MR-blob: Coordinate-Transformed Blobs for Parallel MRI Reconstruction

Motivation: Reducing the number of parameters needed to represent and reconstruct parallel MRI measurements. Goal(s): Reconstruct parallel MRI measurements with coordinate-transformed Gaussian functions (blobs) where the forward model is formulated directly. We term this MR-blob. Approach: MR-blob directly represents parallel MRI measurements; where coil sensitivities are modelled as isotropic Gaussians and the image is represented by coordinate-transformed blobs. Results: Noisy, undersampled parallel MRI simulations of Shepp-Logan phantom are reconstructed with a pixelised image, a coordinate-transformed blob-based image, and MR-blob; all with total variation regularisation. Quality measures are shown to be consistent across methods and regularisation strengths. Impact: Parameter-efficient image representations have the potential to reduce computational burden. This work defines parallel MRI forward model for coordinate-transformed blobs. This includes auto-calibrating coil sensitivities that re-scale and translate to fit the parallel MRI measurements.