Zero line and star artifacts

A bright linear signal in a dashed pattern that decreases in intensity across the screen and can occur as a line or star pattern, depending on the position of the patient in the ‘phase-frequency space’.^[1] Zero line and star artifacts are due to system noise or any cause of RF pollution within the room (Faraday cage). If this pattern persists, check for sources of system noise such as bad electronics or alternating current line noise, loose connections to surface coils, or any source of RF pollution. If a star pattern is encountered, the manufacturer needs to readjust the system software so that the image is moved off the zero point.^[1]

Zipper artifacts

Although less common, zippers are bands through the image centre due to an imperfect Faraday cage, with RF pollution in, but originating from outside, the cage.^[12] Residual free induction decay stimulated echo also causes zippers.^[1]

Preliminaries

The TAMER Method utilizes the SENSE forward model (described below) that has been modified to include the effects of motion in a 2D multi-shot imaging sequence. Note: the following modified SENSE model is described in detail in Melissa Haskell's doctoral dissertation, Retrospective Motion Correction for Magnetic Resonance Imaging.^[17]

Suppose that we have ${\displaystyle C}$ coils. Let ${\displaystyle x}$ be a ${\displaystyle nN_{sh}\times 1}$ column vector of image voxel values where ${\displaystyle n}$ is the number of k space samples acquired per shot and let ${\displaystyle s}$ be the ${\displaystyle nN_{sh}C\times 1}$ signal data from ${\displaystyle C}$ coils. Let ${\displaystyle E_{\theta }{\text{ be an }}nN_{sh}C\times nN_{sh}}$ encoding matrix for a given ${\displaystyle M\times 1}$ patient motion trajectory vector, ${\displaystyle \theta }$. ${\displaystyle E_{\theta }}$ is composed of ${\displaystyle N_{sh}}$ many ${\displaystyle nC\times nN_{sh}}$ sub-matrices ${\displaystyle E_{\theta _{i}}=U_{i}FCT_{xy,i}T_{z,i}R_{i}}$ (encoding matrices for each shot ${\displaystyle i}$).

For each shot ${\displaystyle i}$, we have the sub-matrix ${\displaystyle E_{\theta _{i}}=U_{i}FCT_{xy,i}T_{z,i}R_{i}}$ which is the encoding matrix for that particular shot ${\displaystyle i}$ where:

${\displaystyle U_{i}}$ is the ${\displaystyle nC\times nN_{sh}C}$ under-sampling operator

${\displaystyle F}$ is the Fourier Encoding Operator

${\displaystyle T_{xy,i}}$ is the in-place translation operator

${\displaystyle Tz,i}$ is the through-plane translation operator

${\displaystyle R_{i}}$ is the rotation operator

SENSE Motion Forward Model: ${\displaystyle s=Ex}$

SENSE model Extended to describe a 2D multi-shot imaging sequence:

$${\displaystyle s=E_{\theta }x{\text{ where }}E_{\theta }={\begin{pmatrix}E_{\theta _{1}}\\E_{\theta _{2}}\\.\\.\\.\\E_{\theta _{Nsh}}\end{pmatrix}}{\text{ and }}E_{\theta _{i}}=U_{i}FCT_{xy,i}T_{z,i}R_{i}{\text{ for shot }}i=1,2,...,N_{sh}}$$

The rigid-body motion forward model is nonlinear and the process of solving for estimations of both the motion trajectory and the image volume is computationally challenging and time-consuming. In the effort to speed up and simplify computations, the TAMER method separates the vector of image voxel values, ${\displaystyle x}$, into a vector of target voxel values, ${\displaystyle x_{t}}$ , and a vector of fixed voxels, ${\displaystyle x_{f}}$. Given any choice of target voxels and fixed voxels, we have the following:

${\displaystyle x={\binom {x_{t}}{x_{f}}}}$

${\displaystyle s=s_{t}+s_{f}=E_{\theta }(t)x_{t}+E_{\theta }(f)x_{f}}$ ${\displaystyle s_{t}=s-E_{\theta }(f)x_{f}=E_{\theta }(t)x_{t}}$

Note: The length of ${\displaystyle x_{t}}$ only makes up about 5% of the total length of ${\displaystyle x}$.

