Trilateral Filtering: A Non-linear Noise Reduction Technique for MRI

INTRODUCTION Filtering is a preliminary process in many medical image processing applications, which is aimed at restoring a noise-corrupted image to its noiseless counterpart. Post-processing tasks, e.g., visualization, segmentation and quantification, may benefit from the reduction of noise. Diffusion equations with scalar-valued and tensor-valued diffusivities [1] and non-linear filters [2] have been used to perform smoothing in medical images. In this paper, we present a novel filtering method, integrating geometric, photometric and local structural similarities, to achieve edge-preserving smoothing in medical images. It is simple to implement and is applicable to multi-dimensional signals. The experimental results have shown that this new technique provides greater noise reduction than other denoising techniques. Our method uses a narrow spatial window (3 pixels in each dimension) and takes only a few iterations (3 iterations in the experiments in this work) in the smoothing process. METHODS Bilateral filtering (BF) [3] is a simple, non-iterative and local approach to edge-preserving smoothing. A filtered image is obtained by replacing the intensity value of each pixel with an average value weighted by the geometric and photometric similarities between neighboring pixels within a spatial window. The novel filtering method proposed in this paper, namely trilateral filtering (TF), works along the same lines as BF; it takes the geometric, photometric and local structural similarities to smooth the images with a narrow spatial window while preserving the edges. Local structural information is used to determine inhomogeneity in the images and influence the smoothing process with orientation information. On one hand, low-pass filtering is performed in the homogeneous regions. On the other hand, smoothing along edges is achieved by considering the three similarities between neighborhoods in the inhomogeneous regions. We found that this new approach provides greater noise reduction than that of BF with a 3-pixel-width spatial window. TF is expressed as follows: