Ruoxun Zi^{1}, Patricia Johnson^{1,2}, and Florian Knoll^{3}

^{1}Center for Biomedical Imaging, Department of Radiology, NYU School of Medicine, New York, NY, United States, ^{2}Center for Advanced Imaging Innovation and Research (CAI2R), NYU School of Medicine, New York, NY, United States, ^{3}Department Artificial Intelligence in Biomedical Engineering, FAU Erlangen-Nuremberg, Erlangen, Germany

Although deep learning has received much attention for accelerated MRI reconstruction, it shows instabilities to certain tiny perturbations resulting in substantial artifacts. There has been limited work comparing the stability of DL reconstruction with conventional reconstruction methods such as parallel imaging and compressed sensing. In this work, we investigate the instabilities of conventional methods and the Variational Network (VN) with different accelerations. Our results suggest that CG-SENSE with an optional regularization is also impacted by perturbations but shows less artifacts than the VN. Each reconstruction method becomes more vulnerable with higher acceleration and VN shows severe artifacts with 8-fold acceleration.

$$\min_{x} \parallel{y-Ex}\parallel_2^2 + R(x)$$

where $$$y$$$ is the undersampled k-space data, $$$x$$$ is the image, and $$$E$$$ is the encoding operator. $$$R()$$$ is an additional regularizer, e.g. Tikhonov

As an example of DL-based method, the variational network with a Unet

$$\max_{r} \parallel{f(y+Er)-f(y)}\parallel_2^2 - \lambda\parallel{r}\parallel_2^2$$

where $$$r$$$ is the perturbation in image domain, and $$$f$$$ models the given reconstruction method (conventional or deep learning reconstruction). $$$\lambda$$$ is the weighting parameter on the l2-norm of the perturbation, which was chosen empirically. Gradient ascent with momentum was used to find the optimal solution of $$$r$$$

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Figure 1. Perturbations, reconstruction results with and without a perturbation and 10x reconstruction difference of conventional CG-SENSE (top), CG-SENSE with Tikhonov (middle) and CG-SENSE with TV (bottom) with R = 4 acceleration and uniform undersampling.

Figure 2. Perturbations, reconstruction results with and without perturbation, and 10x reconstruction difference of VN with R = 4 (top), 6 (middle), and 8 (bottom) acceleration with uniform undersampling.

Table 1. The mean square error (MSE) between reconstruction results with R = 4, 6 and 8 acceleration and the ground truth reconstructed with fully sampled k-space data.

DOI: https://doi.org/10.58530/2022/0951