12,874 research outputs found
Random noise in Diffusion Tensor Imaging, its Destructive Impact and Some Corrections
The empirical origin of random noise is described, its influence on DTI variables is illustrated by a review of numerical and in vivo studies supplemented by new simulations investigating high noise levels. A stochastic model of noise propagation is presented to structure noise impact in DTI. Finally, basics of voxelwise and spatial denoising procedures are presented. Recent denoising procedures are reviewed and consequences of the stochastic model for convenient denoising strategies are discussed
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
Self-gravity, resonances and orbital diffusion in stellar discs
Fluctuations in a stellar system's gravitational field cause the orbits of
stars to evolve. The resulting evolution of the system can be computed with the
orbit-averaged Fokker-Planck equation once the diffusion tensor is known. We
present the formalism that enables one to compute the diffusion tensor from a
given source of noise in the gravitational field when the system's dynamical
response to that noise is included. In the case of a cool stellar disc we are
able to reduce the computation of the diffusion tensor to a one-dimensional
integral. We implement this formula for a tapered Mestel disc that is exposed
to shot noise and find that we are able to explain analytically the principal
features of a numerical simulation of such a disc. In particular the formation
of narrow ridges of enhanced density in action space is recovered. As the
disc's value of Toomre's is reduced and the disc becomes more responsive,
there is a transition from a regime of heating in the inner regions of the disc
through the inner Lindblad resonance to one of radial migration of
near-circular orbits via the corotation resonance in the intermediate regions
of the disc. The formalism developed here provides the ideal framework in which
to study the long-term evolution of all kinds of stellar discs.Comment: 11 pages, 7 figure
Scalar transport in compressible flow
Transport of scalar fields in compressible flow is investigated. The
effective equations governing the transport at scales large compared to those
of the advecting flow are derived by using multi-scale techniques. Ballistic
transport generally takes place when both the solenoidal and the potential
components of the velocity do not vanish, despite of the fact that it has zero
average value. The calculation of the effective ballistic velocity is
reduced to the solution of one auxiliary equation. An analytic expression for
is derived in some special instances, i.e. flows depending on a single
coordinate, random with short correlation times and slightly compressible
cellular flow. The effective mean velocity vanishes for velocity fields
which are either incompressible or potential and time-independent. For generic
compressible flow, the most general conditions ensuring the absence of
ballistic transport are isotropy and/or parity invariance. When vanishes
(or in the frame of reference moving with velocity ), standard diffusive
transport takes place. It is known that diffusion is always enhanced by
incompressible flow. On the contrary, we show that diffusion is depleted in the
presence of time-independent potential flow. Trapping effects due to potential
wells are responsible for this depletion. For time-dependent potential flow or
generic compressible flow, transport rates are enhanced or depleted depending
on the detailed structure of the velocity field.Comment: 27 pages, submitted to Physica
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 1Ć1Ć1mm^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
- ā¦