The complex data denoising in MR images based on the directional extension for the undecimated wavelet transform

- The directional information is abundant in MR image is addressed in this paper.
- The DEUWT is able to handle the directional information of images.
- The DEUWT provides translation-invariant property by the undecimated process.
- We propose a complex data denoising algorithm based on the DEUWT in MR images.
- The proposed algorithm is comparable to the state-of-the-art methods.

Magnetic resonance (MR) images are commonly affected by noises. Denoising is an important issue that has been frequently discussed in recent years. In this paper, an interesting phenomenon is found that the directional information is abundant in MR images. Therefore, high-quality reconstructed MR images could be obtained if the related directional information is considered. To address the issue, the directional extension for the undecimated wavelet transform (DEUWT), an effective tool that is able to handle the directional information and provides the translation-invariant (TI) property as well, is employed to process MR images. Based on the DEUWT, we present a novel and fast wavelet domain complex data denoising algorithm for MR images. In the presented algorithm, we combine the DEUWT with the stein's unbiased risk estimator (SURE) thresholding, and treat the real and imaginary components of the MR image as a single complex entity. The experimental results show that the proposed algorithm outperforms existing state-of-the-art methods on both simulated complex images and complex phantoms.