Zimu Huo

Zimu Huo

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

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Burst imaging simulation

less than 1 minute read

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An ultrafast excitation and acquisition technique.

This demo demonstrates how you can implement a sequence with just a few lines of code (in under 10 seconds) and visualize both the EPG and isochromat simulations with my simulation toolbox

View the BURST demo here

Simulatenous Mulit-slice reconstruction tutorial 5

less than 1 minute read

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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.

View the SMS tutorial 5 here

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

bSSFP simulation tutorial 2

less than 1 minute read

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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.

View the SSFP tutorial 2 here

bSSFP simulation tutorial 1

less than 1 minute read

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In bSSFP, the entire spin evolution can be modeled mathematically through bloch equations, which can be broken down into three components: excitation E, relaxation R, and precession P. These three components are matrix operators representing the sequence events. Immediately after the RF pulse R, the spin undergoes T1 and T2 relaxation E and off-resonance precession P. The bSSFP sequence achieves the steady state by repetitively executing these operations, while ensuring that the gradients are refocused within each TR.

View the SSFP tutorial 1 here

Partial Fourier reconstruction tutorial 3

less than 1 minute read

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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

Partial Fourier reconstruction tutorial 2

less than 1 minute read

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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 Projection onto Convex Sets (POCS) algorithm that finds the optimal solution by considering two criteria: 1. consistency with the acquired phase, and 2. consistency with the acquired k-space data.

View the Partial Fourier tutorial 2 here

Partial Fourier reconstruction tutorial 1

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 straightforward reconstruction method based on the conjugate symmetry of k-space

View the Partial Fourier tutorial 1 here

Low Rank reconstruction tutorial

less than 1 minute read

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The low rank based method will recover the missing data by enforcing self-consistency among neighboring k-space points in Cartesian space when minimizing the rank of the structured Hankel matrix. The self-consistency refers to the annihilation relationship being satisfied for all locations in k-space. Directly solving rank problems is computationally challenging and falls under the category of NP-hard problems. To address this, the non-convex rank function is replaced with its convex relaxation, which is replacing the non-convex rank function with its convex approximation, known as the nuclear norm.

View the Low Rank tutorial here

Simulatenous Mulit-slice reconstruction tutorial 4

less than 1 minute read

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The slice grappa tries to reduce the total artefact without placing constraints on the intraslice and interslice artifacts. So the artefacts can be arbitrarily large(like vectors pointing in opposite directions can cancel out each other, also called artefact cancellation). The split slice trades interslice artefact with intraslice artefact (lower interslice artefact and higher intraslice artefact) by forming a “correlation matrix” that contrains the interslice leakage to be minimum.

View the split slice slice GRAPPA tutorial here

Simulatenous Mulit-slice reconstruction tutorial 3

less than 1 minute read

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What if we combine SMS and inplane undersampling ?

In this case, the sms data is acquired with slice fatctor of ns, and in plane factor of R (total = ns * R). To unfold the aliasing, one could arrange the data reconstruction as two separate steps.

1. the slice grappa is used to separate the slice
2. the conventional grappa is then used along with reference data to unfold each individual slice.

View the slice GRAPPA with inplane acceleration tutorial here

Simulatenous Mulit-slice reconstruction tutorial 1

1 minute read

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Simultaneous Multislice (SMS) is a data acceleration technique that acquires multiple slices at the same time, rather than skipping lines within an acquisition. This method can be visualized as capturing all images within an extended field of view and then undersampling with a slice factor in a simulation. In practice, the signals from all slices are acquired together and superimposed linearly, causing multiple slices to overlap in the final image. The objective of the reconstruction process is to separate these slices with the highest possible quality.

In this simulation of the SMS experiment, we concatenate multiple slices into an extended field of view. Techniques like SENSE and GRAPPA treat this extended field as a single image, applying the reconstruction in their original, unmodified form. However, GRAPPA techniques encounter difficulties in this scenario due to the CAIPI shift causing a phase discontinuity between the images. This sharp change cannot be captured by a small GRAPPA kernel. Since the GRAPPA kernel is small and bandlimited, its image domain representation is smooth and slowly varying, making it inadequate for capturing the sharp phase change.

View the SENSE/GRAPPA tutorial here

EPI distortion correction tutorial 1

less than 1 minute read

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Echo-planar imaging (EPI) offers rapid imaging capabilities by capturing an entire k-space data set in a single acquisition. However, this technique is prone to geometric distortions, which significantly degrade image quality. These distortions are primarily caused by field inhomogeneities, leading to voxel shifts. The voxel shifts are especially pronounced in the phase-encode direction. In this context, we explore the blip up and blip down approaches. I present a straightforward correction method based on line integrals to address these issues.

View the EPI distortion correction tutorial 1 here

EPI PEC-SENSE phase correction tutorial

less than 1 minute read

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Due to the alternating direction of the EPI readout lines, hardware imperfections such as timing delays, eddy currents, and gradient coil heating can cause misalignment of the forward and reverse lines in k-space. This misalignment manifests itself in the images as a Nyquist (N/2) ghost in the phase encode direction and sinusoidal modulation of the object in the frequency encode direction.

The sampling incoherence is removed when interleving the positive and negative echos. However, a 2x acceleration is introduced to each dataset, resulting noise amplification

View the SENSE based EPI correction tutorial here

EPI referenceless phase correction tutorial

less than 1 minute read

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Due to the alternating direction of the EPI readout lines, hardware imperfections such as timing delays, eddy currents, and gradient coil heating can cause misalignment of the forward and reverse lines in k-space. This misalignment manifests itself in the images as a Nyquist (N/2) ghost in the phase encode direction and sinusoidal modulation of the object in the frequency encode direction.

The entropy-based method attempts to minimize the image entropy of the magnitude image to minimize EPI misalignment artifacts

View the Entropy based EPI correction tutorial here

The low rank method attempts to promote self consistency in k-space to minimize EPI misalignment artifacts

View the Low Rank based EPI correction tutorial here

Joint GRAPPA reconstruction tutorial

less than 1 minute read

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bSSFP suffers from unique banding artifacts, which are commonly corrected by using multiple phase cycles. These banding artifacts are a form of spatial modulation. While it is tricky to exploit this with SENSE (you will need coil maps and bssfp profile maps), this additional redundancy can be easily utilized by GRAPPA. To achieve this, we simply extend the GRAPPA kernel to include the phase cycle dimensions.

View the Joint GRAPPA reconstruction tutorial here

SENSE reconstruction tutorial

less than 1 minute read

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SENSE is a parallel imaging technique used to accelerate data acquisition in MRI.

In the original implementation of SENSE, the full-resolution coil sensitivity maps are estimated based on low-resolution calibration data. Consequently, high-resolution information is inherently absent. This contrasts with GRAPPA reconstruction, where high-resolution information is retained.

The advantage of SENSE lies in its simplicity, allowing for easy formulation as a forward model that can be solved through iterative reconstruction. See the next post for CG-SENSE (iterative reconstruction)

View the SENSE reconstruction tutorial here

GRAPPA reconstruction tutorial

less than 1 minute read

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GRAPPA is a widely used parallel imaging technique designed for accelerating data acquisition in MRI. It takes advantage of two key facts: first, MRI data is collected from multiple receivers, and second, k-space can be linearly interpolated due to its shift invariance properties.

View the GRAPPA reconstruction tutorial here

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Signal Processing

Undergraduate course, Teaching assistant, Imperial College London, Department of Bioengineering, 2023