A noise correction model incorporating weighted neighborhood information for liver R2* mapping

Changqing Wang^{1,2,3}, Xinyuan Zhang^{2}, Yanying Ma^{4}, Xiaoyun Liu^{1}, Diego Hernando^{3}, Scott B. Reeder^{3,5,6,7,8}, Wufan Chen^{1,2}, and Yanqiu Feng^{2}

** Theory:**
In
multi-coil systems, fitting the expectation value of noisy signal to the
first-moment noise-corrected model (M

$$\min_{S_0, R2^*}\sum_{x_j\in\Omega_i}w(x_i, x_j)\parallel{S_{x_j}-f(S_0, R2^*)}\parallel_2^2,$$

where *x _{j}* denotes the neighboring
voxels in search window Ω

$$w(x_i,x_j)=\left\{\begin{array}{} exp(-\frac{\parallel{S_{x_i}-S_{x_j}}\parallel_2^2}{h^2}) & \forall x_j\in\Omega_i \ and\ x_j\neq x_i,\\ max{\{w(x_i,x_j), \forall x_j \in \Omega_i \ and\ x_j\neq x_i\}} & if x_j=x_i,\end{array}\right.$$

where *h* acts as a smoothing parameter and controls the decay of the weights.
High
weights are assigned to voxels that have similar decay signals and small weights
to dissimilar voxels.

** Simulation Experiments:**
A
mask delineating liver anatomy (including parenchyma and blood vessels) and a nonuniform

** In Vivo Experiments:** Two subjects with moderate and severe iron loading levels were retrospectively analyzed after IRB approval and informed consent was obtained. In vivo experiments were performed on a 1.5T scanner (Sonata, Siemens Medical Solutions, Erlangen, Germany) using a 6-channel anterior array coil combined a 2-channel spine array coil and 2D spoiled gradient echo acquisition with fat saturation. Scan parameters included: number of echoes=12, TE

The proposed method was compared with two methods: the original M^{1}NCM model^{2} and nonlocal means (NLM) filter^{4}-based M^{1}NCM model^{5} (two-step operation: denoising multi-echo MR images by the NLM filter, then curve fitting by the original M^{1}NCM model).
Note that for the proposed and NLM-based methods, the search window size was set to 11×11 and smoothing parameter *h* was determined using root-mean-square error (RMSE)^{5} criterion. Quantitative analysis was performed for both simulation and in vivo data. RMSE and averaged R2* estimates over parenchyma for each combination of SNRs and R2* reference values were calculated in the simulation study. For the in vivo data, the statistical distributions of R2* estimated in liver were shown.

1. Feng Y, He T, Gatehouse PD, et al. Improved MRI R2 * relaxometry of iron-loaded liver with noise correction. Magn Reson Med 2013;70(6):1765-1774.

2. Wang C, He T, Liu X, et al. Rapid look-up table method for noise-corrected curve fitting in the R2* mapping of iron loaded liver. Magn Reson Med 2015;73(2):865-871.

3. Raya JG, Dietrich O, Horng A, et al. T2 measurement in articular cartilage: impact of the fitting method on accuracy and precision at low SNR. Magn Reson Med 2010;63(1):181-193.

4. A. Buades, B. Coll, Morel JM. A Review of Image Denoising Algorithms, with a New One. Multiscale Modeling & Simulation 2005;4(2):490-530.

5. Feng Y, He T, Feng M, et al. Improved pixel-by-pixel MRI R2* relaxometry by nonlocal means. Magn Reson Med 2014;72(1):260-268.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

1914