Improved<i>k</i>–<i>t</i>BLAST and<i>k</i>–<i>t</i>SENSE using FOCUSS

TLDR

Dynamic MR imaging of time‑varying objects such as beating hearts or brain hemodynamics requires rapid data acquisition without losing spatial resolution, and recent model‑based methods like k–t BLAST, k–t SENSE, and k–t SPARSE have been developed to address this challenge, with k–t SPARSE employing compressed sensing rather than training. The paper proposes a unified theory and algorithm that integrates these approaches while overcoming their limitations. The authors develop an algorithm that generalizes k–t BLAST and k–t SENSE, achieving asymptotic optimality from a compressed‑sensing perspective. Experiments demonstrate that the algorithm reconstructs high‑resolution cardiac and functional MRI sequences from severely undersampled k–t data without aliasing artifacts typical of conventional methods.

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 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 abovementioned 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.