A barrier to the adoption of non-Cartesian parallel magnetic resonance imaging for real-time applications has been the times required for the image reconstructions. These times have exceeded the underlying acquisition time thus preventing real-time display of the acquired images. We present a reconstruction algorithm for commodity graphics hardware (GPUs) to enable real time reconstruction of sensitivity encoded radial imaging (radial SENSE). We demonstrate that a radial profile order based on the golden ratio facilitates reconstruction from an arbitrary number of profiles. This allows the temporal resolution to be adjusted on the fly. A user adaptable regularization term is also included and, particularly for highly undersampled data, used to interactively improve the reconstruction quality. Each reconstruction is fully self-contained from the profile stream, i.e., the required coil sensitivity profiles, sampling density compensation weights, regularization terms, and noise estimates are computed in real-time from the acquisition data itself. The reconstruction implementation is verified using a steady state free precession (SSFP) pulse sequence and quantitatively evaluated. Three applications are demonstrated; real-time imaging with real-time SENSE 1) or k- t SENSE 2) reconstructions, and 3) offline reconstruction with interactive adjustment of reconstruction settings.

We present an adaptive parametrization scheme for dynamic mesh refinement in the application of parametric image registration. The scheme is based on a refinement measure ensuring that the control points give an efficient representation of the warp fields, in terms of minimizing the registration cost function. In the current work we introduce multivariate B-splines as a novel alternative to the widely used tensor B-splines enabling us to make efficient use of the derived measure.The multivariate B-splines of order n are Cn-1smooth and are based on Delaunay configurations of arbitrary 2D or 3D control point sets. Efficient algorithms for finding the configurations are presented, and B-splines are through their flexibility shown to feature several advantages over the tensor B-splines. In spite of efforts to make the tensor product B-splines more flexible, the knots are still bound to reside on a regular grid. In contrast, by efficient non- constrained placement of the knots, the multivariate B- splines are shown to give a good representation of inho- mogeneous objects in natural settings. The wide applicability of the method is illustrated through its application on medical data and for optical flow estimation.

Nonlinear registration is mostly performed after initialization by a global, linear transformation (in this work, we focus on similarity transformations), computed by a linear registration method. For the further processing of the results, it is mostly assumed that this preregistration step completely removes the respective linear transformation. However, we show that in deformable settings, this is not the case. As a consequence, a significant linear component is still existent in the deformation computed by the nonlinear registration algorithm. For construction of statistical shape models (SSM) from deformations, this is an unwanted property: SSMs should not contain similarity transformations, since these do not capture information about shape. We propose a method which performs an a posteriori extraction of a similarity transformation from a given nonlinear deformation field, and we use the processed fields as input for SSM construction. For computation of minimal displacements, a closed-form solution minimizing the squared Euclidean norm of the displacement field subject to similarity parameters is used. Experiments on real inter-subject data and on a synthetic example show that the theoretically justified removal of the similarity component by the proposed method has a large influence on the shape model and significantly improves the results.

We present a fast parallel algorithm to compute the nonequispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform as it was previously its most time consuming part. We describe the performance for two common sample distributions in medical imaging (radial and spiral trajectories), and for different convolution kernels as these parameters all influence the speed of the algorithm. The GPU-accelerated convolution is up to 85 times faster as our reference, the open source NFFT library on a state-of-the-art 64 bit CPU. The accuracy of the proposed GPU implementation was quantitatively evaluated at the various settings. To illustrate the applicability of the transform in medical imaging, in which it is also known as gridding, we look specifically at non-Cartesian magnetic resonance imaging and reconstruct both a numerical phantom and an in vivo cardiac image.

In this paper we present a new method for constructing diffeomorphic statistical deformation models in arbitrary dimensional images with a nonlinear generative model and a linear parameter space. Our deformation model is a modified version of the diffeomorphic model introduced by Cootes et al. The modifications ensure that no boundary restriction has to be enforced on the parameter space to prevent folds or tears in the deformation field. For straightforward statistical analysis, principal component analysis and sparse methods, we assume that the parameters for a class of deformations lie on a linear manifold and that the distance between two deformations are given by the metric introduced by the L2-norm in the parameter space. The chosen L2-norm is shown to have a clear and intuitive interpretation on the usual nonlinear manifold. Our model is validated on a set of MR images of corpus callosum with ground truth in form of manual expert annotations, and compared to Cootes's model. We anticipate applications in unconstrained diffeomorphic synthesis of images, e.g. for tracking, segmentation, registration or classification purposes.