Design of Temporally Constrained Compressed Sensing Methods for Accelerated Dynamic MRI

Introduction: Many clinical applications necessitate a limited scan time for dynamic MRI acquisition, e.g. due to breath hold or contrast passage. This often restricts attainable spatial and temporal resolution, limiting potential diagnostic or research applications. To reconstruct significantly undersampled time frames at clinically desired spatial/temporal resolution a number of approaches have been proposed, including compressed sensing (CS) CS reconstruction from incomplete data relies on the assumption that the underlying signal has a sparse representation in some basis. Typically, CS utilizes spatial sparsity of the image itself or its discrete gradient. However, in time-resolved imaging, the level of spatial sparsity may not be sufficient to support the required high accelerations, leading to residual artifacts and loss of spatial resolution. Temporal filtering methods based on quadratic minimization such as k-t SENSE were shown to mitigate these problems [1]. However, recent reports indicated limitations on acceleration achievable with such techniques [2]. CS approaches exploiting sparsity in temporal dimension in addition to or instead of spatial dimensions promise to overcome these limitations. Previously proposed methods include utilization of the temporal derivative [3-5] and sparsity in x-f space [6]. Critical to success of such approaches is the choice of the sparsifying basis, as an improper choice may lead to significant image artifacts and loss of spatial/temporal resolution [2]. In this work, we propose a novel approach that uses 2 temporal derivative for improved temporal waveform fidelity and hybrid 1 l / 2 l norm penalty on