The design of composite adaptive morphological filter and applications to Rician noise reduction in MR images

Abstract

Composite filters based on morphological operators are getting considerably attractive to medical image denoising. Most of such composite filters depend on classical morphological operators. In this article, an optimal composite adaptive morphological filter (FCAMF) is developed through a genetic programming (GP) training algorithm by using new nonlocal amoeba morphological operators. On one hand, we propose a novel method for formulating and implementing nonlocal amoeba structuring elements (SEs) for input-adaptive morphological operators. The nonlocal amoeba SEs in the proposed strategy is divided into two parts: one is the patch distance based amoeba center, and another is the geodesic distance based amoeba boundary, by which the nonlocal patch distance and local geodesic distance are both taken into consideration. On the other hand, GP as a supervised learning algorithm is employed for building the FCAMF. In GP module, FCAMF is evolved through evaluating the fitness of several individuals over certain number of generations. The proposed method does not need any prior information about the Rician noise variance. Experimental results on both standard simulated and real MRI data sets show that the proposed filter produces excellent results and outperforms existing state-of-the-art filters, especially for highly noisy image.