Research Article: Multi-channel framelet denoising of diffusion-weighted images

Date Published: February 6, 2019

Publisher: Public Library of Science

Author(s): Geng Chen, Jian Zhang, Yong Zhang, Bin Dong, Dinggang Shen, Pew-Thian Yap, Dzung Pham.


Diffusion MRI derives its contrast from MR signal attenuation induced by the movement of water molecules in microstructural environments. Associated with the signal attenuation is the reduction of signal-to-noise ratio (SNR). Methods based on total variation (TV) have shown superior performance in image noise reduction. However, TV denoising can result in stair-casing effects due to the inherent piecewise-constant assumption. In this paper, we propose a tight wavelet frame based approach for edge-preserving denoising of diffusion-weighted (DW) images. Specifically, we employ the unitary extension principle (UEP) to generate frames that are discrete analogues to differential operators of various orders, which will help avoid stair-casing effects. Instead of denoising each DW image separately, we collaboratively denoise groups of DW images acquired with adjacent gradient directions. In addition, we introduce a very efficient method for solving an ℓ0 denoising problem that involves only thresholding and solving a trivial inverse problem. We demonstrate the effectiveness of our method qualitatively and quantitatively using synthetic and real data.

Partial Text

Diffusion MRI affords in vivo insights into brain tissue microstructure and allows reconstruction of white matter pathways for neuroscience studies involving development, aging, and disorders [1–5]. However, since diffusion MRI derives its contrast from MR signal attenuation, it suffers from low signal-to-noise-ratio (SNR), which complicates subsequent quantitative analyses. To improve SNR, multiple repetitive scans are typically acquired and averaged for noise reduction. This however inevitably prolongs acquisition times and is hence prohibitive in clinical settings. Post-acquisition algorithms, such as total variation (TV) denoising [6], have been widely adopted due to their ability to remove noise without requiring additional acquisition time.

We will provide first a brief introduction to framelets, followed by details on how framelets can be incorporated into an ℓ0 minimization framework for DWI denoising.

The main goal in the following experiments is to demonstrate that denoising performance can be improved by using

In this paper, we have introduced a method that harnesses correlations between DW images scanned with similar gradient directions for effective edge-preserving denoising. Our main contributions lie in three aspects. Firstly, UEP was employed to generate frames that were discrete analogues to differential operators of various orders; Secondly, instead of the conventional ℓ1 regularization, a very efficient method was proposed in order to solve an ℓ0 denoising problem that involves only thresholding and a trivial inverse problem; Thirdly, DW images acquired using neighboring gradient directions were used for collaborative denoising.

In conclusion, we have proposed a method to remove the noise in DW images. The proposed method takes advantage of multi-channel framelet and the correlations among DW images for effective noise removal. The associated ℓ0 optimization problem is solved by an effective iterative hard thresholding algorithm. Extensive experiments on synthetic data and real data demonstrate the advantage of our method over various noise reduction methods, including TV regularization, NLM, and the ℓ1 counterpart of our method.




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