To compare the performance of iterative direct and indirect parametric reconstruction methods with indirect deep learning-based reconstruction methods in estimating tracer-kinetic parameters from highly undersampled DCE-MR Imaging breast data and provide a systematic comparison of the same. Methods: Estimation of tracer-kinetic parameters using indirect methods from undersampled data requires to reconstruct the anatomical images initially by solving an inverse problem. This reconstructed images gets utilized in turn to estimate the tracer-kinetic parameters. In direct estimation, the parameters are estimated without reconstructing the anatomical images. Both problems are ill-posed and are typically solved using prior-based regularization or using deep learning. In this study, for indirect estimation, two deep learning-based reconstruction frameworks namely, ISTA-Net + and MODL, were utilized. For direct and indirect parametric estimation, sparsity inducing priors (L1 and Total-Variation) and limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm as solver was deployed. The performance of these techniques were compared systematically in estimation of vascular permeability (K trans) from undersampled DCE-MRI breast data using Patlak as pharmaco-kinetic model. The experiments involved retrospective undersampling of the data 209, 509, and 1009 and compared the results using PSNR, nRMSE, SSIM, and Xydeas metrics. The K trans maps estimated from fully sampled data were utilized as ground truth. The developed code was made available as https://github.com/Medical-Imaging-Group/DCE-MRI-Compare open-source for enthusiastic users. Results: The reconstruction methods performance was evaluated using ten patients breast data (five patients each for training and testing). Consistent with other studies, the results indicate that direct parametric reconstruction methods provide improved performance compared to the indirect parameteric reconstruction methods. The results also indicate that for 209 undersampling, deep learningbased methods performs better or at par with direct estimation in terms of PSNR, SSIM, and nRMSE. However, for higher undersampling rates (509 and 1009) direct estimation performs better in all metrics. For all undersampling rates, direct reconstruction performed better in terms of Xydeas metric, which indicated fidelity in magnitude and orientation of edges. Conclusion: Deep learning-based indirect techniques perform at par with direct estimation techniques for lower undersampling rates in the breast DCE-MR imaging. At higher undersampling rates, they are not able to provide much needed generalization. Direct estimation techniques are able to provide more accurate results than both deep learning-and parametric-based indirect methods in these high undersampling scenarios.
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 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 and 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 stateof -the-art performance compared to standard image reconstruction methods and is shown to work across all undersampling rates.
To propose a generic deep learning based medical image reconstruction model (named as SpiNet) that can enforce any Schatten p-norm regularization with 0 < p ≤ 2, where the p can be learnt (or fixed) based on the problem at hand. Methods: Model-based deep learning architecture for solving inverse problems consists of two parts, a deep learning based denoiser and an iterative data consistency solver. The former has either L2 norm or L1 norm enforced on it, which are convex and can be easily minimized. This work proposes a method to enforce any p norm on the noise prior where 0 < p ≤ 2. This is achieved by using Majorization-Minimization algorithm, which upper bounds the cost function with a convex function, thus can be easily minimized. The proposed SpiNet has the capability to work for a fixed p or it can learn p based on the data. The network was tested for solving the inverse problem of reconstructing magnetic resonance (MR) images from undersampled k space data and the results were compared with a popular model-based deep learning architecture MoDL which enforces L2 norm along with other compressive sensing-based algorithms. This comparison between MoDL and proposed SpiNet was performed for undersampling rates (R) of 2×, 4×, 6×, 8×, 12×, 16×, and 20×. Multiple figures of merit such as PSNR, SSIM, and NRMSE were utilized in this comparison. A two-tailed t test was performed for all undersampling rates and for all metrices for proving the superior performance of proposed SpiNet compared to MoDL. For training and testing, the same dataset that was utilized in MoDL implementation was deployed. Results: The results indicate that for all undersampling rates, the proposed SpiNet shows higher PSNR and SSIM and lower NRMSE than MoDL. However, for low undersampling rates of 2× and 4×, there is no significant difference in performance of proposed SpiNet and MoDL in terms of PSNR and NRMSE. This can be expected as the learnt p value is close to 2 (norm enforced by MoDL). For higher undersampling rates ≥6×, SpiNet significantly outperforms MoDL in all metrices with improvement as high as 4 dB in PSNR and 0.5 points in SSIM. Conclusion:As deep learning based medical image reconstruction methods are gaining popularity, the proposed SpiNet provides a generic framework to incorporate Schatten p-norm regularization with 0
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