Learning-based Algorithms for Inverse Problems in MR Image Reconstruction and Quantitative Perfusion Imaging

Medical imaging has become an integral part of the clinical pipeline through its widespread use in the diagnosis, prognosis and treatment planning of several diseases. Magnetic Resonance Imaging (MRI) is particularly useful because it is free from ionizing radiation and is able to provide excellent soft tissue contrast. However, MRI suffers from drawbacks like long scanning durations that increase the cost of imaging and render the acquired images vulnerable to artifacts like motion. In modalities like Arterial Spin Labeling (ASL), which is used for non-invasive and quantitative perfusion imaging, low signal-to-noise ratio and lack of precision in parameter estimates also present significant problems. In this thesis, we develop and present algorithms whose focus can be divided into two broad categories. First, we investigate the reconstruction of MR images from fewer measurements, using data-driven machine learning to fill in the gaps in acquisition, thereby reducing the scan duration. Specifically, we first combine a supervised and an unsupervised (blind) learned dictionary in a residual fashion as a spatial prior in MR image reconstruction, and then extend this framework to include deep supervised learning. The latter, called blind primed supervised (BLIPS) learning, proposes that there exists synergy between features learned using shallower dictionary-based methods or traditional prior-based image reconstruction and those learned using newer deep supervised learning-based approaches. We show that this synergy can be exploited to yield reconstructions that are approx. 0.5-1 dB better in PSNR (in avg. across undersampling patterns). We also observe that the BLIPS algorithm is more robust to a scarcity of available training data, yielding reconstructions that are approx. 0.8 dB better (in terms of avg. PSNR) compared to strict supervised learning reconstruction when training data is very limited. Secondly, we aim to provide more precise estimates for multiple physiological parameters and tissue properties from ASL scans by estimation-theory-based optimization of ASL scan design, and combination with MR Fingerprinting. For this purpose, we use the Cramer-Rao Lower Bound (CRLB) for optimizing the scan design, and deep learning for regression-based estimation. We also show that regardless of the estimator used, optimization improves the precision in parameter estimates, and enables us to increase the available ‘useful’ information obtained in a fixed scanning duration. Specifically, we successfully improve the theoretical precision of perfusion estimates by 4.6% compared to a scan design where the repetition times are randomly chosen (a popular choice in literature) thereby yielding a 35.2% improvement in the corresponding RMSE in our in-silico experiments. This improvement is also visually evident in our in-vivo studies on healthy human subjects.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169819/1/anishl_1.pd

Convolutional Dictionary Learning: Acceleration and Convergence

Convolutional dictionary learning (CDL or sparsifying CDL) has many applications in image processing and computer vision. There has been growing interest in developing efficient algorithms for CDL, mostly relying on the augmented Lagrangian (AL) method or the variant alternating direction method of multipliers (ADMM). When their parameters are properly tuned, AL methods have shown fast convergence in CDL. However, the parameter tuning process is not trivial due to its data dependence and, in practice, the convergence of AL methods depends on the AL parameters for nonconvex CDL problems. To moderate these problems, this paper proposes a new practically feasible and convergent Block Proximal Gradient method using a Majorizer (BPG-M) for CDL. The BPG-M-based CDL is investigated with different block updating schemes and majorization matrix designs, and further accelerated by incorporating some momentum coefficient formulas and restarting techniques. All of the methods investigated incorporate a boundary artifacts removal (or, more generally, sampling) operator in the learning model. Numerical experiments show that, without needing any parameter tuning process, the proposed BPG-M approach converges more stably to desirable solutions of lower objective values than the existing state-of-the-art ADMM algorithm and its memory-efficient variant do. Compared to the ADMM approaches, the BPG-M method using a multi-block updating scheme is particularly useful in single-threaded CDL algorithm handling large datasets, due to its lower memory requirement and no polynomial computational complexity. Image denoising experiments show that, for relatively strong additive white Gaussian noise, the filters learned by BPG-M-based CDL outperform those trained by the ADMM approach.Comment: 21 pages, 7 figures, submitted to IEEE Transactions on Image Processin