Abstract
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.
Highlights
MethodsThe main goal in the following experiments is to demonstrate that denoising performance can be improved by using 1
We propose a group l0 minimization denoising framework that utilizes tight wavelet frames and takes advantage of the correlation between DW images scanned with neighboring gradient directions
We have introduced a method that harnesses correlations between DW images scanned with similar gradient directions for effective edge-preserving denoising
Summary
The main goal in the following experiments is to demonstrate that denoising performance can be improved by using 1. UEP-based tight wavelet frames, which avoids the staircasing effect; 2. Collaborative utilization of angularly neighboring DW images. We used the piecewise linear tight wavelet frame with L = 2 levels of decomposition. The optimal λ values for l0 and l1 were in (1, 8], determined using grid search from 0.2 to 50 in steps of 0.2 based on the maximal peak signal-to-noise ratio (PSNR) defined MAX2. PSNR 1⁄4 10 log MSE ; ð27Þ where MAX is the maximal signal value and MSE is the mean square error. The noise level is estimated from the image background using the method described in [24]. More advanced noise estimation methods [23, 25] can be used for improved accuracy
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