# Local software projects/MRI ghost artifact detection

Jump to: navigation, search

#  MRI Ghost Artifact Detection

The main goal of this project is to implement an efficient, metric-based software algorithm that would be able to evaluate the level of ghosting artifact in MR images and distinguish the severely damaged images from the good ones. The algorithm can then work as a part of a quality assurance unit in MR centre's database and can be set up to send emails to people letting them know if their scan has been severely affected by ghosting artifact and whether or not they need to come back and redo it.

#  Background

Magnetic Resonance Imaging (MRI) is a powerful, non-invasive imaging modality that is widely used for research and medical applications, but is inherently prone to artifacts and usually has a low signal to noise ratio. It creates a great soft tissue contrast and can generally be used to image many parts of the body. Our focus in this project is going to be on brain images, because first of all, "Vista" lab is more interested in studying the brain, and second of all, over 30-35% of all MR scans are done on brains.

Creating a 3D image of the brain slice by slice using MRI, is not like taking a photograph of that slice using a camera, it does not happen instantly. It takes time to build up an entire image of one slice. While the physics behind MRI seems to be very complicated, the math behind it turns out to be very elegant: The signals you get from an MRI device at each point in time turn out to be the samples of the Fourier transform of the object you are trying to image. So, what happens is that, you need to excite the spins in the object (in our case the brain) in a special way, then wait a certain amount of time for them to relax (depending on how much contrast you want in your image) and then the signal you get is a set of samples from the Fourier transform of the object. Then, you have to excite the spins again, repeat the sequence and get another set of samples and so on. After covering the whole frequency space (which we will call the K-space), you can take the inverse Fourier transform of the data and reconstruct the object. There are several sequences you can use to cover the K-space, each having its own advantages over the others. The first and probably most obvious one is covering K-space in a line by line fashion. this sequence is called the "2DFT" or "Cartesian" sequence, and is very popular.




Over time, researchers have come up with many new sequences that can improve quality of the images or shorten the scan time. One of the most common ones is the Echo-planar Imaging (EPI) technique. Echo-planar imaging is a very fast MRI technique that can acquire an entire MR image in only a fraction of a second. The main idea behind EPI is to cover the K-space in a raster-line fashion but collect the data from all lines from only one excitation. You can see how using this sequence instead of a regular 2DFT would shorten the scan time.




While this technique offers major advantages over conventional MRI techniques, the images acquired with this method often suffer from artifacts that are usually more severe than those resulting from standard imaging techniques. One of the most common ones which is the subject of my study, is the N/2 or Nyquist "ghosting" artifact. Ghosts are the repeated versions of the image or part of the image that appear in our reconstructed image in addition to the original object and are usually blurred and smeared and shifted with respect to the original image. Once overlapping with the original image, ghosts can severely compromise the image quality and the data accuracy in those regions. Below you can see a ghosted MR image acquired using EPI technique.

In general ghosts can result from patient motion, cardiac or respiratory motions and system imperfections. In this study we focus on the ghosts resulting from the third source. The reason is that since we are using EPI sequences to scan our subjects, the scan time is short enough to be sure that patient motion artifacts are not going to be that severe. But in contrast, inconsistencies and discontinuities in the phase-encoding direction can result in significant ghosts in the resulting EP images. More specifically, the discontinuities arise because we are collecting data from alternating positive and negative readout gradients. So, after collecting the data, the reconstruction computer should time-reverse the data lines obtained with the negative gradient lobe relative to the ones obtained from the positive lobes. Unfortunately, due to many reasons like system imperfections, time delays in the sequence and eddy currents, this time reversal leads to a phase mismatch between every other line. This is why with a single shot EPI this discontinuities lead to Nyquist or N/2 ghosting artifact, which consists of two ghosts one shifted up and one shifted down by N/2 voxels with respect to the original image. The ghosted image you saw earlier is an example of this kind of ghosting. This kind of ghosts in the image can be identified by their location and orientation within the image.

