Methods for scan-specific k-space interpolation reconstruction in magnetic resonance imaging using machine learning
Methods for reconstructing images from undersampled k-space data using a machine learning approach to learn non-linear mapping functions from acquired k-space lines to generate unacquired target points across multiple coils are described.
1. A method for reconstructing an image from undersampled k-space data acquired with a magnetic resonance imaging (MRI) system, the steps of the method comprising:
(a) providing to a computer system, undersampled k-space data and calibration data acquired with an MRI system;
(b) processing the calibration data with a computer system to learn parameters for a machine learning algorithm implemented with a hardware processor and memory of the computer system;
(c) estimating missing k-space data by inputting the undersampled k-space data to the machine learning algorithm; and
(d) reconstructing an image from the undersampled k-space data and the estimated missing k-space data.
2. The method as recited in claim 1 , wherein the machine learning algorithm is a neural network.
3. The method as recited in claim 2 , wherein the neural network includes at least one layer that implements a non-linear activation function.
4. The method as recited in claim 2 , wherein the neural network is a convolutional neural network.
5. The method as recited in claim 4 , wherein the convolutional neural network comprises a plurality of layers in which each layer includes applying a convolution operation on data input to that layer, wherein each of the plurality of layers comprises a number of input channels and a number of output channels, and wherein at least some of the plurality of layers comprise applying non-linear processing on an output of the convolution operation.
6. The method as recited in claim 5 , wherein the learned parameters comprise weights for the convolution operation in each layer.
7. The method as recited in claim 6 , wherein the learned parameters further comprise biases for at least some of the plurality of layers.
8. The method as recited in claim 5 , wherein the non-linear processing includes applying an activation function to the output of the convolution operation.
9. The method as recited in claim 8 , wherein the activation function comprises a rectified linear unit.
10. The method as recited in claim 5 , wherein the non-linear processing includes applying batch normalization to the output of the convolution operation.
11. The method as recited in claim 2 , wherein the neural network comprises a plurality of layers in which at least some of the plurality of layers implement non-linear processing.
12. The method as recited in claim 11 , where each of the plurality of layers except a last one of the plurality of layers implement non-linear processing.
13. The method as recited in claim 1 , wherein the calibration data are acquired as auto-calibration signal (ACS) data together with the undersampled k-space data.
14. The method as recited in claim 1 , wherein the calibration data are acquired in a separate scan from the undersampled k-space data.
15. The method as recited in claim 1 , wherein the undersampled k-space data are complex-valued data, and step (c) includes embedding the undersampled k-space data in a higher dimensional real space before inputting the undersampling k-space data to the machine learning algorithm.
16. The method as recited in claim 1 , wherein step (b) includes applying a linear k-space interpolation to the calibration data to increase a size of the calibration data before processing the calibration data to learn the parameters for the machine learning algorithm.
17. The method as recited in claim 1 , wherein step (a) includes acquiring the undersampled k-space data and the calibration data with the MRI system and providing the undersampled k-space data and the calibration data to the computer system.
18. The method as recited in claim 1 , where processing the calibration data with a computer system to learn the parameters for the machine learning algorithm includes minimizing a loss function.
19. The method as recited in claim 18 , wherein the loss function is a mean squared error.
20. The method as recited in claim 1 , wherein the undersampled k-space data sample k-space using a Cartesian sampling pattern.
21. The method as recited in claim 1 , wherein the undersampled k-space data sample k-space using a non-Cartesian sampling pattern.
22. The method as recited in claim 1 , wherein the undersampled k-space data are three-dimensional k-space data.
23. The method as recited in claim 1 , wherein the undersampled k-space data were acquired from multiple different slices simultaneously using a simultaneous multislice acquisition and the calibration data include calibration data for each of the multiple different slices.
24. The method as recited in claim 1 , wherein estimating the missing k-space data in step (c) further comprises estimating replacement values for at least some of the undersampling k-space data by inputting the undersampled k-space data to the machine learning algorithm, and wherein values in the undersampled k-space data for which replacement values are estimated are replaced by the replacement values before reconstructing the image in step (d).
25. A method for reconstructing an image from undersampled k-space data acquired with a magnetic resonance imaging (MRI) system, the steps of the method comprising:
(a) providing to a computer system, undersampled k-space data and calibration data acquired with an MRI system;
(b) processing the calibration data in a k-space domain to learn a non-linear mapping from the calibration data;
(c) estimating missing k-space data by directly applying the non-linear mapping to the undersampled k-space data; and
(d) reconstructing an image from the undersampled k-space data and the estimated missing k-space data.