DTI denoising for data with low signal to noise ratios

Low signal to noise ratio (SNR) experiments in diffusion tensor imaging (DTI) give key information about tracking and anisotropy, e. g., by measurements with small voxel sizes or with high b values. However, due to the complicated and dominating impact of thermal noise such data are still seldom analysed. In this paper Monte Carlo simulations are presented which investigate the distributions of noise for different DTI variables in low SNR situations. Based on this study a strategy for the application of spatial smoothing is derived. Optimal prerequisites for spatial filters are unbiased, bell shaped distributions with uniform variance, but, only few variables have a statistics close to that. To construct a convenient filter a chain of nonlinear Gaussian filters is adapted to peculiarities of DTI and a bias correction is introduced. This edge preserving three dimensional filter is then validated via a quasi realistic model. Further, it is shown that for small sample sizes the filter is as effective as a maximum likelihood estimator and produces reliable results down to a local SNR of approximately 1. The filter is finally applied to very recent data with isotropic voxels of the size 1×1×1mm^3 which corresponds to a spatially mean SNR of 2.5. This application demonstrates the statistical robustness of the filter method. Though the Rician noise model is only approximately realized in the data, the gain of information by spatial smoothing is considerable

On-Manifold Preintegration for Real-Time Visual-Inertial Odometry

Current approaches for visual-inertial odometry (VIO) are able to attain highly accurate state estimation via nonlinear optimization. However, real-time optimization quickly becomes infeasible as the trajectory grows over time, this problem is further emphasized by the fact that inertial measurements come at high rate, hence leading to fast growth of the number of variables in the optimization. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes into single relative motion constraints. Our first contribution is a \emph{preintegration theory} that properly addresses the manifold structure of the rotation group. We formally discuss the generative measurement model as well as the nature of the rotation noise and derive the expression for the \emph{maximum a posteriori} state estimator. Our theoretical development enables the computation of all necessary Jacobians for the optimization and a-posteriori bias correction in analytic form. The second contribution is to show that the preintegrated IMU model can be seamlessly integrated into a visual-inertial pipeline under the unifying framework of factor graphs. This enables the application of incremental-smoothing algorithms and the use of a \emph{structureless} model for visual measurements, which avoids optimizing over the 3D points, further accelerating the computation. We perform an extensive evaluation of our monocular \VIO pipeline on real and simulated datasets. The results confirm that our modelling effort leads to accurate state estimation in real-time, outperforming state-of-the-art approaches.Comment: 20 pages, 24 figures, accepted for publication in IEEE Transactions on Robotics (TRO) 201

Spatial Smoothing for Diffusion Tensor Imaging with low Signal to Noise Ratios

Though low signal to noise ratio (SNR) experiments in DTI give key information about tracking and anisotropy, e.g. by measurements with very small voxel sizes, due to the complicated impact of thermal noise such experiments are up to now seldom analysed. In this paper Monte Carlo simulations are presented which investigate the random fields of noise for different DTI variables in low SNR situations. Based on this study a strategy for spatial smoothing, which demands essentially uniform noise, is derived. To construct a convenient filter the weights of the nonlinear Aurich chain are adapted to DTI. This edge preserving three dimensional filter is then validated in different variants via a quasi realistic model and is applied to very new data with isotropic voxels of the size 1x1x1 mm3 which correspond to a spatial mean SNR of approximately 3

Predicting respiratory motion for real-time tumour tracking in radiotherapy

Purpose. Radiation therapy is a local treatment aimed at cells in and around a tumor. The goal of this study is to develop an algorithmic solution for predicting the position of a target in 3D in real time, aiming for the short fixed calibration time for each patient at the beginning of the procedure. Accurate predictions of lung tumor motion are expected to improve the precision of radiation treatment by controlling the position of a couch or a beam in order to compensate for respiratory motion during radiation treatment. Methods. For developing the algorithmic solution, data mining techniques are used. A model form from the family of exponential smoothing is assumed, and the model parameters are fitted by minimizing the absolute disposition error, and the fluctuations of the prediction signal (jitter). The predictive performance is evaluated retrospectively on clinical datasets capturing different behavior (being quiet, talking, laughing), and validated in real-time on a prototype system with respiratory motion imitation. Results. An algorithmic solution for respiratory motion prediction (called ExSmi) is designed. ExSmi achieves good accuracy of prediction (error $4-9$ mm/s) with acceptable jitter values (5-7 mm/s), as tested on out-of-sample data. The datasets, the code for algorithms and the experiments are openly available for research purposes on a dedicated website. Conclusions. The developed algorithmic solution performs well to be prototyped and deployed in applications of radiotherapy

Smoothing of orbital tracking data: Mission planning, mission analysis and software formulation

The problem created by the presence of wild or outlying data points among orbital tracking data, is addressed. Consideration is given to the effects of such outliers on the orbit determination process, and methods for minimizing or even eliminating these effects are proposed. Some preliminary efforts implementing these new methods are described, and the results thus far obtained are summarized. Based on these ideas and results, recommendations are made for future investigation

The Extraordinarily Rapid Expansion of the X-ray Remnant of Kepler's Supernova (SN1604)

Four individual high resolution X-ray images from ROSAT and the Einstein Observatory have been used to measure the expansion rate of the remnant of Kepler's supernova (SN 1604). Highly significant measurements of the expansion have been made for time baselines varying from 5.5 yrs to 17.5 yrs. All measurements are consistent with a current expansion rate averaged over the entire remnant of 0.239 (+/-0.015) (+0.017,-0.010) % per yr, which, when combined with the known age of the remnant, determines the expansion parameter m, defined as $R\propto t^m$, to be 0.93 (+/-0.06) (+0.07,-0.04). The error bars on these results include both statistical (first set of errors) and systematic (second set) uncertainty. According to this result the X-ray remnant is expanding at a rate that is remarkably close to free expansion and nearly twice as fast as the mean expansion rate of the radio remnant. The expansion rates as a function of radius and azimuthal angle are also presented based on two ROSAT images that were registered to an accuracy better than 0.5 arcseconds. Significant radial and azimuthal variations that appear to arise from the motion of individual X-ray knots are seen. The high expansion rate of the X-ray remnant appears to be inconsistent with currently accepted dynamical models for the evolution of Kepler's SNR.Comment: 14 pages, including 7 postscript figs, LaTeX, emulateapj. Accepted by Ap

Realtime State Estimation with Tactile and Visual sensing. Application to Planar Manipulation

Accurate and robust object state estimation enables successful object manipulation. Visual sensing is widely used to estimate object poses. However, in a cluttered scene or in a tight workspace, the robot's end-effector often occludes the object from the visual sensor. The robot then loses visual feedback and must fall back on open-loop execution. In this paper, we integrate both tactile and visual input using a framework for solving the SLAM problem, incremental smoothing and mapping (iSAM), to provide a fast and flexible solution. Visual sensing provides global pose information but is noisy in general, whereas contact sensing is local, but its measurements are more accurate relative to the end-effector. By combining them, we aim to exploit their advantages and overcome their limitations. We explore the technique in the context of a pusher-slider system. We adapt iSAM's measurement cost and motion cost to the pushing scenario, and use an instrumented setup to evaluate the estimation quality with different object shapes, on different surface materials, and under different contact modes