Over the years, researchers have performed many studies to correct for the ghosts in the image and retrieve the original data. Most commonly, the ghosts are corrected for, using the phase data from a reference scan performed prior to the actual scan. The problem with this method, is that it requires a separate reference scan for each slice, and also any changes in the system performance, for example system instability due to heat, or etc. between the reference scan and the actual one can affect our calculations. To overcome these problems, people have proposed other techniques for somehow changing the sequence parameters to obtain better images.

Another way to approach this problem is to use image-based phase correction techniques. These techniques, need access to the raw K-space data from the scanners. For example, one way is to derive the necessary phase corrections by filtering the images reconstructed from the even and odd echoes separately[6]. Other methods propose looking at the ghosting artifact as a special case of motion artifact and therefore applying the motion correction methods to the ghosted images. These methods usually apply a phase correction to the image, then evaluate a certain metric (usually the cross-correlation metric, more on this later) and then iterate to minimize that metric[15,19]. Newer methods, suggest that we model the ghost as a function of two phase components: the zeroth and the first order phase corrections and then use metric-based minimization of ghosting by guessing these two correction factors and then iterate on them. As an example, Skare et al. [15], suggest the entropy of the image as their metric and iterate on the zeroth and first order phase-correction factors to minimize this metric.

Up to now, we briefly reviewed the literature existing on ghost-correction algorithms which span from various sequence-based to several image-based techniques. But, another very important concern in MR imaging field before attempting to eliminate the ghosts of the image, is to be able to measure the degree and nature of ghost in the images as part of the quality assurance operations that each MR centre needs. To my best knowledge, there are not as many articles focusing on this issue. Most of the research works done on ghosting artifacts are trying to develop algorithms to eliminate ghosting and if they need a metric in the end to do the optimization around it or to evaluate how much ghost is still present in the image after performing a correction, the generally use one of the cross-correlation or entropy metrics. The motivation for my project was to test the robustness of these metrics in terms of how good they can predict the level of ghosting in MR images, and also try to come up with other meaningful metrics that we think can better assess the level of ghost in the images. Once fully developed, this ghost assessment technique can be embedded in an MR database centre to evaluate the quality of the images immediately after they enter the database and determine whether or not the data can be used in research applications or if the scan should be redone.

#  Methods

###  Subjects

In order to test the performance of different image quality metrics on MR images, I have used brain scans from 55 young and healthy subjects each having a different level of ghosting artifact. These images were originally resulted from a DTI scan, but I used only the b=0 image from each subject which does not have any diffusion weighting. From my experience, the ghosting artifact was consistent throughout the entire volume, so I have used only the middle axial slice of each subject in which the ghosting artifact is more observable to the eye, for my studies. This was approximately the 25th axial slice and the resulting 2D image was a 128X128 matrix.

###  Metrics

In order to evaluate the performance of different metrics for determining the degree of ghosting in MR images, the first step was to observe the images by eye and rank them based on their degree of ghosting. We used "fslview" which is an image visualization tool and is part of the fsl software library (which contain different MRI analysis tools), to load the images (which were save in NIFTI format in the database) and look at them. The next step was to rank the images based on the degree of ghosting present in them. In some of the images (for example the left image below) the ghost was very obvious and had corrupted the data in the brain. But in others (for example the one below on right) the ghost was barely noticeable and the data seemed very clean.

Since ranking 55 images based on their quality can be very overwhelming and may blind the observer in long run, I used bubble sorting technique on the images, which means I went through the whole set of images 55 time to be able to rank them fairly based on the level of ghosting available in them. The initials of the ranked subjects were saved in a MATLAB .mat file.

After this, a binary classification was also performed on the images, meaning they were divided into two groups: the ones which I thought the data was not severely affected by the ghosts and the ones in which the data was so corrupted by the ghost that it would later affect the analysis (specially those including for example studying the Fractional Anisotropy (FA) in them). 13 out of 55 subjects were identified as damaged images.

Another thing that needed to be done before we could start testing different metrics on our ghosted images was the need to extract the brain mask from each ghosted image, so that we have an idea of where the borders of the true image are. This was done using fsl brain extraction or "BET" command, which is again part of fsl libraries and when performed on an image, will extract the main outline of the true image and delete the non-brain or ghost images around it. This command is called in the following format:

# bet <input> <output>

the inputs and outputs can be NIFTI images.

