Abstract—MR images are increasingly used for diagnostic and surgical procedures, as they offer better soft tissue contrast and advanced imaging capabilities. Similar to other imaging modalities, MR images are also subjected to various forms of noises and artifacts. The noise affecting MRI images is known as Rician noise and displays a nonlinear and signal dependent behavior. In this paper we propose a nonlinear filtering method for Rician noise denoising. Nonlinear filters are more capable in addressing signal dependent behavior of noise and offer good denoising with better edge preserving capabilities. A nonlinear filter based on homomorphic filter characteristics has been designed to address Rician noise in MR images. The proposed filter has been implemented on synthetic images and MR images of the articular cartilage. The efficiency of the proposed filtering method is verified by computing the PSNR and SSIM index of the image. The proposed nonlinear filter performs good denoising with improvement in the image quality as observed from the PSNR values of the image. It also offers edge preservation and can be used for both structural MRI and soft tissue study effectively Index Terms—Homomorphic filters, MRI denoising, Rician noise, signal dependent filtering. I. INTRODUCTION The noise affecting MR images is known as Rician noise. This noise is introduced because of the magnitude image formation of MRI data and follows a Rice distribution function [1]. MRI images are converted to magnitude images and phase images by using magnitude and phase details from the k-space data obtained during image acquisition, respectively [1], [2]. The noise in k-space MRI data is usually assumed to be Gaussian white noise with zero mean [1], [2]. This reconstruction of the raw MRI data in to magnitude image; results in nonlinear behaviour of noise. It also affects both the SNR and the contrast of the MR image and makes noise dependent on the signal [2]. A wide variety of filters and filtering procedures have been studied to obtain adequate denoising in presence of Rician noise. Denoising techniques using wavelets, non-local means, median filters and anisotropic diffusion filters have all been previously suggested for Rician noise removal. The non-local means method is primarily designed for Gaussian noise removal and makes use of local neighbourhood within the image for filtering [3]. It computes Gaussian weights by using Euclidean distance between similar intensity patches within the image to perform denoising [3]. Non-local means filtering does not consider noise in the image to be Rician and Manuscript received April 30, 2013; revised July 5, 2013. The authors are with School of Engineering, University of Tasmania, Hobart, TAS-7001, Australia (e-mail: isaarya@ utas.edu.au, danchi.jiang@utas.edu.au, T.Gale@utas.edu.au). can cause excessive blurring if filtering parameter is not correct [3]. Anisotropic diffusion filters proposed by Perona and Malik are nonlinear filters and work by using local intensity within the homogenous regions for smoothing [4].The smoothing operation is controlled by a diffusion process, obtained from partial differential equation of heat and stops in the presence of an edge, thus preserving edge details [4]. Median filters too are nonlinear filters and make use of local statistics for noise removal, but are found to be more suitable for suppressing impulsive noise [5]. Median filters and anisotropic diffusion filters are both nonlinear filters with good edge preserving capabilities. Most of the above mentioned procedures do not consider the effect of dependent noise on the signal while filtering. Hence even though these procedures offer sufficient denoising they are not able to isolate noise from the true MR signal and may face limitation while estimating true signal intensity, when denoising. We know that Rice noise due to their signal dependent nature modifies the true intensity of the signal and changes contrast levels in the image. Hence, in this paper we will address Rician denoising based on signal dependent behaviour of noise with help of nonlinear filters. Section II will briefly describe signal dependent filters and noise, while Section III will explain the proposed denoising method with simulation results in Section IV, followed by conclusion in Section V. II. SIGNAL-DEPENDENT FILTER AND NOISE Our investigation of the signal dependent behaviour of Rice noise brought us to homomorphic filters for nonlinear filtering of noise [6]. Homomorphic filters are nonlinear filters in the spatial domain [6]. They require a transformation function, to separate signal and noise in the image, thus making noise linear and independent of signal [6]. Noise in this form is no longer signal dependent and can be easily filtered from the image with existing denoising procedures [6]. Homomorphic filters also require an equivalent inverse transformation function to return the filtered data back to the original equation [6]. A similar concept has been developed to make Rician noise independent of the true signal intensity. Once the noise has been made independent of the signal it undergoes filtering for noise removal and later the filtered data is transformed back into the magnitude equation. This process leads to betters estimation of the true signal intensity and is computationally more efficient. Noise can only be considered independent of signal, if its probability distribution function is no longer dependent on the signal parameter and it can be written in a linear form [7]. Signal dependent noise can be broadly classified into Signal Dependent Rician Noise Denoising Using Nonlinear Filter Isshaa Aarya, Danchi Jiang, and Timothy Gale Lecture Notes on Software Engineering, Vol. 1, No. 4, November 2013 344 DOI: 10.7763/LNSE.2013.V1.74