Quasi-Newton MRI deep learning reconstruction
Systems and methods reconstruction for a medical imaging system using a quasi-newton method. An unrolled iterative reconstruction process is used to reconstruct an image from the scan data. The unrolled iterative reconstruction process includes a plurality of cascades that include at least a data-consistency step and a regularization step. The data-consistency step is modified based at least in part on information of already calculated gradients of one or more previous cascades of the plurality of cascades using a quasi-newton computation.
1 . A system for reconstruction of a magnetic resonance image, the system comprising:
a medical imaging scanner configured to acquire under sampled k-space data of a patient; and
an image processor configured to reconstruct and output the magnetic resonance image from the under sampled k-space data using an unrolled iterative reconstruction process comprising an inverse problem, wherein each iteration of the unrolled iterative reconstruction process comprises a data-consistency step and a regularization step performed by a trained neural network, wherein the image processor is configured to compute the data-consistency step, for each cascade, using a quasi-Newton preconditioner that is dynamically adapted to a locally trained data-consistency loss of a current cascade by an:
initialization of the quasi-Newton preconditioner using a direct sensitivity encoding (SENSE) pseudo-inverse matrix;
an update of the quasi-Newton preconditioner using a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm with gradients and inputs retained from previous cascades; and
an application of the updated quasi-Newton preconditioner to a gradient direction that is weighted in the k-space domain by a learned density-compensation function.
2 . The system of claim 1 , further comprising:
a display configured to display the magnetic resonance image.
3 . The system of claim 1 , wherein the under sampled k-space data is under sampled using a general pattern.
4 . The system of claim 3 , wherein the unrolled iterative reconstruction process comprises a proximal optimization step that balances the data-consistency steps and the regularization steps.
5 . The system of claim 1 , wherein the under sampled k-space data is under sampled using a regular pattern.
6 . The system of claim 1 , wherein the image processor is configured to calculate coil sensitivity data from a reference scan and perform a singular value decomposition to compute a data-consistency term for the data-consistency step.
7 . A method for MR image reconstruction, the method comprising:
acquiring, by a medical imaging scanner, under sampled k-space data acquired using a general pattern;
reconstructing the MR image from the under sampled k-space data using an unrolled iterative reconstruction comprising an inverse problem, wherein each iteration of the unrolled iterative reconstruction comprises a data-consistency step and a regularization step performed by a trained neural network, wherein the data-consistency step is computed, for each cascade, using a quasi-Newton preconditioner that is dynamically adapted to a locally trained data-consistency loss of the current cascade by:
initializing of the quasi-Newton preconditioner using a direct sensitivity encoding (SENSE) pseudo-inverse matrix;
updating the quasi-Newton preconditioner using a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm with gradients and inputs retained from previous cascades; and
applying the updated quasi-Newton preconditioner to a gradient direction that is weighted in the k-space domain by a learned density-compensation function; and
outputting the reconstructed MR image.
8 . The method of claim 7 , wherein for the unrolled iterative reconstruction, an image prior is weighted differently in an image space.
9 . The method of claim 7 , further comprising applying a density-compensation function to the optimization that weights k-space coefficients differently.
10 . The method of claim 7 , wherein the regularization step is performed using a convolutional neural network.
11 . A method for MR image reconstruction, the method comprising:
acquiring, by a medical imaging scanner, under sampled k-space data acquired using a regular sampling pattern;
reconstructing the MR image using an unrolled iterative reconstruction that is formulated as an inverse problem, wherein each iteration of the unrolled iterative reconstruction comprises a data-consistency step and a regularization step performed by a trained neural network, wherein the data-consistency step is computed, for each cascade, using a quasi-Newton preconditioner that is dynamically adapted to a locally trained data-consistency loss of the current cascade by:
initializing of the quasi-Newton preconditioner using a direct sensitivity encoding (SENSE) pseudo-inverse matrix;
updating the quasi-Newton preconditioner using a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm with gradients and inputs retained from previous cascades; and
applying the updated quasi-Newton preconditioner to a gradient direction that is weighted in the k-space domain by a learned density-compensation function; and
outputting the reconstructed MR image.
12 . The method of claim 11 , wherein initializing the quasi-Newton preconditioner using the direct sensitivity encoding (SENSE) pseudo-inverse matrix comprises performing a singular value decomposition of an encoding matrix that represents a combination of a Fourier operator, a coil-sensitivity matrix, and a sampling operator, and computing a regularized inverse of an encoding matrix from the singular value decomposition by truncating or thresholding small singular values to improve conditioning of the quasi-Newton preconditioner.
13 . The method of claim 12 , further comprising:
calculating a coil sensitivity data from a reference scan;
decoupling an encoding matrix into aliased blocks; and
performing the singular value decomposition on each of the aliased blocks.