High resolution dynamic MRI using compressed sensing

Abstract

The dynamic MR imaging of time-varying objects, such as beating hearts or brain hemodynamics, requires a significant reduction of the data acquisition time without sacrificing spatial resolution. The classical approaches for this goal include parallel imaging, temporal filtering, and their combinations. Recently, model-based reconstruction methods called k-t BLAST and k-t SENSE have been proposed which largely overcome the drawbacks of the conventional dynamic imaging methods without {\em a priori} knowledge of the spectral support. Another recent approach called k-t SPARSE also does not require exact knowledge of the spectral support. However, unlike the k-t BLAST/SENSE, k-t SPARSE employs the so-called compressed sensing theory rather than using training. The main contribution of this paper is a new theory and algorithm that unifies the abovementioned approaches while overcoming their drawbacks. Specifically, in chapter 1, we show that the celebrated k-t BLAST/SENSE is the special case of our algorithm, k-t FOCUSS, which is asymptotically optimal from the compressed sensing theory perspective. Then, in chapter 2, we propose an extension of k-t FOCUSS to a more general framework with prediction and residual encoding, where the prediction provides initial estimate and the residual encoding takes care of the remaining residual signals. Two prediction methods, RIGR and motion estimation/compensation scheme are proposed, which significantly sparsify the residual signals. Then, using more sophisticated random sampling pattern and optimized temporal transform, the residual signal can be effectively estimated from very small number of k-t samples. Experimental results show that excellent reconstruction can be achieved even from severely limited k-t samples without aliasing artifacts.