Greybox: A hybrid algorithm for direct estimation of tracer kinetic parameters from undersampled DCE-MRI data.

BACKGROUND: A variety of deep learning-based and iterative approaches are available to predict Tracer Kinetic (TK) parameters from fully sampled or undersampled dynamic contrast-enhanced (DCE) MRI data. However, both the methods offer distinct benefits and drawbacks. PURPOSE: To propose a hybrid algorithm (named as 'Greybox'), using both model- as well as DL-based, for solving a multi-parametric non-linear inverse problem of directly estimating TK parameters from undersampled DCE MRI data, which is invariant to undersampling rate. METHODS: The proposed algorithm was inspired by plug-and-play algorithms used for solving linear inverse imaging problems. This technique was tested for its effectiveness in solving the nonlinear ill-posed inverse problem of generating 3D TK parameter maps from four-dimensional (4D; Spatial + Temporal) retrospectively undersampled k-space data. The algorithm learns a deep learning-based prior using UNET to estimate the K trans $\mathbf {K_{trans}}$ and V p $\mathbf {V_{p}}$ parameters based on the Patlak pharmacokinetic model, and this trained prior was utilized to estimate the TK parameter maps using an iterative gradient-based optimization scheme. Unlike the existing DL models, this network is invariant to the undersampling rate of the input data. The proposed method was compared with the total variation-based direct reconstruction technique on brain, breast, and prostate DCE-MRI datasets for various undersampling rates using the Radial Golden Angle (RGA) scheme. For the breast dataset, an indirect estimation using the Fast Composite Splitting algorithm was utilized for comparison. Undersampling rates of 8 × $\times$ , 12 × $\times$ and 20 × $\times$ were used for the experiments, and the results were compared using the PSNR and SSIM as metrics. For the breast dataset of 10 patients, data from four patients were utilized for training (1032 samples), two for validation (752 samples), and the entire volume of four patients for testing. Similarly, for the prostate dataset of 18 patients, 10 patients were utilized for training (720 samples), five for validation (216 samples), and the whole volume of three patients for testing. For the brain dataset of nineteen patients, ten patients were used for training (3152 samples), five for validation (1168 samples), and the whole volume of four patients for testing. Statistical tests were also conducted to assess the significance of the improvement in performance. RESULTS: The experiments showed that the proposed Greybox performs significantly better than other direct reconstruction methods. The proposed algorithm improved the estimated K trans $\mathbf {K_{trans}}$ and V p $\mathbf {V_{p}}$ in terms of the peak signal-to-noise ratio by up to 3 dB compared to other standard reconstruction methods. CONCLUSION: The proposed hybrid reconstruction algorithm, Greybox, can provide state-of-the-art performance in solving the nonlinear inverse problem of DCE-MRI. This is also the first of its kind to utilize convolutional neural network-based encodings as part of the plug-and-play priors to improve the performance of the reconstruction algorithm.

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.

SpiNet: A deep neural network for Schatten p-norm regularized medical image reconstruction.

PURPOSE: 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 

SiameseGAN: A Generative Model for Denoising of Spectral Domain Optical Coherence Tomography Images.

Optical coherence tomography (OCT) is a standard diagnostic imaging method for assessment of ophthalmic diseases. The speckle noise present in the high-speed OCT images hampers its clinical utility, especially in Spectral-Domain Optical Coherence Tomography (SDOCT). In this work, a new deep generative model, called as SiameseGAN, for denoising Low signal-to-noise ratio (LSNR) B-scans of SDOCT has been developed. SiameseGAN is a Generative Adversarial Network (GAN) equipped with a siamese twin network. The siamese network module of the proposed SiameseGAN model helps the generator to generate denoised images that are closer to groundtruth images in the feature space, while the discriminator helps in making sure they are realistic images. This approach, unlike baseline dictionary learning technique (MSBTD), does not require an apriori high-quality image from the target imaging subject for denoising and takes less time for denoising. Moreover, various deep learning models that have been shown to be effective in performing denoising task in the SDOCT imaging were also deployed in this work. A qualitative and quantitative comparison on the performance of proposed method with these state-of-the-art denoising algorithms has been performed. The experimental results show that the speckle noise can be effectively mitigated using the proposed SiameseGAN along with faster denoising unlike existing approaches.