Now the optimization can be reduced to fitting the signal contribution of the target voxels to the correct target voxel values ${\displaystyle x_{t}}$ and the correct motion, ${\displaystyle \theta }$.

TAMER Algorithm

The TAMER algorithm has 3 main stages: Initialization, Jumpstart of Motion Parameter Search, and the Joint Optimization Reduced Model Search.

Initialization: The first stage of the TAMER algorithm acquires the initial reconstruction of the full image volume, ${\displaystyle x_{0}}$, by assuming that all motion parameters are zero. One can solve for ${\displaystyle x_{0}}$ by minimizing the least squared error of the SENSE forward model without motion i.e. solve the system ${\displaystyle (E_{0}^{H}E_{0})x_{0}=E_{0}^{H}s}$ where ${\displaystyle E_{0}=UFC}$ and ${\displaystyle E_{0}^{H}}$ is the conjugate transpose of ${\displaystyle E_{0}}$.^[16] We have discussed the notion of separating the sense model into ${\displaystyle s=s_{t}+s_{f}=E_{\theta }(t)x_{t}+E_{\theta }(f)x_{f}}$; however, we haven't yet discussed how the target voxels are chosen. Voxels that are strongly coupled together indicate motion. In a motion-free Cartesian acquisition, each voxel would only be coupled to itself, so our goal is to essentially un-couple these voxels. As described in the paper Targeted Motion Estimation and Reduction (TAMER): Consistency Based Motion Mitigation for MRI using a Reduced Model Joint Optimization, as part of the IEEE Transactions on Medical Imaging Journal, the TAMER algorithm converges fastest when choosing target voxels that are highly coupled. ^[16] The target voxels can be entirely determined by the sequence parameters and coil sensitivities.^[16]

Target Voxel Selection Process:

1. Group coils based on artifact properties. The model error is first computed assuming no motion. The model correlation is then computed across all channels. TAMER is applied to groups of coils with the largest correlation artifacts to attain the motion and image estimation.^[17]
2. The initial target voxels are selected by first choosing a root voxel (generally the center of the image). Once the root voxel is chosen, the correlation between the root voxel and all other voxels is determined by attaining the column vector of the correlation matrix ${\displaystyle E^{H}E}$ corresponding to the root voxel. The magnitude of the entries in this column vector represent the strength of interaction between the root voxel and all of the other voxels.^[16] The root voxel along with the voxels that have the strongest interaction with the root voxel are then chosen to be the initial target voxels.

Note: For each iteration of the TAMER process, the target voxels are selected by shifting the target voxels from the previous iteration perpendicularly to the phase encode direction by a preset amount.

Jumpstart of Motion Parameter Search:

Now the initial guess of the patient's motion is determined by evaluating the data consistency metric over a range of values for each of the ${\displaystyle M}$ motion parameters and the best value for each parameter is selected to construct the initial guess.^[17]

Joint Optimization Reduced Model Search:

We now have the initial target voxels, motion estimate, and coil groupings. The following procedure is now executed.

Let ${\displaystyle \theta ^{(i)}}$ be the motion trajectory estimate for the ${\displaystyle i^{th}}$search step. Let ${\displaystyle i_{max}}$ be the max number of iterations.

While ${\displaystyle i<i_{max}{\text{ and }}\nabla ^{(i)}>\Delta \epsilon _{max}}$ repeat the following:

1. Solve for ${\displaystyle s_{t}^{\left(i\right)}\,\to s_{t}^{\left(i\right)}\,=\,s\,-\,E_{\theta ^{\left(i\right)}}\left(f\right)x_{f}=\,E_{\theta ^{\left(i\right)}}\left(t\right)x_{t}}$
2. Solve for ${\displaystyle x_{t}^{\left(i\right)}\,\to E_{\theta ^{\left(i\right)}}^{H}\left(t\right)E_{\theta ^{\left(i\right)}}\left(t\right)\,x_{t}^{\left(i\right)}=\,E_{\theta ^{\left(i\right)}}^{H}\left(t\right)x_{f}}$
3. Set ${\displaystyle \epsilon ^{(i)}=||s-E_{\theta ^{(i)}}x^{(i)}||}$
4. Set ${\displaystyle \,\theta ^{\left(i+1\right)}\,=\,\theta ^{\left(i\right)}\,+\,\nabla ^{\left(i\right)}\,\to \,\,\nabla ^{\left(i\right)}\,=\epsilon ^{(i)}-||s-E_{\left(\theta ^{\left(i\right)}\,+\,d\theta ^{\left(i\right)}\right)\,}x^{\left(i\right)}||_{2}}$
5. Set ${\displaystyle i=i+1}$

