Region-optimized virtual (ROVir) coils
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A method for suppressing or isolating signals from specific spatial regions in MRI using sensor-domain beamforming
Blog posts
2025
2024
Burst imaging simulation
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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
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
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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.
bSSFP simulation tutorial 1
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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.
2023
Partial Fourier reconstruction tutorial 3
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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.
Partial Fourier reconstruction tutorial 2
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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.
Partial Fourier reconstruction tutorial 1
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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 straightforward reconstruction method based on the conjugate symmetry of k-space
Low Rank reconstruction tutorial
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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.
Simulatenous Mulit-slice reconstruction tutorial 4
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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.
2022
Simulatenous Mulit-slice reconstruction tutorial 3
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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 2
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Slice GRAPPA is used exclusively for SMS, ensuring that the output dimensions match the input dimensions. The kernel is trained for each slice, allowing it to project the SMS data onto each individual slice. Similarly, the slice GRAPPA kernel is obtained through a least squares fit.
Simulatenous Mulit-slice reconstruction tutorial 1
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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.
EPI distortion correction tutorial 3
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Basic information about EPI has been shared in the previous post. Here, I share a reconstruction pipeline to correct the distortion using a third party package called FSL.
EPI distortion correction tutorial 2
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Basic information about EPI has been shared in the previous post. Here, I share another straightforward method for correcting EPI field distortions, utilizing nonrigid image registration.
EPI distortion correction tutorial 1
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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.
EPI PEC-SENSE phase correction tutorial
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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
EPI referenceless phase correction tutorial
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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
Joint GRAPPA reconstruction tutorial
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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.
CG SENSE reconstruction tutorial
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I really enjoy the CG SENSE framework. It enables everything to be formulated as a forward model in the form of a least squares problem. This also allows for the application of various regularization techniques.
SENSE reconstruction tutorial
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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)
GRAPPA reconstruction tutorial
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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.