Lorentz microscopy of optical fields.

In electron microscopy, detailed insights into nanoscale optical properties of materials are gained by spontaneous inelastic scattering leading to electron-energy loss and cathodoluminescence. Stimulated scattering in the presence of external sample excitation allows for mode- and polarization-selective photon-induced near-field electron microscopy (PINEM). This process imprints a spatial phase profile inherited from the optical fields onto the wave function of the probing electrons. Here, we introduce Lorentz-PINEM for the full-field, non-invasive imaging of complex optical near fields at high spatial resolution. We use energy-filtered defocus phase-contrast imaging and iterative phase retrieval to reconstruct the phase distribution of interfering surface-bound modes on a plasmonic nanotip. Our approach is universally applicable to retrieve the spatially varying phase of nanoscale fields and topological modes.

Formulation and Efficient Computation of l1 - and Smoothness Penalized Estimates for Microstructure-Informed Tractography.

Fiber tractography based on diffusion-weighted magnetic resonance imaging is to date the only method for the three-dimensional visualization of nerve fiber bundles in the living human brain noninvasively. However, various existing methods suffer from reconstructing anatomically implausible fiber tracks due to exclusive local treatment of the input data. A method that seeks to filter out invalid tracks in a postprocessing step by solving a convex optimization problem with l1 -norm regularization was recently introduced in the work by Daducci et al. In this paper, we derive an improved version of this method by adding Sobolev-norm regularization terms. Furthermore, we present a robust and efficient strategy using the alternating direction method of multipliers and dimension reduction using truncated singular value decomposition to solve the resulting optimization problem. The qualitative results show the applicability of the algorithm to large in vivo data sets. The quantitative results and numerical experiments for diffusion phantom data with known ground truth show the benefits of the proposed method.

An eigenvalue approach for the automatic scaling of unknowns in model-based reconstructions: Application to real-time phase-contrast flow MRI.

The purpose of this work is to develop an automatic method for the scaling of unknowns in model-based nonlinear inverse reconstructions and to evaluate its application to real-time phase-contrast (RT-PC) flow magnetic resonance imaging (MRI). Model-based MRI reconstructions of parametric maps which describe a physical or physiological function require the solution of a nonlinear inverse problem, because the list of unknowns in the extended MRI signal equation comprises multiple functional parameters and all coil sensitivity profiles. Iterative solutions therefore rely on an appropriate scaling of unknowns to numerically balance partial derivatives and regularization terms. The scaling of unknowns emerges as a self-adjoint and positive-definite matrix which is expressible by its maximal eigenvalue and solved by power iterations. The proposed method is applied to RT-PC flow MRI based on highly undersampled acquisitions. Experimental validations include numerical phantoms providing ground truth and a wide range of human studies in the ascending aorta, carotid arteries, deep veins during muscular exercise and cerebrospinal fluid during deep respiration. For RT-PC flow MRI, model-based reconstructions with automatic scaling not only offer velocity maps with high spatiotemporal acuity and much reduced phase noise, but also ensure fast convergence as well as accurate and precise velocities for all conditions tested, i.e. for different velocity ranges, vessel sizes and the simultaneous presence of signals with velocity aliasing. In summary, the proposed automatic scaling of unknowns in model-based MRI reconstructions yields quantitatively reliable velocities for RT-PC flow MRI in various experimental scenarios.

Semi-local tractography strategies using neighborhood information.

Fiber tractography based on Diffusion MRI measurements is a valuable tool for the detection and visual representation of neural pathways in vivo. We present a novel fiber orientation distribution function (ODF) based streamline tractography approach which incorporates information of neighboring regions derived from a Bayesian model. In each iteration step, the proposed algorithm defines a set of candidate fiber fragments continuing the already tracked path and assigns an a-posteriori probability. We compute the posterior as the normalized product of a likelihood function based on the given ODF-field and a prior distribution representing anatomical plausibility of a candidate fiber fragment with respect to tract curvature derived from the previously tracked fiber path by an extrapolation strategy. We derive both a deterministic tractography algorithm obtaining in each iteration a tracking direction by maximum a-posteriori estimation, as well as a probabilistic version drawing a direction from the marginalized posterior distribution. Compared to fiber tracking methods that rely only on the local ODF, the proposed algorithm proves more robust in the presence of noise and partial volume effects. We demonstrate the effectiveness of both our deterministic and probabilistic method on simulated, phantom, and in vivo data.

Regularized Newton methods for x-ray phase contrast and general imaging problems.

Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an accurate forward model describing the generally nonlinear image formation from a given object to the observations is often available, explicit inversion formulas are typically not known. Moreover, the measured data might be insufficient for stable image reconstruction, in which case it has to be complemented by suitable a priori information. In this work, regularized Newton methods are presented as a general framework for the solution of such ill-posed nonlinear imaging problems. For a proof of principle, the approach is applied to x-ray phase contrast imaging in the near-field propagation regime. Simultaneous recovery of the phase- and amplitude from a single near-field diffraction pattern without homogeneity constraints is demonstrated for the first time. The presented methods further permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval and tomographic inversion. We demonstrate the potential of this approach by three-dimensional imaging of a colloidal crystal at 95nm isotropic resolution.

Image reconstruction by regularized nonlinear inversion--joint estimation of coil sensitivities and image content.

The use of parallel imaging for scan time reduction in MRI faces problems with image degradation when using GRAPPA or SENSE for high acceleration factors. Although an inherent loss of SNR in parallel MRI is inevitable due to the reduced measurement time, the sensitivity to image artifacts that result from severe undersampling can be ameliorated by alternative reconstruction methods. While the introduction of GRAPPA and SENSE extended MRI reconstructions from a simple unitary transformation (Fourier transform) to the inversion of an ill-conditioned linear system, the next logical step is the use of a nonlinear inversion. Here, a respective algorithm based on a Newton-type method with appropriate regularization terms is demonstrated to improve the performance of autocalibrating parallel MRI--mainly due to a better estimation of the coil sensitivity profiles. The approach yields images with considerably reduced artifacts for high acceleration factors and/or a low number of reference lines.

Iterative reconstruction of a refractive-index profile from x-ray or neutron reflectivity measurements.

Analysis of x-ray and neutron reflectivity is usually performed by modeling the density profile of the sample and performing a least square fit to the measured (phaseless) reflectivity data. Here we address the uniqueness of the reflectivity problem as well as its numerical reconstruction. In particular, we derive conditions for uniqueness, which are applicable in the kinematic limit (Born approximation), and for the most relevant case of box model profiles with Gaussian roughness. At the same time we present an iterative method to reconstruct the profile based on regularization methods. The method is successfully implemented and tested both on simulated and real experimental data.