UNBIASED NOISE ESTIMATION AND DENOISING IN PARALLEL MAGNETIC RESONANCE IMAGING Pasquale Borrelli University of Naples Federico II Dept. of Advanced Biomedical Sciences Via Pansini 5, 80131 Naples, Italy Giuseppe Palma, Marco Comerci, Bruno Alfano National Research Council of Italy Inst. of Biostructures and Bioimaging Via De Amicis 95, 80145 Naples, Italy ABSTRACT In magnetic resonance (MR) clinical practice, noise esti- mation is usually performed on Rayleigh-distributed back- ground (no signal area) of magnitude images. Although noise variance in quadrature MR images is considered spatially independent, parallel MRI (pMRI) techniques as SENSE or GRAPPA generate spatially varying noise (SVN) distri- bution. In this scenario noise estimation from background may produce biased results. To address these limitations we introduce a novel noise estimation scheme based on local statistics. Our method turns out to be more accurate than the other pMRI noise estimation schemes previously described in the literature. Denoising performances, measured by vi- sual inspection and peak signal-to-noise ratio (PSNR), of Non-Local Means denoising filters (NLM) are considerably improved using SVN-NLM in case of inhomogeneous noise. Furthermore, SVN-NLM behaves as well as standard NLM when homogeneous noise was added, thus proving to be a robust and powerful denoising algorithm for arbitrary MRI datasets. Index Terms— Noise estimation, denoising, parallel MRI, non-local means, Rician noise 1. INTRODUCTION Noise estimation and, consequently, denoising are crucial steps in most post-processing tasks of MRI and, particu- larly, of MR image quantitation. In standard quadrature MRI (hereafter, sMRI), both real and imaginary images show an uncorrelated Gaussian noise whose variance is uniform all over the field of view (FOV). Once the magnitude of the com- plex images is extracted, the resulting noise follows a Rician distribution, whose variance can be accurately estimated from the variance of the voxel values (Rayleigh-distributed) in the image background (i.e. the no-signal area) [1, 2]. However, as soon as images show a spatially varying noise distribution, such background-based noise estimation schemes produce biased results [3, 4]. This work was partially funded by FIRB-MERIT RBNE08E8CZ and DSB-CNR/MIUR ”Aging” project. Parallel MRI is an emerged technique that increases the image acquisition rate by sampling a reduced amount of k- space data with an array of receiving coils [5, 6]. Generalized auto-calibrating partially parallel acquisition (GRAPPA) and sensitivity-encoded (SENSE) MRI are most common image reconstruction schemes in pMRI. Both reconstruction algo- rithms share the incorporation of coil-sensitivity profiles into the image reconstruction process [7]. In GRAPPA algorithm missing k-space lines are computed before full-image is re- constructed for each receiver channel [8]. On the other hand, SENSE algorithm reconstructs complex image for each re- ceiver channel and then final images are pixel-wise multiplied by appropriate coil sensitivity mask [9]. The application of multi-surface coil arrays and reconstruction filter can influ- ence the statistical distribution of image noise [10]. In this scenario, variance of background regions will lead to innacu- rate estimations of the true local noise if a uniform Rayleigh distribution is erroneously assumed [4]. In the context of denoising algorithms, one of the most performing and robust denoising approaches is the non-local means (NLM) filter, introduced in [11]. NLM filter assumes that the restoring function for a given point is a mean of all the image values, largely weighted according to the radio- metric similarity between voxels and only weakly tied to a spatial proximity criterion. In particular, it has been shown that NLM filter guarantees the homogeneity of flat zones, pre- serves edges and fine structures, and transforms white noise into white noise, thus avoiding the introduction of artifacts and spurious correlated signal [11, 12]. Although there are some algorithm variants that take into account spatially vary- ing noise distribution in image to be filtered [13, 14, 15], at the best of our knowledge, a robust and accurate noise estimation in a NLM pipeline has been poorly investigated. In this paper we present a novel noise estimation based on NLM filter and local statistics. Our local mask does not need an a priori knowledge of sensitivity maps, subsampling factor and geometry factor. Therefore, our noise estimation technique is successfully applicable to MR images with both spatially varying and uniform noise distribution. The plan of the paper is as follows. In §2 we briefly review 2014 IEEE International Conference on Acoustic, Speech and Signal Processing (ICASSP) 978-1-4799-2893-4/14/$31.00 ©2014 IEEE 1239