Interpolating Data from an Arbitrary 2D Sampling Pattern to a Uniform Grid

Gridding serves as a fundamental technique in Magnetic Resonance Imaging (MRI) for interpolating data from arbitrary 2D sampling patterns to uniform grids. This process facilitates rapid image reconstruction, establishing gridding as a critical component in modern MRI technology.

Substantial research publications have documented MR gridding reconstruction methodologies, underscoring the technique's significance in medical imaging. Implementation requires compiling MEX functions from the provided package using MATLAB commands: "mex gridlut_mex.c" generates convolution kernel lookup tables for grid interpolation, while "mex calcdcflut_mex.c" creates density compensation function lookup tables to correct sampling density variations. These commands produce platform-specific binaries (gridlut_mex.mex??? and calcdcflut_mex.mex???) where the extension varies by operating system.

After successful compilation, execute spiralexample.m to demonstrate practical gridding implementation. This script showcases the complete reconstruction pipeline: sampling data interpolation onto Cartesian grids using convolution kernels, followed by inverse Fourier transformation for image generation. The gridding algorithm ensures computationally efficient reconstruction while maintaining accuracy through optimal kernel selection and density compensation, enabling researchers to process MRI datasets with enhanced speed and precision.