Noise estimation and removal in MR imaging: The variance-stabilization approach

Abstract

We develop optimal forward and inverse variance-stabilizing transformations for the Rice distribution, in order to approach the problem of magnetic resonance (MR) image filtering by means of standard denoising algorithms designed for homoskedastic observations.Further, we present a stable and fast iterative procedure for robustly estimating the noise level from a single Rician-distributed image.At each iteration, the procedure exploits variancestabilization composed with a homoskedastic variance-estimation algorithm.Theoretical and experimental study demonstrates the success of our approach to Rician noise estimation and removal through variance stabilization. In particular, we show that the performance of current state-of-the-art algorithms specifically designed for Riciandistributed data can be matched by combining conventional algorithms designed for additive white Gaussian noise with optimal variance-stabilizing transformations.

Advances in Image Pre-Processing to Improve Automated 3d Reconstruction

“…Wavelet-based denoising methods (Nowak & Baraniuk, 1997;Kolaczyk, 1999) propose adaptation of the transform threshold to the local noise level of the Poisson process. Recent papers on the Anscombe transform by Makitalo &Foi (2011) andFoi (2011), argue that, when combined with suitable forward and inverse variance-stabilizing transformations (VST), algorithms designed for homoscedastic Gaussian noise work just as well as ad-hoc algorithms based on signal-dependent noise models.…”

Algorithms for Efficient Computation of Convolution

“…In case the convolution kernel is separable we can split the hard problem into a sequence of several simpler problems. Let us recall the 3-D naïve convolution from (3). Assume that g 3d is separable, i.e.…”

“…It is employed in filtering [1,2], denoising [3], edge detection [4,5], correlation [6], compression [7,8], deconvolution [9,10], simulation [11,12], and in many other applications. Although the concept of convolution is not new, the efficient computation of convolution is still an open topic.…”

Nonlocal transform-domain denoising of volumetric data with groupwise adaptive variance estimation

“…The first phase of collaborative filtering, executed on Rician observations only, is the application of a variance stabilization transform (VST) specifically designed for the Rice distribution, 13 in order to remove the dependencies between the noise and the underlying grouped data. In this way, the stabilized data can be filtered using the constant standard deviation value c > 0 induced by the VST.…”

“…EachĈ y xi is an estimate of the original C y xi extracted from the unknown volumetric data y. Finally, in case of Rician noise, the filtered group undergoes the exact unbiased inverse variance stabilization transform as in 13 that simultaneously inverts the VST and produces an unbiased estimate for the underlying y.…”