Energy Spectrum-based Variable-Density Sampling Distribution Optimized for MR Angiography at Compressed Sensing Technique

Abstract

The aim of this study was to determine the optimal k-space sampling distribution at a compressed sensing (CS) technique for imaging small blood vessels. First, we calculated the energy spectrum of the target vessel and then used this spectral information and the incoherence of undersampling artifacts by polynomial probability density with a power of decay (p) to determine the k-space sampling distribution for CS undersampling. The optimal p was calculated based on the energy spectra of different target vessels having different diameters which were described with full widths at half maximums (FWHMs). The optimized p together with its randomly sampled k-space was then applied to the data previously obtained with conventional magnetic resonance angiography (MRA) at 7.0 Tesla (T) MRI. Two acceleration factors of CS, such as ×3 and ×5 (33 and 20 %), were reconstructed from the conventional MRA data. The lower p was well fitted to the energy spectra of smaller vessels, in that the sampling density distribution of the lower p was closest to these spectra. However, with the higher acceleration (i.e., 20 %), two p values for small FWHMs, such as 0.56 and 0.84 mm, were not distinguishable because the undersampling of the DC point in k-space for the lower p was infeasible. With an acceleration of 33 %, the optimal p was obtained with the smallest vessels, and it most clearly discriminated the smaller vessels on the MRA images, as compared with other values of p. This study optimized the k-space sampling distribution for small vessels at CS technique. The results suggest that the lower p is suitable for the effective visualization of small vessels. Future studies are needed to appropriately adjust the acceleration factor and optimized p concurrently, since too high acceleration could restrict the applicable range of p and make it difficult to clearly depict smaller vessels.