Zimu Huo

Zimu Huo

I’m interested in developing advanced data acquisition methods and reconstruction algorithms in magnetic resonance imaging (MRI).

NUFFT tutorial

less than 1 minute read

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Challenges arise when reconstructing from non-uniform sampling patterns in the Fourier domain. Performing a direct Fourier transform in such cases incurs a quadratic computation cost of O($N^2$), rendering it impractical for standard practices at high resolutions. This requires transforming non-Cartesian samples back into a uniformly spaced Cartesian grid, enabling the utilization of more efficient FFT algorithms. Typical regridding procedures involve convolving the acquired data with a predefined gridding kernel weighted by the pre-calculated density compensation function, followed by a resampling process onto the Cartesian grid. The ideal gridding kernel is a sinc function, as its Fourier transform results in a rectangular function. However, since the optimal convolution function is of infinite extent, implementing it directly is impractical. To address this, the convolution kernel is truncated and windowed. A popular choice for this purpose is the use of Kaiser-Bessel functions. These methodologies are commonly known as “gridding” and is a special case of non-uniform Fourier transforms (NUFFT).

View the NUFFT tutorial here

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