Iterative image reconstruction that includes a total variation regularization for radial MRI

VTDCE-Net: A time invariant deep neural network for direct estimation of pharmacokinetic parameters from undersampled DCE MRI data

PURPOSE

To propose a robust time and space invariant deep learning (DL) method to directly estimate the pharmacokinetic/tracer kinetic (PK/TK) parameters from undersampled dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) data.

METHODS

DCE-MRI consists of 4D (3D-spatial + temporal) data and has been utilized to estimate 3D (spatial) tracer kinetic maps. Existing DL architecture for this task needs retraining for variation in temporal and/or spatial dimensions. This work proposes a DL algorithm that is invariant to training and testing in both temporal and spatial dimensions. The proposed network was based on a 2.5-dimensional Unet architecture, where the encoder consists of a 3D convolutional layer and the decoder consists of a 2D convolutional layer. The proposed VTDCE-Net was evaluated for solving the ill-posed inverse problem of directly estimating TK parameters from undersampled k - t $k-t$ space data of breast cancer patients, and the results were systematically compared with a total variation (TV) regularization based direct parameter estimation scheme. In the breast dataset, the training was performed on patients with 32 time samples, and testing was carried out on patients with 26 and 32 time samples. Translation of the proposed VTDCE-Net for brain dataset to show the generalizability was also carried out. Undersampling rates (R) of 8× , 12× , and 20× were utilized with PSNR and SSIM as the figures of merit in this evaluation. TK parameter maps estimated from fully sampled data were utilized as ground truth.

RESULTS

Experiments carried out in this work demonstrate that the proposed VTDCE-Net outperforms the TV scheme on both breast and brain datasets across all undersampling rates. For K trans $\mathbf {K_{trans}}$ and V p $\mathbf {V_{p}}$ maps, the improvement over TV is as high as 2 and 5 dB, respectively, using the proposed VTDCE-Net.

CONCLUSION

Temporal points invariant DL network that was proposed in this work to estimate the TK-parameters using DCE-MRI data has provided state-of-the-art performance compared to standard image reconstruction methods and is shown to work across all undersampling rates.

A singular K-space model for fast reconstruction of magnetic resonance images from undersampled data

Reconstructing magnetic resonance images from undersampled k-space data is a challenging problem. This paper introduces a novel method of image reconstruction from undersampled k-space data based on the concept of singularizing operators and a novel singular k-space model. Exploring the sparsity of an image in the k-space, the singular k-space model (SKM) is proposed in terms of the k-space functions of a singularizing operator. The singularizing operator is constructed by combining basic difference operators. An algorithm is developed to reliably estimate the model parameters from undersampled k-space data. The estimated parameters are then used to recover the missing k-space data through the model, subsequently achieving high-quality reconstruction of the image using inverse Fourier transform. Experiments on physical phantom and real brain MR images have shown that the proposed SKM method constantly outperforms the popular total variation (TV) and the classical zero-filling (ZF) methods regardless of the undersampling rates, the noise levels, and the image structures. For the same objective quality of the reconstructed images, the proposed method requires much less k-space data than the TV method. The SKM method is an effective method for fast MRI reconstruction from the undersampled k-space data. Graphical abstract Two Real Images and their sparsified images by singularizing operator.