Autocalibrating and Calibrationless Parallel Magnetic Resonance Imaging as a Bilinear Inverse Problem

Modern reconstruction methods for magnetic resonance imaging (MRI) exploit the spatially varying sensitivity profiles of receive-coil arrays as additional source of information. This allows to reduce the number of time-consuming Fourier-encoding steps by undersampling. The receive sensitivities are a priori unknown and influenced by geometry and electric properties of the (moving) subject. For optimal results, they need to be estimated jointly with the image from the same undersampled measurement data. Formulated as an inverse problem, this leads to a bilinear reconstruction problem related to multi-channel blind deconvolution. In this work, we will discuss some recently developed approaches for the solution of this problem.Comment: 3 pages, 3 figures, 12th International Conference on Sampling Theory and Applications, Tallinn 201

A Multi-GPU Programming Library for Real-Time Applications

We present MGPU, a C++ programming library targeted at single-node multi-GPU systems. Such systems combine disproportionate floating point performance with high data locality and are thus well suited to implement real-time algorithms. We describe the library design, programming interface and implementation details in light of this specific problem domain. The core concepts of this work are a novel kind of container abstraction and MPI-like communication methods for intra-system communication. We further demonstrate how MGPU is used as a framework for porting existing GPU libraries to multi-device architectures. Putting our library to the test, we accelerate an iterative non-linear image reconstruction algorithm for real-time magnetic resonance imaging using multiple GPUs. We achieve a speed-up of about 1.7 using 2 GPUs and reach a final speed-up of 2.1 with 4 GPUs. These promising results lead us to conclude that multi-GPU systems are a viable solution for real-time MRI reconstruction as well as signal-processing applications in general.Comment: 15 pages, 10 figure

Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space

In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more efficient non-Cartesian sampling schemes. As shown here, reconstruction from samples at arbitrary locations can be understood as approximation of vector-valued functions from the acquired samples and formulated using a Reproducing Kernel Hilbert Space (RKHS) with a matrix-valued kernel defined by the spatial sensitivities of the receive coils. This establishes a formal connection between approximation theory and parallel imaging. Theoretical tools from approximation theory can then be used to understand reconstruction in k-space and to extend the analysis of the effects of samples selection beyond the traditional g-factor noise analysis to both noise amplification and approximation errors. This is demonstrated with numerical examples.Comment: 28 pages, 7 figure

Fast T2 Mapping with Improved Accuracy Using Undersampled Spin-echo MRI and Model-based Reconstructions with a Generating Function

A model-based reconstruction technique for accelerated T2 mapping with improved accuracy is proposed using undersampled Cartesian spin-echo MRI data. The technique employs an advanced signal model for T2 relaxation that accounts for contributions from indirect echoes in a train of multiple spin echoes. An iterative solution of the nonlinear inverse reconstruction problem directly estimates spin-density and T2 maps from undersampled raw data. The algorithm is validated for simulated data as well as phantom and human brain MRI at 3 T. The performance of the advanced model is compared to conventional pixel-based fitting of echo-time images from fully sampled data. The proposed method yields more accurate T2 values than the mono-exponential model and allows for undersampling factors of at least 6. Although limitations are observed for very long T2 relaxation times, respective reconstruction problems may be overcome by a gradient dampening approach. The analytical gradient of the utilized cost function is included as Appendix.Comment: 10 pages, 7 figure

Joint T1 and T2 Mapping with Tiny Dictionaries and Subspace-Constrained Reconstruction

Purpose: To develop a method that adaptively generates tiny dictionaries for joint T1-T2 mapping. Theory: This work breaks the bond between dictionary size and representation accuracy (i) by approximating the Bloch-response manifold by piece-wise linear functions and (ii) by adaptively refining the sampling grid depending on the locally-linear approximation error. Methods: Data acquisition was accomplished with use of an 2D radially sampled Inversion-Recovery Hybrid-State Free Precession sequence. Adaptive dictionaries are generated with different error tolerances and compared to a heuristically designed dictionary. Based on simulation results, tiny dictionaries were used for T1-T2 mapping in phantom and in vivo studies. Reconstruction and parameter mapping were performed entirely in subspace. Results: All experiments demonstrated excellent agreement between the proposed mapping technique and template matching using heuristic dictionaries. Conclusion: Adaptive dictionaries in combination with manifold projection allow to reduce the necessary dictionary sizes by one to two orders of magnitude

Suppression of MRI Truncation Artifacts Using Total Variation Constrained Data Extrapolation

The finite sampling of k-space in MRI causes spurious image artifacts, known as Gibbs ringing, which result from signal truncation at the border of k-space. The effect is especially visible for acquisitions at low resolution and commonly reduced by filtering at the expense of image blurring. The present work demonstrates that the simple assumption of a piecewise-constant object can be exploited to extrapolate the data in k-space beyond the measured part. The method allows for a significant reduction of truncation artifacts without compromising resolution. The assumption translates into a total variation minimization problem, which can be solved with a nonlinear optimization algorithm. In the presence of substantial noise, a modified approach offers edge-preserving denoising by allowing for slight deviations from the measured data in addition to supplementing data. The effectiveness of these methods is demonstrated with simulations as well as experimental data for a phantom and human brain in vivo