Chuanjiang Cui^{1}, Jun-Hyeong Kim^{1}, Kyu-Jin Jung^{1}, Jaeuk Yi^{1}, and Dong-Hyun Kim^{1}

^{1}Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea, Republic of

Phase-based EPT algorithm is extremely sensitive to noise. Although many studies have investigated such as linear(Gaussian filter) or non-linear filter(TV norm) to cope with amplification, textured noise and staircasing effect still remain in phase image, which lead to conductivity error such as broadening boundary artifact or high std value in reconstructed conductivity maps. In this study, we propose a deep prior based denoising method, which achieve to not only suppress instability brought by noise amplification but reduce boundary error.

In this study, we investigated the performance of the deep priors to suppress noise amplification and edge preservation for conductivity reconstructions with low-SNR data. We applied the deep prior to real and imaginary components of MR data, and the denoised data was recombined to B1 phase for conductivity reconstructions. Then the proposed algorithm was compared with conventional filtering methods (e.g., Gaussian filter, Total variation filter). To investigate the denoising performance, we applied the Laplacian-based and integral-based

The forward model of conductivity reconstruction with denoising filter can be written as model-based data consistency term with regularization

$$\hat{\sigma}=arg\min[\parallel Cond(\phi^{+})-\sigma\parallel^{2}+\lambda R(\phi^{+})] [1]$$

$$$Cond(\cdot)$$$ is conductivity reconstruction function. In this study, we drop the explicit TV regularization

$$\theta^{*}=arg\min \parallel f_{\theta}(z)-x_{0} \parallel^{2} [2]$$

The $$$f_{\theta}(\cdot)$$$ is CNN as shown in Fig 1. The $$$x_{0}\in R^{H\times W\times 2}$$$ is the combined real and imaginary parts with 2 channels from dataset, and the tensor $$$z\in R^{H\times W \times 32}$$$ is random Gaussian noise with 0.1 std. The minimizer $$$\theta^{*}$$$ is calculated using an ADAM optimizer, starting from a random initialization of the parameters $$$\theta$$$. Given the minimized $$$\theta^{*}$$$ , the denoised phase $$$\hat{\phi}^{+}$$$ is recombined from the denoised real and imaginary components $$$x^{*}=f_{\theta^{*}}(z)$$$, then conductivity is obtained from $$$\hat{\sigma}=Cond(\hat{\phi}^{+})$$$ .

Two different phase-based EPT reconstruction algorithms

Laplacian based algorithm is differential equation, valid in slow varying regions: $$$\sigma =\triangledown^{2}\phi^{+}/\mu_{0}\omega [3]$$$ , $$$\mu_{0}$$$ = vacuum permeability, $$$\omega$$$ = Larmor frequency, and $$$\triangledown^{2}$$$ = Laplacian operator.

Integral based algorithm

The simulation data was calculated from finite-difference time-domain (FDTD) simulation program

Turbo spin-echo (TSE) data were acquired at 3T: 1 healthy volunteer (Tim Trio, Siemens Healthineers: TR/TE=4500/85ms, resolution=1×1mm

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DOI: https://doi.org/10.58530/2022/2914