Introduction

The lengthy acquisition time of MRI due to physical constraints poses a notable obstacle for its clinical usage. Various methods, including parallel imaging and compressed sensing, have been proposed and employed for sparse MR signal recovery to enable under-sampled MRI acquisition and reconstruction (1, 2, 3). In recent years, extensive research and application of deep learning techniques have been applied in computer vision, speech processing, semantic understanding and signal processing. In addition, deep learning methods have been increasingly investigated for under-sampled MRI reconstruction, surpassing even compressed sensing techniques (4). Originally designed for the segmentation of biomedical images (5), U-Net's distinct encoding-decoding structure conserves spatial image details, allowing for pixel-level prediction through end-to-end processing. U-Net has, therefore, been successfully utilized to expedite MRI reconstruction with commendable performance (6). However, the pooling operation employed in the encoding layer may lead to a gridding effect, while the interpolation used in the decoding layer can result in image blurring and artifacts.

In this study, wavelet transform and inverse wavelet transform are introduced to replace pooling and interpolation operations in order to maintain the spatial information of images during the encoding-decoding process within the neural network. With that, we present CAMERA-Net, a multi-level wavelet neural network developed for under-sampled MRI reconstruction.

Methods

The process of under-sampled MRI reconstruction is defined as finding $$$x$$$ from sub-sampled $$$y$$$ as follows: , $$y = SFx + e, [1]$$ Where $$$x$$$ is the target complex valued image, $$$F$$$ denotes Fourier transform, $$$S$$$ is the sub-sampling mask that selects points from k-space to be sampled, and $$$e$$$ represents the signal noise. Equation (1) represents a standard ill-posed inverse problem that must be resolved with a prior knowledge. The underdetermined optimization problem solution using the neural network approach can be represented as follows:$$argmin_{x} \{{\Vert x-f_{net}(y|\theta) \Vert}_2^2 + {\lambda} {\Vert SFx - y \Vert}_2^2 \} , [2]$$ Where $$$\theta$$$ represents all of the structural parameters that define the neural network, which may vary in size depending on the type of the network; $$$y$$$ denotes the subsampled k-space; and $$$f_{net}(y|\theta)$$$ denotes the forward mapping process of the neural network structure defined by $$$\theta$$$ with $$$y$$$ as input, with the aim of producing an image with reduced aliasing artifacts.

Fig. 1 illustrates the CAMERA-Net structure proposed in this research. The method consists of three primary components. First, instead of using pooling and interpolation operations, we apply wavelet transform and inverse wavelet transform during the encoding-decoding process to ensure spatial information preservation. Second, the neural network implements a DC layer to combine predicted data with acquired k-space data for improved data consistency. Finally, the wavelet module and DC layer are executed in an iterative scheme to efficiently propagate the ill- posed inverse problem and allow for flexibility in terms of accuracy, efficiency and model size. Our experimental data is obtained from the fastMRI knee dataset, with the training set comprising 9154 slices and the test set comprising 1768 slices. To test the reconstruction task with R=4, CAMERA-NET adopts the typical SSIM as the loss function.

Results

Five experiments were conducted to evaluate the quantitative performance of CAMERA-NET. The assessment of the effect of DWT and IDWT was validated through a comparison of the performance of U-Net and Wavelet-Net in Table 1 and Fig.2. The PSNR, SSIM and NMSE show that the Wavelet-Net has better performance than U-Net with results of 32.95, 0.8649, and 0.0152 as opposed to 32.72, 0.8621, and 0.0167.

The DC layer was observed to further enhance the reconstruction performance of Wavelet-Net for PSNR, SSIM, and NMSE, as reflected in Table 1, which improved to 33.88, 0.8713, and 0.0133 respectively.

Figure 3 illustrates the effect of the cascade number on reconstruction performance. The metrics for performance reconstruction, including SSIM, PSNR, and NMSE, improve as the number of cascades increases from 1 to 8.

Conclusion & Discussion

Drawing inspiration from both wavelet transform and convolutional neural network, we investigate a novel technique called CAMERA-NET intended for under-sampled MRI reconstruction. Our results demonstrates significant enhancement in reconstructing quality with public fastMRI knee dataset.

Acknowledgements

No acknowledgement found.

References

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