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

Optimized Anisotropic Rotational Invariant Diffusion Scheme on Cone-Beam CT

Cone-beam computed tomography (CBCT) is an important image modality for dental surgery planning, with high resolution images at a relative low radiation dose. In these scans the mandibular canal is hardly visible, this is a problem for implant surgery planning. We use anisotropic diffusion filtering to remove noise and enhance the mandibular canal in CBCT scans. For the diffusion tensor we use hybrid diffusion with a continuous switch (HDCS), suitable for filtering both tubular as planar image structures. We focus in this paper on the diffusion discretization schemes. The standard scheme shows good isotropic filtering behavior but is not rotational invariant, the diffusion scheme of Weickert is rotational invariant but suffers from checkerboard artifacts. We introduce a new scheme, in which we numerically optimize the image derivatives. This scheme is rotational invariant and shows good isotropic filtering properties on both synthetic as real CBCT data

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

Vessel tractography using an intensity based tensor model with branch detection

In this paper, we present a tubular structure seg- mentation method that utilizes a second order tensor constructed from directional intensity measurements, which is inspired from diffusion tensor image (DTI) modeling. The constructed anisotropic tensor which is fit inside a vessel drives the segmen- tation analogously to a tractography approach in DTI. Our model is initialized at a single seed point and is capable of capturing whole vessel trees by an automatic branch detection algorithm developed in the same framework. The centerline of the vessel as well as its thickness is extracted. Performance results within the Rotterdam Coronary Artery Algorithm Evaluation framework are provided for comparison with existing techniques. 96.4% average overlap with ground truth delineated by experts is obtained in addition to other measures reported in the paper. Moreover, we demonstrate further quantitative results over synthetic vascular datasets, and we provide quantitative experiments for branch detection on patient Computed Tomography Angiography (CTA) volumes, as well as qualitative evaluations on the same CTA datasets, from visual scores by a cardiologist expert

Fast space-variant elliptical filtering using box splines

The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying size, elongation and orientation using a fixed number of computations per pixel. The associated algorithm, which is based on a family of smooth compactly supported piecewise polynomials, the radially-uniform box splines, is realized using pre-integration and local finite-differences. The radially-uniform box splines are constructed through the repeated convolution of a fixed number of box distributions, which have been suitably scaled and distributed radially in an uniform fashion. The attractive features of these box splines are their asymptotic behavior, their simple covariance structure, and their quasi-separability. They converge to Gaussians with the increase of their order, and are used to approximate anisotropic Gaussians of varying covariance simply by controlling the scales of the constituent box distributions. Based on the second feature, we develop a technique for continuously controlling the size, elongation and orientation of these Gaussian-like functions. Finally, the quasi-separable structure, along with a certain scaling property of box distributions, is used to efficiently realize the associated space-variant elliptical filtering, which requires O(1) computations per pixel irrespective of the shape and size of the filter.Comment: 12 figures; IEEE Transactions on Image Processing, vol. 19, 201

Anisotropic Diffusion Filter with Memory based on Speckle Statistics for Ultrasound Images

Ultrasound imaging exhibits considerable difficulties for medical visual inspection and for the development of automatic analysis methods due to speckle, which negatively affects the perception of tissue boundaries and the performance of automatic segmentation methods. With the aim of alleviating the effect of speckle, many filtering techniques are usually considered as a preprocessing step prior to automatic analysis methods or visual inspection. Most of the state-of-the-art filters try to reduce the speckle effect without considering its relevance for the characterization of tissue nature. However, the speckle phenomenon is the inherent response of echo signals in tissues and can provide important features for clinical purposes. This loss of information is even magnified due to the iterative process of some speckle filters, e.g., diffusion filters, which tend to produce over-filtering because of the progressive loss of relevant information for diagnostic purposes during the diffusion process. In this work, we propose an anisotropic diffusion filter with a probabilistic-driven memory mechanism to overcome the over-filtering problem by following a tissue selective philosophy. Specifically, we formulate the memory mechanism as a delay differential equation for the diffusion tensor whose behavior depends on the statistics of the tissues, by accelerating the diffusion process in meaningless regions and including the memory effect in regions where relevant details should be preserved. Results both in synthetic and real US images support the inclusion of the probabilistic memory mechanism for maintaining clinical relevant structures, which are removed by the state-of-the-art filters

Oriented tensor reconstruction: tracing neural pathways from diffusion tensor MRI

In this paper we develop a new technique for tracing anatomical fibers from 3D tensor fields. The technique extracts salient tensor features using a local regularization technique that allows the algorithm to cross noisy regions and bridge gaps in the data. We applied the method to human brain DT-MRI data and recovered identifiable anatomical structures that correspond to the white matter brain-fiber pathways. The images in this paper are derived from a dataset having 121x88x60 resolution. We were able to recover fibers with less than the voxel size resolution by applying the regularization technique, i.e., using a priori assumptions about fiber smoothness. The regularization procedure is done through a moving least squares filter directly incorporated in the tracing algorithm