TAMER: Advantages and Disadvantages

Advantages:

• TAMER retrospectively corrects for motion, so modifications to the MRI exam procedure isn't necessary.
• TAMER doesn't alter the acquisition procedure, so it can be easily integrated into current clinical MRI scans.  
• TAMER significantly reduces computation of the joint optimization model used to estimate motion parameters and image voxels.

Disadvantages:

• Current TAMER implementations have lengthy overall computation times.
• TAMER requires multi-channel data as the motion parameters need additional degrees of freedom which is provided by the multichannel acquisition.^[16]
• The TAMER algorithm assumes static coil profiles that don't change with the motion of the patient. This assumption would be an issue for larger motion.

NAMER

Network Accelerated Motion Estimation and Reduction (NAMER)^[23] is a retrospective motion correction technique that utilizes convolutional neural networks (CNNs), a class of neural networks designed to process and learn from visual information such as images. This is a follow-up from the authors of the TAMER paper titled Network Accelerated Motion Estimation and Reduction (NAMER): Convolutional neural network guided retrospective motion correction using a separable motion model.^[23] Similar to TAMER, the paper aims to correct for motion-related artifacts by way of estimating a desired motion-free image and optimizing parameters for a SENSE forward model describing the relationship between raw k-space data and image space while factoring in rigid motion.

Image Estimation

The CNN attempts to learn the image artifacts from the motion-corrupted input data ${\displaystyle x}$. The estimate for these artifacts, denoted as ${\textstyle CNN(x)}$, are then subtracted from the motion-corrupted input data ${\displaystyle x}$ in order to produce a best estimate for the motion-free image:^[23]

$${\displaystyle x_{CNN}=x-CNN(x)}$$

This serves two purposes: First, it allows the CNN to perform backpropagation and update its model weights by using a mean square error loss function comparing the difference between ${\textstyle x_{CNN}}$ and the known ground-truth motion-free image.^[23] Second, it gives us a good estimate of the motion-free image that gives us a starting point for model parameter optimization.

Optimizing the Optimization Procedure

Before, we used the following to optimize both the image ${\displaystyle x}$ and parameters ${\textstyle \theta }$ at once. Now, we can optimize solely the ${\textstyle \theta }$ values:

$${\displaystyle {\hat {\theta }}=argmin_{\theta }\Vert s-E_{\theta }x_{CNN}\Vert _{2}}$$

On top of this, if a multi-shot acquisition was performed, we can estimate the parameters ${\textstyle \theta _{n}}$ for each of ${\displaystyle n}$ shots separately, and go even further by estimating the parameters ${\textstyle \theta _{n,l}}$ for each line ${\displaystyle l}$ in each shot ${\displaystyle n}$:^[23]

$${\displaystyle {\hat {\theta }}_{n,l}=argmin_{\theta _{n,l}}\Vert s_{n,l}-E_{\theta _{n,l}}x_{CNN}\Vert _{2}}$$

This allows us to massively reduce computation time, from around 50 minutes with TAMER^[16] to just 7 minutes with NAMER.^[23]

Reconstruction

The new model parameters are then used in a standard Least Squares optimization problem to reconstruct an image that minimizes the distance between the k-space data, and the result of applying the SENSE forward model ${\displaystyle E_{\hat {\theta }}}$ under our new parameter estimate ${\textstyle {\hat {\theta }}}$ to our best estimate for the motion-free image:^[23]

$${\displaystyle [{\hat {x}}]=arg\min _{x}\Vert s-E_{\hat {\theta }}x\Vert _{2}}$$

This process is repeated until a desired number of time steps, or when the change in reconstructed image is sufficiently low. The NAMER technique has shown itself to be very effective in correcting for rigid motion artifacts, and converges much faster than other methods including TAMER.^[23] This illustrates the power of deep learning in improving results across myriad fields.

