Zimu Huo

Zimu Huo

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

Partial Fourier reconstruction tutorial 3

less than 1 minute read

Published:

Partial Fourier techniques aim to recover missing data using only half of the k-space. This reconstruction leverages the conjugate symmetry property of k-space, although it is sensitive to phase errors.

Here, I present a Homodyne reconstruction that employs a more signal processing-oriented approach. It treats undersampling as a filter with different weightings for various frequency components in k-space, and attempts to apply the inverse of the filter to reverse the process.

View the Partial Fourier tutorial 3 here

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Simulatenous Mulit-slice reconstruction tutorial 5

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The slice-leakage is an artefact where the information from one slice is unintentionally transmitted to another slice during reconstruction. Any information from slice A that appears in slice B at the end of the reconstruction is considered slice leakage. The current method involves using a Monte Carlo simulation to impose unique frequency modulations on each slice. After reconstructions, the slice leakage can be determined by quantifying the frequency modulations on each individual slice. For example, if we add a 4 Hz modulation on slice A and a 6 Hz modulation on slice B, any 6 Hz component found on slice A after the reconstruction could be used to indicate slice leakage.

NUFFT tutorial

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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).

bSSFP simulation tutorial 2

less than 1 minute read

Published:

Here, I present various variations of bSSFP: standard bSSFP, fluctuating equilibrium, and alternating steady states. Each variation manipulates sequence parameters such as TR, flip angles, and RF phase to generate unique profiles optimized for specific tasks.