Development of Novel Deep Learning Methods for Fast-MRI: Anatomical Image Reconstruction to Quantitative Imaging

Abstract

In medical imaging, the task of estimating interpretable anatomical images from raw scanner data - based on underlying physical principles - is known as an "inverse problem". The solution to such inverse problems can be as simple as inverse Fourier transform for Magnetic Resonance Imaging (MRI). However, MRI is inherently slow due to the requirement of filling in the "k-space data". One of the popular ways of reducing the scan time is to use highly under-sampled data (collecting only a few samples of k-space data). Fast-MRI methods have found greater utility in dynamic imaging (3D+time), like Dynamic Contrast-Enhanced (DCE) MRI for cancer diagnosis and MR angiography. The acceleration in data acquisition time can be achieved using mathematical algorithms that incorporate these techniques' physical principles. This makes the inverse problem more challenging. Data driven methods based on deep learning (DL) have been able to provide promising results with few questions to be addressed like data dependency, lack of interpretability and lack of uncertainty quantification. This thesis work proposes physics-based DL algorithms that work with less training data and are more interpretable with the utilization of a physics-based forward model. The developed networks are also robust to data perturbations. Specifically, this thesis work addressed two problems related to Fast-MRI, with the first one concerning anatomical image reconstruction and the other focusing on quantitative imaging.

Anatomical image reconstruction: In this part, a generic deep learning-based MR image reconstruction model (named SpiNet) was proposed 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. 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 thesis work proposes a method to enforce any p norm on the noise prior where 0 < p ≤ 2. This is achieved by using the Majorization–Minimization algorithm, which upper bounds the cost function with a convex function, and 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 state-of-the-art model-based deep learning architecture (MoDL) which enforces L2 norm along with other compressive sensing-based algorithms. This comparison between the current state of the art methods 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 the proposed SpiNet. The results indicate that for all undersampling rates, the proposed SpiNet shows higher PSNR and SSIM and lower NRMSE than other state-of-the-art methods. However, for low undersampling rates of 2× and 4×, there is no significant difference in performance of proposed SpiNet and other state-of-the-art methods in terms of PSNR and NRMSE. This can be expected as the learnt p value is close to 2 (norm enforced by other methods). For higher undersampling rates grater than 6×, SpiNet significantly outperforms current state-of-the-art method in all metrices with improvement as high as 4 dB in PSNR and 0.05 points in SSIM.

Quantitative imaging: In this second part, this work focussed on estimating the permeability parameters from highly undersampled Dynamic Contrast-Enhanced (DCE) MR images and consists of two investigations. In the first investigation, 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. The investigations concluded that 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. The second investigation is of development novel physics-based DL scheme for permeability parameter estimation called Greybox - an amalgamation of DL (black box) and iterative techniques (white box). This algorithm is invariant to the undersampling rate and tested this algorithm for brain, breast and prostate cancer patients. Additionally, this thesis work also proposed a pure DL based architecture for direct estimation of permeability parameters. Unlike existing architectures, this network has been invariant to the spatial and temporal size of input data.

Deep learning based methods have shown promise for solving inverse problems associated with Fast-MRI. This thesis work shown that deep learning methods can also provide much needed quantitative accuracy, other than the obvious added advantage of being computationally efficient, for making MRI the most preferred imaging modality for quantitative imaging with applications in oncology and neuroimaging. The methods proposed here are able to generalise across anatomical structures and data sets, showing the versatility and making them appealing even in clinical settings.