Structured & learnable regularizers for modeling inverse problems in fast MRI

<p>Contemporary Magnetic Resonance imaging technology has enabled structural, anatomical and functional assessment of various organ systems by allowing in-vivo visualization of those organs in terms of the biophysical parameters of the tissue. MRI still suffers from the slow image acquisition. The prolonged scan time enforces trade-offs between image quality and image acquisition time, often resulting in low spatial resolution, low signal to noise ratio, presence of artifacts resulting from patient or physiological motion. Therefore, the inverse problems that arise from MR image reconstruction tend to maximize image quality from minimally acquired signal observations. We study study the manipulation of the number of observations, based on the knowledge of the underlying image structure.</p><p>We start with studying an existing two step acquisition technique that seems to produce high quality reconstructions of dynamic MR images. We consider the recovery of a matrix X, which is simultaneously low rank and joint sparse, from few measurements of its columns using a two-step algorithm. Here, X captures a dynamic cardiac time-series. Our main contribution is to provide sufficient conditions on the measurement matrices that guarantee the recovery of such a matrix using a particular two-step algorithm. We illustrate the impact of the sampling pattern on reconstruction quality using breath held cardiac cine MRI and cardiac perfusion MRI data, while the utility of the algorithm to accelerate the acquisition is demonstrated on MR parameter mapping.</p><p>In the next study, another structure is explored, where the underlying static image is assumed to be piece-wise constant. Here, we consider the recovery of a continuous domain piecewise constant image from its non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities/edges of the image are localized to the zero levelset of a bandlimited function. The proposed algorithm reformulates the recovery of the unknown Fourier coefficients as a structured low-rank matrix completion problem. We show that exact recovery is possible with high probability when the edge set of the image satisfies an incoherency property, dependent on the geometry of the edge set curve.</p><p>In the previous two studies, the acquisition time burden is manipulated by exploiting the inherent structure of the image to be recovered. We call this the self-learning strategy, where the structure is learned from the current set of measured data. Finally, we consider exemplar learning, where population generic features (structures) are learned from stored examples or training data. We introduce a novel framework to combine deep-learned priors along with complementary image regularization penalties to reconstruct free breathing and ungated cardiac MRI data from highly undersampled multi-channel measurements. This work showed the benefit in combining the deep-learned prior that exploits local and population generalizable redundancies together with self-learned priors, which capitalizes on patient specific information including cardiac and respiratory patterns. is facilitated by the proposed framework.</p>