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A new method for noise filtering in images that follow a Rician model-with particular attention to magnetic resonance imaging-is proposed. To that end, we have derived a (novel) closed-form solution of the linear minimum mean square error (LMMSE) estimator for this distribution. Additionally, a set of methods that automatically estimate the noise power are… (More)

In this paper, we focus on the problem of speckle removal by means of anisotropic diffusion and, specifically, on the importance of the correct estimation of the statistics involved. First, we derive an anisotropic diffusion filter that does not depend on a linear approximation of the speckle model assumed, which is the case of a previously reported filter,… (More)

An estimator of the Orientation Probability Density Function (OPDF) of fiber tracts in the white matter of the brain from High Angular Resolution Diffusion data is presented. Unlike Q-Balls, which use the Funk-Radon transform to estimate the radial projection of the 3D Probability Density Function, the Jacobian of the spherical coordinates is included in… (More)

This paper introduces and analyzes a linear minimum mean square error (LMMSE) estimator using a Rician noise model and its recursive version (RLMMSE) for the restoration of diffusion weighted images. A method to estimate the noise level based on local estimations of mean or variance is used to automatically parametrize the estimator. The restoration… (More)

Noise estimation is a challenging task in magnetic resonance imaging (MRI), with applications in quality assessment, filtering or diffusion tensor estimation. Main noise estimators based on the Rician model are revisited and classified in this article, and new useful methods are proposed. Additionally, all the surveyed estimators are extended to the… (More)

The Funk-Radon Transform (FRT) is a powerful tool for the estimation of fiber populations with High Angular Resolution Diffusion Imaging (HARDI). It is used in Q-Ball imaging (QBI), and other HARDI techniques such as the recent Orientation Probability Density Transform (OPDT), to estimate fiber populations with very few restrictions on the diffusion model.… (More)

In this paper, we focus on the problem of automatic noise parameter estimation for additive and multi-plicative models and propose a simple and novel method to this end. Specifically we show that if the image to work with has a sufficiently great amount of low-variability areas (which turns out to be a typical feature in most images), the variance of noise… (More)

The filtering of the Diffusion Weighted Images (DWI) prior to the estimation of the diffusion tensor or other fiber Orientation Distribution Functions (ODF) has been proved to be of paramount importance in the recent literature. More precisely, it has been evidenced that the estimation of the diffusion tensor without a previous filtering stage induces… (More)

A new filtering method to remove Rician noise from magnetic resonance images is presented. This filter relies on a robust estimation of the standard deviation of the noise and combines local linear minimum mean square error filters and partial differential equations for MRI, as the speckle reducing anisotropic diffusion did for ultrasound images. The… (More)