Local estimation of the noise level in MRI using structural adaptation

We present a method for local estimation of the signal-dependent noise level in magnetic resonance images. The procedure uses a multi-scale approach to adaptively infer on local neighborhoods with similar data distribution. It exploits a maximum-likelihood estimator for the local noise level. The validity of the method was evaluated on repeated diffusion data of a phantom and simulated data using T1-data corrupted with artificial noise. Simulation results are compared with a recently proposed estimate. The method was applied to a high-resolution diffusion dataset to obtain improved diffusion model estimation results and to demonstrate its usefulness in methods for enhancing diffusion data

Structural Adaptive Smoothing in Diffusion Tensor Imaging: The R Package dti

Diffusion weighted imaging has become and will certainly continue to be an important tool in medical research and diagnostics. Data obtained with diffusion weighted imaging are characterized by a high noise level. Thus, estimation of quantities like anisotropy indices or the main diffusion direction may be significantly compromised by noise in clinical or neuroscience applications. Here, we present a new package dti for R, which provides functions for the analysis of diffusion weighted data within the diffusion tensor model. This includes smoothing by a recently proposed structural adaptive smoothing procedure based on the propagation-separation approach in the context of the widely used diffusion tensor model. We extend the procedure and show, how a correction for Rician bias can be incorporated. We use a heteroscedastic nonlinear regression model to estimate the diffusion tensor. The smoothing procedure naturally adapts to different structures of different size and thus avoids oversmoothing edges and fine structures. We illustrate the usage and capabilities of the package through some examples.

Automatic, fast and robust characterization of noise distributions for diffusion MRI

Knowledge of the noise distribution in magnitude diffusion MRI images is the centerpiece to quantify uncertainties arising from the acquisition process. The use of parallel imaging methods, the number of receiver coils and imaging filters applied by the scanner, amongst other factors, dictate the resulting signal distribution. Accurate estimation beyond textbook Rician or noncentral chi distributions often requires information about the acquisition process (e.g. coils sensitivity maps or reconstruction coefficients), which is not usually available. We introduce a new method where a change of variable naturally gives rise to a particular form of the gamma distribution for background signals. The first moments and maximum likelihood estimators of this gamma distribution explicitly depend on the number of coils, making it possible to estimate all unknown parameters using only the magnitude data. A rejection step is used to make the method automatic and robust to artifacts. Experiments on synthetic datasets show that the proposed method can reliably estimate both the degrees of freedom and the standard deviation. The worst case errors range from below 2% (spatially uniform noise) to approximately 10% (spatially variable noise). Repeated acquisitions of in vivo datasets show that the estimated parameters are stable and have lower variances than compared methods.Comment: v2: added publisher DOI statement, fixed text typo in appendix A

High resolution Magnetic Resonance Imaging experiments - lessons in nonlinear statistical modeling

Recent advances in neuro-imaging attempt to enable in-vivo histology of the brain. Doing so requires increased spatial resolution up to a situation where the signal meets the noise floor. The talk will cover research conducted at WIAS, in collaboration with MR physicists, on statistical issues in modeling imaging data characterized by low signal-to-noise ratio (SNR). I'll cover several specific, but interrelated problems: - characterization of the signal distribution in MR experiments, - effects of preprocessing on the signal distribution, - estimation of the noise profile in MR images, - use of spatial information for variance reduction in (collections of) MR images, - bias due to incorrect modeling in MR experiments. I'll consider two specific imaging experiments to illustrate problems, characterize effects that are due to high measurment noise and provide solutions for: - diffusion weighted MR, with an analysis based on data of the Human Connectome Project, - multi-parameter mapping, using data measured at the Wellcome Trust Center for Neuroimaging, London. Literature: S. Becker, K. Tabelow, S. Mohammadi, N. Weiskopf and J. Polzehl, Adaptive smoothing of multi-shell diffusion-weighted MR data by msPOAS, NeuroImage, 95 (2014) pp. 90--105. K. Tabelow, H.U. Voss and J. Polzehl, Local estimation of the noise level in MRI using structural adaptation, Medical Image Analysis, 20 (2015) pp. 76--86. J. Polzehl and K. Tabelow, Low SNR in dMRI models, JASA, 11 (2016) pp. 1480--1490. K. Tabelow, Ch. D'Alonzo, L. Ruthotto, M. F. Callaghan, N. Weiskopf, J. Polzehl and S. Mohammadi, Removing the estimation bias due to the noise floor in multi-parameter maps, ISMRM annual meeting 2017