The BET command was run on all 55 subjects and the brain masks were saved in NIFTI formats. Below you can see an example of a ghosted image along with the mask that BET algorithm has extracted from it.

The next step was to think of different metrics, write codes in MATLAB that would test that metric on an image, and then collect data from the 55 subjects. Here is a list of different metrics used in this project along with explanations about their meaning in terms of image quality and their implementation:

####  1- Percentage Mean Signal

The first and probably most intuitively understandable metric that comes to mind for evaluating the level of ghost in images is calculating the percentage mean signal of the ghost compared to the original image. In fact, scientists used to use this metric on their MR images to manually evaluate the level of ghost in them. The way they used to do it was to measure the mean signal in three regions of interest positioned 1) in the true image, 2) in the ghost present in phase-encode direction and 3) in the background noise. Then they would express the level of ghost as a percentage of the true signal. The higher this number is, the stronger the ghost would be and therefore it can more severely affect the true image in the regions where they overlap.

The same technique was used in this project as a metric with the following modifications: first, our method is no longer manual, instead I have written a MATLAB code ghosting_metrics_mean.m that when ran on an image will do all the work and return the percentage mean signal of the ghost. Second, since in this project we are dealing with a certain type of ghosting artifact known as N/2 or Nyquist ghosting, one can take advantage of the fact that the location and orientation of ghosts in this images are known in this type of ghosting. By that, we mean that instead of just taking a random region of interest in the brain and in the ghost, we can calculate the mean signal in a pure ghost region and then calculate the mean signal in the same region of the brain in the pure signal region and then compare them to each other. More specifically, we followed the following steps:

• Step 1: cutting the mask: First we take the mask, shift it one time N/2 (in our case 64) units to the right and one time to the left and save the new images as mask1 and mask2. Then take the original mask, and only keep the pixels in which mask1 and mask2 images are zero. The remaining region of the mask (which is shown in the below figure) is what we will use as our pure brain mask.

• Step 2: shifting the mask: First we shift the pure brain mask N/2 (in our case 64) units to the left to get it to the right position for the left-ghost to be evaluated. This would be our pure brain region:

• Step 3: extracting the respective pure brain region: Now we take the original ghosted image and the shifted mask and wherever the pixel values of the mask is zero, we make the ghosted image zero too. This way we end up with the exact same region of the brain as in step 1, except this time it is a pure ghost region:

• Step 4: calculating the mean signal in these two regions

• Step 5: calculating the ratio between the mean signals of the pure ghost and the pure signal regions

• Step 6: repeat steps 2-5 for the right ghost in the image

• Step 7: average the results of steps 4 and 5: This is what we would use as our mean signal metric.

As mentioned before, these steps were implemented in a MATLAB code and then the metric was evaluated on all 55 subjects and the results were saved in a table. It is worth mentioning that in order to evaluate the level of noise in our images, a ROI of size 30X60 in the background noise was also selected in each image and the mean of this ROI was compared to the mean of a ROI in the mask, and the results for all the subjects turned out to be almost the same: the noise level in our images was 5% of the true image.

####  2- Entropy

As mentioned in the background section, another metric that is widely used in the MR literature for evaluating the level of ghost in images is the entropy measure of the entire image. The logic behind the usage of this metric in my opinion is that if you look at the histogram of the intensity values of a highly ghosted image (left figure) compared to a clean image (right figure), you can see that the histogram of the clean image consists of a peak in low intensities for noise pixels, then a gap in intensities and then again a set of high intensity pixels for the pixels in the true image. But, in the highly ghosted image the histogram has no such noticeable gap between these two sets and the gap is filled by ghosted pixels having intensities generally higher than noise but lower than actual signal, so the intensities are more smoothly spread in the ghosted image. As we know from information theory, a random variable with a more uniform distribution of its possible values has more entropy than a random variable with for example two separated peaks in its distribution. Therefore, we can say that generally a highly ghosted image is expected to have a higher entropy than a clean image.

