Hao Peng^{1,2}, Chao Zou^{2}, Wenzhong Liu^{1}, Chuanli Cheng^{2,3}, Yangzi Qiao^{2}, Qian Wan^{2,3}, Changjun Tie^{2}, Xin Liu^{2}, and Hairong Zheng^{2}

Purpose: To propose an robust fat water separation method using binary decision tree algorithm.

Methods: In this paper, a novel fat-water separation algorithm using binary decision tree is proposed. Pixels are firstly clustered into sub-regions. Different from existing region growing algorithms, the proposed method solves the phasor ambiguity problem region by region. The method was tested on data sets from ISMRM 2012 Challenge.

Results:Fat-water separation were successfully achieved by the proposed method in the datasets.

Conclusion: A novel method using binary decision tree algorithm is proposed for robust and accurate water-fat separation.

Introducing the definition of ‘phasor’ ^{2}, the globally optimal phasor solution($$$P_G$$$) for one pixel can be
obtained through one dimensional search ^{3} . Let the swapped solution
of $$$P_G$$$ be $$$\overline{P_G}$$$. Define $$$P_w$$$ is either $$$P_G$$$ or $$$\overline{P_G}$$$, of
which the corresponding separation results in $$$|ρ_w |$$$ > $$$|ρ_f |$$$, while $$$P_f$$$ as that $$$|ρ_f |$$$ > $$$|ρ_w |$$$. The two candidate phasor solutions are classified into
two groups, namely, $$$P_w$$$ and $$$P_f$$$.

Figure 1 shows the principle of decision tree algorithm. The red starts in Fig. 1(a) represents three adjacent pixels in different tissues. There are two possible phasor solutions for each pixel, making there are 8 solution combinations for the three pixels. Fig. 1(b) aligns the eight combinations in a tree form according to the binary choice of $$$P_w$$$ or $$$P_f$$$ for each pixel. Among all combinations , the combination that is marked in yellow has the least phasor change through the tree paths (marked in red). The phasor solutions, along with the identification of fat and water for the three pixels are therefore decided.

Applying the decision tree to whole image pixel by pixel would be computationally intensive as there might be $$$2^N$$$ phasor solution combinations for N pixels. Therefore, neighboring pixels that have both similar $$$P_w$$$ and $$$P_f$$$ are firstly clustered as one region. As a result, the whole image is partitioned into several sub-regions (usually 20-50). Note that pixels inside each sub-regions have consistent choices of phasor solutions, either all from $$$P_w$$$ or all from $$$P_f$$$. The decision tree is then applied to the sub-regions to make the algorithm computationally feasible.

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3. D.Hernando, J.P.Haldar, B.P.Sutton, J.Ma, P.Kellman, Z.-P. Liang. Jiont estimation of water/fat images and field inhomogeneity map. Magn Reson Med 2008; 59:571-580;

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5. Chuanli Cheng, Chao Zou, Changhong Liang, Xin Liu, Hairong Zheng. Fat-water separation using a region-growing algorithm with self-feeding phasor estimation. Magn Reson Med 2017;77:2390-2401.

Figure 1: The red stars in (a) marked with A, B, and C are three pixels in muscle, subcutaneous fat and skin respectively. (b)the principle of the binary decision tree algorithm applied to this three pixels. The true phasor solutions for the three pixels are marked in yellow, meanwhile, the pixels can be identified to fat or water accordingly.

Figure 2: Binary decision tree for regional phasor estimation, the number in the brackets indicates the cost function of this path. Colorbar represents for the colored phasor maps. Red crosses marked below the phasor maps imply that the cost function of the corresponding path is larger than a predefined threshold, therefore, the tree path finding following the node is terminated. Once phasor solutions of all the sub-regions are identified, as in Figure H, the field map(Fig I) is obtained by region-growing algorithm.

Figure 3: phasor maps and water/fat components of: (a) ankle; (b) coronal slice of c-spine; (c) thighs from ISMRM 2012 Challenge dataset.