Generative adversarial networks

Other more advanced techniques take advantage of generative adversarial networks (GANs) which aim to learn the underlying latent representation of data in order to synthesize new examples that are indistinguishable from real data. Here, two neural networks, a Generator Network and a Discriminator Network, are modelled as agents competing in a game. The Generator Network's goal is to produce synthetic images that are as close as possible to images from the true distribution, while the Discriminator Network's goal is to distinguish generated synthetic images from the true data distribution. Specific to motion artifact correction in MRI, the Generator Network takes in an image with motion artifacts, and outputs an image without motion artifacts. The Discriminator Network then differentiates between the synthesized image and ground truth data. Various studies^[25][26] have shown that GANs perform very well in correcting for motion artifacts.

External Objects

B1 inhomogeneity due to constructive or destructive interference from the permittivity of body tissue can be mitigated using external objects with high dielectric constants and low conductivity.^[27] These objects, called radiofrequency/dielectric cushion, can be placed over or near the imaging slice to improve B1 homogeneity. The combination of high dielectric constant and having low conductivity allows the cushion to alter the phase of the RF standing waves and has been shown to reduce signal loss due to B1 inhomogeneity. This correction method was shown to have the greatest effect on sequences that suffer from B1 inhomogeneity artifacts but has no effect on those with B0 inhomogeneity. In one study, the dielectric cushion improved image quality for turbo spin echo‐based T2‐weighted sequences but not on gradient echo‐based T2‐weighted sequences.^[27]

Coil Mitigated Corrections

B1 inhomogeneity has been successfully mitigated by adjusting coil type and configurations.

Active Power modulation

Actively modulating the RF transmit power for each slice position compensates for B1 inhomogeneity.^[32] This method focuses on inhomogeneity along the axial, or z axis, direction since it is the most dominant in terms of poor homogeneity and least sample dependent.

Prior to inhomogeneity correction, measurement of the B1 profile along the z-axis of the coil is necessary for calibration. Once calibrated, the B1 data can be used for active transmit power modulation. For a specific pulse sequence, the values of each slice position are pre-determined and the appropriate RF transmitter power scale values are read from a look-up table. Then, while the sequence runs, a real time slice counter varies the attenuation of the RF transmit power.^[32]

This method is advantageous for reducing artifacts at the source, particularly when accurate flip angle is critical and for increasing signal to noise ratio. Even though this technique can only be used to compensate for the B1 variation along the z-axis in axially acquired images, it's still significant since B1 inhomogeneity is most dominant along this axis.

B1 insensitive adiabatic pulses

One way to achieve perfect spin inversion despite B1 inhomogeneity is to use adiabatic pulses. This correction method works by removing the source of the problem and applying pulses that will not generate flip angle errors. Specific sequences that employ adiabatic pulses for increased flip angle uniformity include a slice selective spin-echo pulse, adiabatic 180 degrees inversion RF pulses, and 180 degrees refocusing pulses. ^{[33] [34] [35]}

Image post-processing

Post-processing techniques correct for intensity inhomogeneity (IIH) of the same tissue over an image domain. This method applies a filter to the data, typically based on a pre-acquired IIH map of the B1 field. If a map of the IIH in the image domain is known, then the IIH can be corrected by division into the pre-acquired image.^[36] This popular model in describing the IIH effect is:

• ${\displaystyle x=\alpha x'+\xi }$ ^[36]

Where ${\displaystyle x}$ is the measured intensity, ${\displaystyle x'}$ is the true intensity, ${\displaystyle \alpha }$ is the IIH effect and ξ is the noise.

This method is advantageous because it can be conducted offline, i.e., the patient is not required to be in the scanner. Therefore, correction time is not an issue. However, this technique does not improve SNR and contrast of the image because it only utilizes information that was already acquired. Since the B1 field was not homogeneous when the images were acquired, the flip angles and subsequent acquired signals are imprecise.

The effects of an AI-based image post-scan processing denoising system in brain scans have been demonstrated to be effective in higher image quality and morphometric analysis. Post-scan image processing systems enable noise reduction while retaining contrast. The subsequent image enhancement can be processed with shorter scan times for higher throughput and plausible earlier detection.^[37][38]