The entropy measure that was used in this study is defined as: $-\sum_{i=1}^N p_i*log_2(p_i)$ , where p contains the histogram counts for each intensity level bin. A MATLAB code called ghosting_metrics_entropy.m was written that would first normalize the images to their maximum value and then use the entropy function to return the entropy measure for each image. The metric was evaluated on all 55 subjects and the results were saved in a table.

####  3- Mutual Information Metrics

As will be thoroughly discussed in the results section, while implementing the entropy metric, I noticed that it was not working as expected from theory. So, I decided to take the entropy measure one step further and use mutual information and joint entropy metrics.

After looking at many ghosted images, my hypothesis was that, the more severe the ghosts in the image are, the more they have the structure of a brain in them, in other words in low-level ghosted images, the ghost was a more noise-like image, but in severely-ghosted images, the ghost was almost a replica of the brain structure in which you could actually distinguish the features of a real brain structure for example the ventricles, etc. and so the mutual information between the pure brain region and the pure ghost region would be higher, meaning that the pure brain region tells us something about the structure of the ghost and the ghost is not completely random. So, I decided to calculate the joint entropy and the mutual information between a pure ghost region and the same region in a pure signal area, and then measure some standard metrics on them.

The pure signal and the respective pure ghost regions were cut out from the image as described in steps 1-6 of the percentage mean signal section. They were normalized to their maximum value. The joint entropy measure between two images in this project, was calculated using a MATLAB code that I wrote (ghosting_jointEntropy.m). This code uses the joint histogram of the two images to calculate the probability of joint intensities and then calculate the joint entropy. Another MATLAB code (ghosting_metrics_mutualInfo.m) was written to calculate the marginal entropies and the mutual information between these two regions. The mutual information between two images is defined as: $I(x;y) = H(x)+H(y)-H(x;y)$. The ghosting_metrics_mutualInfo.m MATLAB code was run on all 55 images and the resulting mutual information and joint entropies were saved in a table.

In order to be able to compare the distance between the two images in terms of how much one predicts the structure of the other, I needed some normalized and standard metrics based on their mutual information. Three standard metrics were used:

• Jaccard distance: Defined as $D(X,Y) = 1- \frac{I(X;Y)}{H(X;Y)}$. It is a measure between zero and one. Since it is a distance measure the closer it is to one, the more severe the ghost is considered to be, and the more it is closer to zero, the more noise-like and therefore less severe the ghost is.
• Redundancy measure: Defined as $1- \frac{H(X;Y)}{max(H(x),H(y)}$. It is a measure of how redundant one image is given the second one. It is again normalized between zero and one. The more closer this measure to one is, the more redundant the ghost is given the image, so the more severe the ghosting is.
• Similarity measure: Defined as $\frac{H(X)+H(Y)}{H(x;y)}$ , this is as its name suggest, a similarity measure and is normalized between zero and one.

All of this measures were measured on all the 55 images and the results were saved in tables.

####  4- Entropy of the Ratio

After testing a number of entropy and mutual information metrics, since they were not reflecting the similarity of the structure of ghost with the brain as expected (discussed more in the results section), my next idea was to think of a new measure that for example can distinguish between when the ghost is very severe and say it is so similar to the actual brain that it is only a scaled version of the brain and when it is just a random, noise-like structure and has no relation to the pure brain. The metric that I came up with is this: First we take the pure brain and the pure mask regions as described in the percentage mean signal section. Then, we take the ratio image between these two images. Finally, we calculate the entropy of this ratio image. The logic behind this metric is that, if the ghost is severe and it has the same structure as the brain (say a scaled version of it), then the ratio image would be an intensity image which has a constant value at every pixel and so the entropy of it is going to be zero. But, if the ghost is more noise like and random, then the ratio image is going to have a lot of different intensity values and therefore the entropy is going to be higher. I have written a MATLAB code (ghosting_metrics_entropyRatio.m) to calculate this metric and have run it on all 55 subjects and saved the results in a table.

####  5- Cross-Correlation

The next measure that is usually used in the existing literature, is the cross-correlation measure, which is a measure of how much two signals are similar. I used the cross-correlation measure in two different ways in my project.

