumptions on the type of motions, for example, that it is a translation or rotation, and use special properties of k-space for these transformations. Such methods, however, cannot be generalized easily to nonrigid types of motions, and even rotations in multiple shots can be a problem. Here, a method is presented that can handle general nonrigid motion models. A general matrix equation gives the corrupted image from the ideal object. Thus, inversion of this system allows us to get the ideal image from the corrupted one. This inversion is possible by efficient methods mixing Fourier transforms with the conjugate gradient method. A faster but empirical inversion is discussed as well as methods to determine the motion. Simulated three-dimensional affine data and two-dimensional pulsation data and in vivo nonrigid data are used for demonstration. All examples are multishot images where the object moves between shots. The results indicate that it is now possible to correct for nonrigid types of motion that are representative of many types of patient motion, although computation times remain an issue.

A rigorous framework for diffusion tensor calculus.

In biological tissue, all eigenvalues of the diffusion tensor are assumed to be positive. Calculations in diffusion tensor MRI generally do not take into account this positive definiteness property of the tensor. Here, the space of positive definite tensors is used to construct a framework for diffusion tensor analysis. The method defines a distance function between a pair of tensors and the associated shortest path (geodesic) joining them. From this distance a method for computing tensor means, a new measure of anisotropy, and a method for tensor interpolation are derived. The method is illustrated using simulated and in vivo data.

Anisotropic noise propagation in diffusion tensor MRI sampling schemes.

The subject of this study is the controversial choice of directions in diffusion tensor MRI (DT-MRI); specifically, the numerical algebra related to this choice. In DT-MRI, apparent diffusivities are sampled in six or more directions and a least-squares equation is solved to reconstruct the diffusion tensor. Numerical characteristics of the system are considered, in particular the condition number and normal matrix, and are shown to be dependent on the relative orientation of the tensor with respect to the laboratory frame. As a consequence, noise propagation can be anisotropic. However, the class of icosahedral direction schemes is an exception, and icosahedral directions have the same condition number and normal matrix for direction encoding as the ideal scheme with an infinite number of directions. This normal matrix and its condition number are rotationally invariant. Numerical simulations show that for icosahedral schemes with 30 directions the standard deviation of the fractional anisotropy is both low and nearly independent of fiber orientation. The recommended choice of directions for a DT-MRI experiment is therefore the icosahedral set of directions with the highest number of directions achievable in the available time.

Validation of a two- to three-dimensional registration algorithm for aligning preoperative CT images and intraoperative fluoroscopy images.

We present a validation of an intensity based two- to three-dimensional image registration algorithm. The algorithm can register a CT volume to a single-plane fluoroscopy image. Four routinely acquired clinical data sets from patients who underwent endovascular treatment for an abdominal aortic aneurysm were used. Each data set was comprised of two intraoperative fluoroscopy images and a preoperative CT image. Regions of interest (ROI) were drawn around each vertebra in the CT and fluoroscopy images. Each CT image ROI was individually registered to the corresponding ROI in the fluoroscopy images. A cross validation approach was used to obtain a measure of registration consistency. Spinal movement between the preoperative and intraoperative scene was accounted for by using two fluoroscopy images. The consistency and robustness of the algorithm when using two similarity measures, pattern intensity and gradient difference, was investigated. Both similarity measures produced similar results. The consistency values were rotational errors below 0.74 degree and in-plane translational errors below 0.90 mm. These errors approximately relate to a two-dimensional projection error of 1.3 mm. The failure rate was less than 8.3% for three of the four data sets. However, for one of the data sets a much larger failure rate (28.5%) occurred.

Medical image registration.

Radiological images are increasingly being used in healthcare and medical research. There is, consequently, widespread interest in accurately relating information in the different images for diagnosis, treatment and basic science. This article reviews registration techniques used to solve this problem, and describes the wide variety of applications to which these techniques are applied. Applications of image registration include combining images of the same subject from different modalities, aligning temporal sequences of images to compensate for motion of the subject between scans, image guidance during interventions and aligning images from multiple subjects in cohort studies. Current registration algorithms can, in many cases, automatically register images that are related by a rigid body transformation (i.e. where tissue deformation can be ignored). There has also been substantial progress in non-rigid registration algorithms that can compensate for tissue deformation, or align images from different subjects. Nevertheless many registration problems remain unsolved, and this is likely to continue to be an active field of research in the future.