Abstract. The majority of existing denoising algorithms obtain good results for a specific noise model, and when it is known previously. Nonetheless, there is a lack in denoising algorithms that can deal with any unknown noisy images. Therefore, in this paper, we study the use of aggregation functions for denoising purposes, where the noise model is not necessary known in advance; and how these functions affect the visual and quantitative results of the resultant images.

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In order to accelerate the acquisition process in multiple-coil Magnetic Resonance scanners, parallel techniques were developed. These techniques reduce the acquisition time via a subsampling of the k-space and a reconstruction process. From a signal and noise perspective, the use of a acceleration techniques modify the structure of the noise within the image. In the most common algorithms, like SENSE, the final magnitude image after the reconstruction is known to follow a Rician distribution for each pixel, just like single coil systems. However, the noise is spatially non-stationary, i.e. the variance of noise becomes x-dependent. This effect can also be found in magnitude images due to other processing inside the scanner. In this work we propose a method to adapt well-known noise filtering techniques initially designed to deal with stationary noise to the case of spatially variant Rician noise. The method copes with inaccurate estimates of variant noise patterns in the image, showing its robustness in realistic cases. The method employs a consensus strategy in conjunction with a set of aggregation functions and a penalty function. Multiple possible outputs are generated for each pixel assuming different unknown input parameters. The consensus approach merges them into a unique filtered image. As a filtering technique, we have selected the Linear Minimum Mean Square Error (LMMSE) estimator for Rician data, which has been used to test our methodology due to its simplicity and robustness. Results with synthetic and in vivo data confirm the good behavior of our approach.

The image capturing process still today introduces degradations that are unavoidable. The research community is compromised with this issue developing algorithms for the noise removal task. Most of the existing approaches in the literature are parametric, i.e. some information from the underlying model is required. However, there are situations in which this information cannot be captured accurately and the use of these approaches is dismissed. Therefore, we propose an approach where averaging functions are applied over different realizations of a parametric filter. Then, the required information for the parametric filter is extracted and combined from the different parameter configurations used. So, we give the possibility to use parametric approaches in situations where some information is missing. Results show that the averaging functions present promising outcomes for the nonstationary noise removal task