Pushing CT and MR Imaging to the Molecular Level for Studying the “Omics”: Current Challenges and Advancements

Figure 5

The reconstruction process of SENSE and GRAPPA. The example used a four-channel array coil for the acceleration rate of two. Each of the aliased pixels (𝐴₁, 𝐴₂, and so on) came from 𝐼_𝐴 and 𝐼_𝐵 with different weightings depending on the coil sensitivity values. It could be represented as 𝐴_𝑖=𝐼_𝐴𝐶_𝐴𝑖+𝐼_𝐵𝐶_𝐵𝑖, where 𝐴 was the aliased pixel, 𝐼 was the intensity of the unaliased pixel, and 𝐶 was the coil sensitivity weighting from the corresponding location. It could be possible to reconstruct the data by finding the inverse matrices of coil sensitivity maps, which could be written as 𝐴𝐶⁻¹=𝐼. GRAPPA reconstructed the undersampled 𝑘-space using ACS fittings to calculate the GRAPPA weightings and refill the missing lines from each coil. Each restored full 𝑘-space was transformed to obtain the single-coil images, which were then combined together to finalize the reconstruction.