The first idea was that, if you have an image without any ghosts and you take that image and move it around on itself in the phase encoding direction to calculate its auto-correlation with itself, the resulting function would peak at zero, and then die off as you move away from the true image to the left or right on the phase-encoding direction. But, if you have a heavily ghosted image and you take the mask and move it around in the same fashion on the ghosted image, you expect to get a peak at the origin (when the mask and the ghosted image coincide), but also you would expect to get two local maxima as the mask coincides with the ghosts at the right and left of the image. So, by looking at the height of these local maxima, you would get an idea of how severe the ghost is. In order to test this hypothesis, I wrote a MATLAB code (ghosting_metrics_xcorr.m), that or each image would take the mask and move it left and right in the phase encoding direction and calculate the cross correlation between them. Also, as a sanity check, for each image the code will take the mask and calculate its auto-correlation with itself, because the mask does not have a ghost outside the brain, the local maxima should not happen in this auto-correlation function.

After running the code on the first few images, I noticed that there is no noticeable difference between the shape of the auto-correlation curve and the cross-correlation curve. They both had a peak at the origin as expected, but they also both had two local maxima which was not even happening at the expected position (N/2). I realized these peaks are only happening because of the way we are normalizing the correlation metric to be between zero and one.

But, one interesting thing was happening in the curves, and it was that as you can see in the below figure, the cross-correlation and the auto-correlation curve for a low-level ghosted image (the red curves), were closer to each other than the ones for a high-level ghosted image (the blue curves). Therefore, as a metric, I calculated the difference between these two curves for each image point by point and then averaged it to announce one number as the correlation difference metric. This metric was measured on all 55 images and the results were saved.




The second idea, was to use the cross-correlation as a similarity measure between the pure ghost and the pure brain regions, as discussed in the earlier section. This metric was also evaluated for all 55 subjects.

####  6- Edge Detection

While looking at a ghosted image, one realizes that the reason a human observer can easily tell whether or not an image is severely ghosted, is because they see that edge happening inside the brain (where the ghost overlap with the actual image). In other words, if a human observer had never seen an image of a healthy brain before, they would not be able to distinguish the ghost in one. So, the idea for the next metric, was to somehow take advatage of this edge, and be able to see how severe that edge in the brain is. The fortunate thing about Nyquist or N/2 ghosting is that we know exactly where that ghost in the brain should happen. So, the first idea was to take every pixel and calculate the difference between that and the adjacent picture and form a new image. The hope was that in this new image the edge would be more pronounced and so by taking the average of this pixel-difference image on the edge (which we know where it should be), we would get a higher number for severly ghosted images and a lower number for low-level ghosted images. This was done on all the images, using the MATLAB code ghosting_metrics_edge.m . This code takes the image, calculate the pixel difference image from it. Then to extract the edge, we take the mask, shift it by N/2 units to the left, and take the respective pixels at the edge of this shifted mask in the pixel difference image as the edge. An example of the resulting pixel-difference image is shown below. The left one is the image in gray scale and the right one is the same image which has been color coded.

you can see how the edge is very noticeable in these images, because the image that was used to create these was heavily ghosted. This metric was calculated on all 55 images and the results were saved.

####  7- Percentage Image Area Affected by Ghost

The final idea was to see what percentage of the true brain image was affected by the ghost overlapping with it. This idea came to me while looking at ghosted images. I noticed that depending on the shape of the brain the affected area changes. For example in more round-shaped brains, no matter how bad the ghost was, since it was affecting only a small part of the brain, it doesn't matter. And, if the brain is more elongated in the phase encoding direction, the affected area is going to be bigger. So this metric was also evaluated using ghosting_metrics_affectedArea.m MATLAB code for all 55 images. It is worth mentioning that this metric has more value when it is considered along with other metrics. For example, when the ghost level in an image is distinguished as high, then we can check to see how much of the image is affected by the ghost. If it is not a lot, then the image can be considered as OK.

#  Results

In this section, we evaluate the performance of each metric based on how robust they work in terms of distinguishing severely ghosted images from the relatively clean ones.

