Improved k–t BLAST and k–t SENSE using FOCUSS

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 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 k-t BLAST/SENSE, k-t SPARSE employs the so-called compressed sensing (CS) theory rather than using training. The main contribution of this paper is a new theory and algorithm that unifies the above mentioned approaches while overcoming their drawbacks. Specifically, we show that the celebrated k-t BLAST/SENSE are the special cases of our algorithm, which is asymptotically optimal from the CS theory perspective. Experimental results show that the new algorithm can successfully reconstruct a high resolution cardiac sequence and functional MRI data even from severely limited k-t samples, without incurring aliasing artifacts often observed in conventional methods.