Radial k-t FOCUSS using motion estimation and compensation

Recently, a model based dynamic imaging algorithm called k-t BLAST/SENSE has drawn significant attentions from MR imaging community due to its improved spatio-temporal resolution for dynamic MR imaging. In our previous work, we proved that k-t BLAST/SENSE can be derived as the first step of FOCal Underdetermined System Solver (FOCUSS) that exploits the sparsity of x-f support. Furthermore, the newly derived algorithm called k-t FOCUSS can be shown optimal from compressed sensing perspective. In this paper, the k-t FOCUSS algorithm is extended to radial trajectory. More specifically, the radial data are transformed to Cartesian domain implicitly during the FOCUSS iterations without explicit gridding to prevent error propagation. Thanks to the implicit gridding that allows fast Fourier transform, we can reduce the computational burden significantly. Additionally, a novel concept of motion estimation and compensation (ME/MC) is proposed to improve the performance of the algorithm significantly. In our ME/MC framework, we additionally obtain one reference sinogram with the full view, then the reference signogram is subtracted from all the radial data. Then, we can apply motion estimation / motion compensation (ME/MC) to improve the final reconstruction. The experimental results show that our new method can provide very high resolution even from very limited radial data set