The first metric was the percentage mean signal. In order to see how this metric works, I have plotted the results of this metric for all 55 subjects. The ones considered as OK images are shown as green dots and the damaged or severely ghosted ones are plotted as red dots. Now, the way the plot should look like for an ideal image is that, there should be green dots on one side and the red dots on the other side, and then a safe margin in between, so that you can set a golden rule for the value of that metric that would robustly distinguish between low-level and high level ghosted images. Below you can see the resulting plot from the first metric:

As you can see, the percentage mean signal metric is not working very well. The red and green dots overlap with each other, so we cannot set a golden rule for this metric.

The second metric was the entropy measure of the ghosted image. The same plot was generated for this metric:

As you can see, this plot is even worse than the previous one, the red dots are all over the space, and there is no obvious border between the two kinds of dots. So, at least for the kind of ghosting that we are dealing with here, the entropy metric is not working very robustly.

The next group of metrics were the mutual information metrics. These metric values were also plotted, but they didn't give any consistent results over the set of images as expected by theory. They were highly varying and there was no obvious pattern among the images. Therefore, they are not plotted here.

The next metric that we are going to consider is the edge metric. The plot resulted from this method is shown below:

As you can see, this metric is working really well. The green dots are on one side, the red ones are on the other side and there is even a safe margin. You can easily put a golden rule in the middle for this metric that can tell which images are OK and which are heavily ghosted.

The next metric is the entropy of the ratio metric. Here is the resulting plot:

As you can see this metric is also working. Not as good as the edge metric, but at least the green dots are on one side and the red dots are on the other side.

The other metric was the cross-correlation difference metric. Here is the resulting plot:

Despite what was predicted by theory, this metric is not working as well as was expected. The red and the green dots are somewhat interfering with each other.

#  Summary and Future Work

Throughout this project we have come up with different metrics and tested their performance in terms of assessing the level of ghost in MR images. The edge detection metric and the entropy of the ratio metric seemed to work better than the other ones. Some of the other metrics work better than the others, but none of them are individually giving consistent results for the whole data set. Some ideas for the future of this project would be to come up with a scoring system, that would use several of these metrics to rank the images in term of the level of ghost present in them. Since you don't want to throw away valuable data, this scoring system would help you choose appropriate images for different applications. Another idea is to use the two metrics that worked the best, to create a 2D measure for each image and turn this problem to a 2D SVM classifying problem. Another idea is to try and see if the signal in the affected ghosted region in the actual image can be written as a weighted some of the ghost and the true signal. If this is true, we can somehow deghost the image and then use this clean image as a baseline and compare our metric values to those for these images. And also, there is always the possiblity of finding better metrics that would work more robustly on the images.

#  References

Here are the literature review references that I found for this project:

##  Acquisition-Based Ghost Correction

[1] Richard Winkelmann et al., "Ghost Artifact Removal Using a Parallel Imaging Approach" , Magnetic Resonance in Medicine, 54:1002–1009, 2005

[2] Wietske van der Zwaag et al., "Minimization of Nyquist Ghosting for Echo-Planar Imaging at Ultra-High Fields Based on a Negative Readout Gradient Strategy", Journal of magnetic resonance imaging, 30:1171–1178, 2009

[3] Nan-kuei Chen et al., "Removal of EPI Nyquist Ghost Artifacts With Two-Dimensional Phase Correction", Magnetic Resonance in Medicine 51:1247–1253, 2004

[4] Vincent J. Schmithorst et al.,"Simultaneous Correction of Ghost and Geometric Distortion Artifacts in EPI Using a Multiecho Reference Scan", IEEE transactions on medical imaging, VOL. 20, NO. 6, JUNE 2001 535

[5] Julian R. Maclaren et al., "A modified view ordering for artifact reduction in MRI", Proceedings of the 29th Annual International Conference of the IEEE EMBS Cité Internationale, Lyon, France, August 23-26, 2007

[6] Yoon-Chul Kim et al., "Automatic Correction of Echo-Planar Imaging (EPI) Ghosting Artifacts in Real-Time Interactive Cardiac MRI Using Sensitivity Encoding", Journal of magnetic resonance imaging, 27:239–245, 2008

[7] Peter Kellman et al., "Phased array ghost elimination", NMR Biomed. , 19(3): 352–361, 2006 May

