Abstract: Blurring and noise artifacts in magnetic resonance (MR) images caused by off-resonant image components may be corrected with convolutional neural networks, particularly feed forward networks with skip connections. Demodulating complex blurred images with off-resonant artifacts at a selected number of frequencies forms a respective real component frame of the MR data and a respective imaginary component frame for each image. A convolutional neural network is used to de-blur the images. The network has a plurality of residual blocks with multiple convolution calculations paired with respective skip connections. The method outputs, from the convolutional neural network, a de-blurred real image frame and a de-blurred imaginary image frame of the MR data for each complex blurred image.

Abstract: A computer implemented method of reconstructing magnetic resonance images (MRI) in Cartesian coordinates uses acquired magnetic resonance data and implements a Fourier transform to place the MRI data in k-space. The method allows for under-sampling the k-space and achieving an accurate output image by selecting an image model to map the sampled data and iteratively converge the model to an output that matches a region of interest subject to the MRI. The image model may be an alternating direction method of multipliers (ADMM) or an ADMM with non-convex low rank regularization algorithm. A de-noising algorithm may be at least one of a plug and play block matching and 3D filtering (PnP-BM3D), a plug and play weighted nuclear norm minimization (WNNM), or a plug and play denoising convolutional neural networks (PnP-DnCNN) algorithm. An iterative optimization of the variables of the model yields an output image.

Abstract: A computer implemented method of training a deep learning convolutional neural network (CNN) to correct output magnetic resonance images includes acquiring magnetic resonance image (MRI) data for a region of interest of a subject and saving the MRI data in frames of k-space data. The method includes calculating ground truth image data from the frames k-space data. The method includes corrupting the k-space data with real noise additions into the lines of the k-space data and saving in computer memory, training pairs a ground truth frame and a corrupted frame with real noise additions. By applying the training pairs to a U-Net convolutional neural network, the method trains the U-Net to adjust output images by correcting the output images for the real noise additions.

Abstract: Training a neural network to correct motion-induced artifacts in magnetic resonance images includes acquiring motion-free magnetic resonance image (MRI) data of a target object and applying a spatial transformation matrix to the motion-free MRI data. Multiple frames of MRI data are produced having respective motion states. A Non-uniform Fast Fourier Transform (NUFFT) can be applied to generate respective k-space data sets corresponding to each of the multiple frames of MRI; the respective k-space data sets can be combined to produce a motion-corrupted k-space data set and an adjoint NUFFT can be applied to the motion-corrupted k-space data set. Updated frames of motion-corrupted MRI data can be formed. Using the updated frames of motion corrupted MRI data, a neural network can be trained that generates output frames of motion free MRI data; and the neural network can be saved.

Abstract: Blurring and noise artifacts in magnetic resonance (MR) images caused by off-resonant image components may be corrected with convolutional neural networks, particularly feed forward networks with skip connections. Demodulating complex blurred images with off-resonant artifacts at a selected number of frequencies forms a respective real component frame of the MR data and a respective imaginary component frame for each image. A convolutional neural network is used to de-blur the images. The network has a plurality of residual blocks with multiple convolution calculations paired with respective skip connections. The method outputs, from the convolutional neural network, a de-blurred real image frame and a de-blurred imaginary image frame of the MR data for each complex blurred image.

Abstract: MR image data can be improved by using a complex de-noising convolutional neural network such as a non-blind C-DnCNN, a network for MRI denoising that leverages complex-valued data with phase information and noise level information to improve denoising performance in various settings. The proposed method achieved superior performance on both simulated and in vivo testing data compared to other algorithms. The utilization of complex-valued operations allows the network to better exploit the complex-valued MRI data and preserve the phase information. The MR image data is subject to complex de-noising operations directly and simultaneously on both real and imaginary parts of the image data. Complex and real values are also utilized for block normalization and rectified linear units applied to the noisy image data. A residual image is predicted by the C-DnCNN and a clean MR image is available for extraction.

Abstract: Training a neural network to correct motion-induced artifacts in magnetic resonance images includes acquiring motion-free magnetic resonance image (MRI) data of a target object and applying a spatial transformation matrix to the motion-free MRI data. Multiple frames of MRI data are produced having respective motion states. A Non-uniform Fast Fourier Transform (NUFFT) can be applied to generate respective k-space data sets corresponding to each of the multiple frames of MRI; the respective k-space data sets can be combined to produce a motion-corrupted k-space data set and an adjoint NUFFT can be applied to the motion-corrupted k-space data set. Updated frames of motion-corrupted MRI data can be formed. Using the updated frames of motion corrupted MRI data, a neural network can be trained that generates output frames of motion free MRI data; and the neural network can be saved.