# Noise reduction in MR images

MR images are usually distorted by various random factors called noise.

The principal sources of the noise in magnetic resonance imaging can be subdivided into two types: due to the hardware (acquisition coil arrays, gradient coils, current or field inhomogeneity, etc.) and due to the subject (physiological noise including body motions, cardiac pulsation, respiratory motions, etc.).

These factors negatively affect the resolution and reproducibility of the images. Therefore, a proper noise treatment is important for improving the performance of clinical and research investigations. Noise reduction becomes especially critical if signal-to-noise ratio (SNR) is low, and this is often the case in DTI experiments at high b-values.

The standard methods for signal correction usually assume a uniform distribution of the noise standard deviation within the image and evaluate a single correction parameter for the whole image. We pursue a more advanced approach based on the assumption of the inhomogeneous distribution of the noise in space and evaluate correction factors for each voxel individually. A proper correction of the measured signal using the spatially variable noise field improves the estimation of diffusion tensors and an accuracy of fibre-tracking analysis. In general, spatially variable noise fields are to be considered in any MRI studies subject to low SNR. More detailed investigations are required.

Algorithm: a new algorithm has been developed for the calculation of the spatially distributed noise taking into account both the high SNR regions (in which the measured signal is approximated by the Gaussian distribution) as well as in the regions with the low SNR in which the Rician distribution is to be considered. To reduce the computational time of the algorithm we use a mask of the brain excluding the background voxels.

1. Compute a median absolute deviation (MAD) for the given voxel. One can also use another robust estimator such as Sn or Qn one. MAD can be estimated using a set of data with multiple repetitions or multiple directions.
2. Compute the Gaussian standard deviation (SD) using the robust estimator.
3. Compute the Rician correction for previous SD estimation.
4. Correct the noisy image using the spatially distributed SD.

Examples of MR images and noise fields. Rows: 1. original diffusion weighted images; 2. corresponding Gaussian noise fields; 3. corresponding Rician noise fields; 4. corresponding correction-function maps.