##  Image-Based Ghost Correction

[1] K. J. Lee et al.,"A Method of Generalized Projections (MGP) Ghost Correction Algorithm for Interleaved EPI", IEEE transactions on medical imaging, VOL. 23, NO. 7, JULY 2004

[2] David G. Kruger et al.,"An Orthogonal Correlation Algorithm for Ghost Reduction in MRI", MRM 38:678-686, 1997

[3]Peter Kellman et al., "Artifact Cancellation using SENSE Spatial Array Processing", Proc. Intl. Soc. Mag. Reson. Med 9, 2001

[4] Alfred Stadler et al., "Artifacts in body MR imaging: their appearance and how to eliminate them", Eur Radiol 17: 1242–1255, 2007

[5] Stuart M. Grieve et al.,"Elimination of Nyquist Ghosting Caused by Read-Out to Phase-Encode Gradient Cross-Terms in EPI",Magnetic Resonance in Medicine 47:337–343, 2002

[6] Michael H. Buonocore et al., "Ghost Artifact Reduction for Echo Planar Imaging Using Image Phase Correction", MRM 38:89-100, 1997

[7] Avideh Zakhor,"Ghost Cancellation Algorithms for MRI Images", IEEE transactions on medical imaging, VOL. 9. NO. 3., september 1990

[8] K.J. Lee, et al., "Image-Based EPI Ghost Correction Using an Algorithm Based on Projection Onto Convex Sets (POCS)", Journal of magnetic resonance 134, 206–213, 1998

[9] Qing-San Xiang et al., "Motion Artifact Reduction with Three-point Ghost Phase Cancellation", JMRl November/December, 1991

[10] Huairen Zeng et al., "New Approach for Correcting Distortions in Echo Planar Imaging", Magnetic Resonance in Medicine 52:1373–1378, 2004

[11] David L. Foxall et al.,"Rapid Iterative Reconstruction for Echo Planar Imaging", Magnetic Resonance in Medicine 42:541–547, 1991

[12] Xin Wan et al.,"Reduction of Phase Error Ghosting Artifacts in Thin Slice Fast Spin-Echo Imaging", MRM W632-638, 1995

[13] Weiliang Du et al.,"Reduction of Spectral Ghost Artifacts in High-Resolution Echo-Planar Spectroscopic Imaging of Water and Fat Resonances", Magnetic Resonance in Medicine 49:1113–1120, 2003

[14] Nan-kuei Chen et al., "Removal of EPI Nyquist Ghost Artifacts With Two-Dimensional Phase Correction", Magnetic Resonance in Medicine 51:1247–1253, 2004

[15] Skare et al., "A fast and robust minimum entropy based non-interactive Nyquist ghost correction algorithm"

[16] A. Nordell et al.,"Major Speed-Up of Nyquist Ghost Correction in ramp-sampled EPI", Proc. Intl. Soc. Mag. Reson. Med. 15,2007

[17] S. Clare et al., "Iterative Nyquist Ghost Correction for Single and Multi-shot EPI using an Entropy Measure", Proc. Intl. Soc. Mag. Reson. Med. 11, 2003

[18] H. Bruder et al., “Image reconstruction for echo planar imaging with nonequidistant k-space sampling,”Magn. Reson. Med., vol. 23, no. 2, pp. 311–323, 1992.

[19] D. Atkinson et al.,“Automatic correction of motion artifacts in magnetic resonance images using an entropy focus criterion,” IEEE Trans. Med. Imag., vol. 16, pp.903–910, Dec. 1997.

##  Ghost Detection

[1] N.J. Taylor et al., "A Simple Phantom to Locate the Origin of MRI Ghost Artifacts", Magnetic Resonance Imaging, Vol. 16, No. 1, pp. 73-76, 1998

[2] Scott B. Reeder et al.,"Quantification and Reduction of Ghosting Artifacts in Interleaved Echo-Planar Imaging", Magn Reson Med. 1997 September ; 38(3): 429–439

[3] Weifang Yang et al.,"Using an MRI Distortion Transfer Function to Characterize the Ghosts in Motion-Corrupted Images",IEEE transactions on medical imaging, VOL. 19, NO. 6, JUNE 2000