Itzik Malkiel^{1}, Sangtae Ahn^{2}, Zac Slavens^{3}, Valentina Taviani^{4}, and Christopher J Hardy^{2}

We propose a densely connected deep convolutional network for reconstruction of highly undersampled MR images. Eight-channel 2D brain data with fourfold undersampling were used as inputs, and the corresponding fully-sampled reconstructed images as references for training. The algorithm produced notably higher-quality images than state-of-the-art parallel imaging and compressed sensing methods, both in terms of reconstruction error and perceptual quality. The dense architecture was found to significantly outperform a similar network without dense connections.

The DCI-Net (Fig. 1), receives M coils of undersampled k-space data at its input. The network is an unrolled compressed-sensing (CS) iterative reconstruction with N = 40 iterations, each of which includes a data-consistency unit and a regularization unit (Fig. 1B). Skip-layer connections between the output of each iteration and the following G iterations - where typically G = 16 - are represented as curved lines in Fig. 1A. This results in an input to each block composed of skip and direct connections concatenated to form a G+1 channel complex image. (The number of skip connections is ramped down in the final iterations until there is only one channel at the output of the network.) Each data-consistency unit shades the input image with each coil sensitivity map, transforms the resulting images to k-space, imposes the sampling mask, calculates the difference relative to acquired k-space and returns them to the image domain, multiplied by a learned weight. Each regularization unit (Fig. 1C) has three sequences consisting of 5x5 convolution, bias, and leaky-ReLU layers. The output of the final iteration (Fig. 1A) is converted to a magnitude image and compared to the fully sampled reference image to generate a loss function, using either mean square error (MSE) or structural similarity index (SSIM).

Fully sampled multi-slice brain datasets (256x256 T1-FLAIR and T2-FLAIR, in axial, coronal, and sagittal orientations), along with separately acquired sensitivity maps, were acquired after informed consent from 12 healthy volunteers at 3T using an 8-channel receive array. The data were retrospectively down-sampled using 11 central lines of k-space and a fixed pseudo-random sampling pattern outside the central region, resulting in a net undersampling factor of 3.6. Complex coil-combined zero-filled reconstructions were used as input to the network. The undersampled k-space data were also input directly into each iterative block of the network (Fig. 1A) for use in the data-consistency units. The fully sampled k-space data were reconstructed to form reference images for comparison with the network output. In total, 1130 slices were collected, of which 948 were used to train the networks, 89 for validation and 93 for testing. The same undersampled data were also reconstructed using compressed sensing (with both total variation and wavelets). Parallel imaging (ARC) reconstructions were performed as well, but with regular undersampling in outer k space.

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