Introduction:

Magnetic Resonance (MR) images can be reconstructed from the acquired raw data (known as k-space) which are the 2D or 3D Fourier transforms of real images. Standard scans are acquired on a Cartesian grid and reconstructed with an inverse Fourier transform. To acquire images in less time, only a portion of the k-space samples are measured. K-space is “undersampledâ€. This then requires more sophisticated image reconstruction algorithms and/or creates artifacts. Radial or polar sampling instead of Cartesian is typically more robust to undersampling. In this abstract, we compared different methods for reconstruction of undersampled radial k-space based on a constrained reconstruction framework.

Methods:

Reconstruction of undersampled radial data is performed by iteratively minimizing a cost function of a data fidelity term and constraint terms. The data fidelity term minimizes the mismatch between the estimated solution and acquired data. The constraint terms contains the temporal constraint term that assumes the temporal redundancy and the spatial constraint term that assumes piecewise images.

For implementation, three different methods were investigated. Pre-interpolation to Cartesian approximates the acquired data to the nearest integer neighbor point and matches the 2D FFT of estimated solution to the approximated data. Gridding method interpolates k-space data from 2D FFT of estimated solution to radial sampling pattern, and match them to the acquired data. Radon transform method does 1D FFT of radon transformed estimated solution, and matches them to the acquired data.

Both phantom and cardiac dynamic perfusion studies were performed on a Siemens 3T MRI scanner. The data was acquired at 96 interleaved angles, and at each time frame, 24 rays were acquired with adjacent angle of 180/24; an offset angle of 180/96 was set for adjacent time frames.

Results and Discussion

All of the methods were very dependent on the constraint weights and on any filtering within the iterations. The pre-interpolation to Cartesian method gave surprisingly good image quality, especially when the undersampling ratio was high. Work is ongoing to improve and speed up the reconstruction algorithms.