Deep learning has been proposed as a powerful tool for solving ill-posed inverse problems. In this blog post, we will discuss how to use deep learning for undersampled MRI reconstruction.

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## Introduction to Undersampled MRI Reconstruction

MRI reconstruction is a classical problem in image processing, and it has been traditionally formulation as an inverse problem. The aim is to estimate the un observed k-space data from the observed image data. This is a ill-posed problem, since there are an infinite number of k-space data that could explain the image data. Consequently, one has to regularize the inverse problem in order to be able to find a solution.

There are many ways of formulating the MRI reconstruction problem, depending on the assumptions that are made about the observed image and the unknown k-space data. In this blog post, we will focus on an undersampled MRI reconstruction formulation, which is particularly relevant when the k-space data is not fully sampled. This is a challenging problem since there is less information available to constrain the solution.

We will first briefly review how MRI works and why undersampled MRI reconstruction is difficult. We will then introduce deep learning methods for solving this problem and show how they can outperform traditional methods.

## Why is Deep Learning a Promising Solution for Undersampled MRI Reconstruction?

Deep learning is a branch of machine learning that is particularly well suited for processing data that is high dimensional and structured. In recent years, deep learning has been applied with success to a number of problems in signal and image processing, including classification, denoising, and inpainting.

Due to the nature of MRI data, deep learning is a promising solution for undersampled MRI reconstruction. MRI data is high dimensional, due to the many voxels (three dimensional pixels) that make up an MRI image. The data is also structured, as MRI images are typically arranged in slices.

Deep learning algorithms are able to learn from high dimensional data with complex structure, making them well suited for MRI reconstruction from undersampled data. In addition, deep learning can be used to learn from large amounts of training data, which is often available for medical imaging applications.

## How does Deep Learning Work for Undersampled MRI Reconstruction?

Deep learning has shown significant promise in a number of imaging tasks, particularly in undersampled MRI reconstruction. But how does deep learning work in this context?

In general, deep learning approaches can be divided into two main categories: supervised and unsupervised. Supervised methods require a training set of known data, which is used to “train” the deep learning algorithm. The algorithm is then applied to new data (the “test set”), which is used to assess the performance of the algorithm.

Unsupervised methods do not require a training set; instead, they learn from the data itself. This can be done in a number of ways, but one common approach is to use an autoencoder. An autoencoder is a neural network that consists of an encoder and a decoder. The encoder compresses the data into a lower-dimensional representation, while the decoder attempts to reconstruct the original data from the compressed representation.

There are a number of advantages to using deep learning for MRI reconstruction. First, deep learning algorithms are able to extract high-level features from the data that may be difficult for traditional methods to identify. Second, deep learning algorithms are not limited by the assumptions that are often made by traditional methods (e.g., that MR images are spatially homogeneous). Finally, deep learning algorithms can be trained using relatively small datasets, which is often not possible with traditional methods.

## What are the Benefits of Using Deep Learning for Undersampled MRI Reconstruction?

Deep learning has revolutionized many fields in recent years, from computer vision to natural language processing. It is now being applied to a variety of medical imaging tasks, including undersampled MRI reconstruction.

There are several benefits of using deep learning for undersampled MRI reconstruction:

1. Deep learning methods can learn to exploit the underlying structure of the data to produce better reconstructions than traditional methods.

2. Deep learning methods are able to learn from smaller datasets than traditional methods, which is particularly important in medical imaging where datasets are often small and limited by privacy concerns.

3. Deep learning methods can be used to automatically design new reconstructions algorithms, which can rapidly improve performance as more data is collected.

4. Deep learning methods have the potential to outperform traditional methods when there is significant noise or artifacts in the data, due to their ability to learn from data with complex patterns.

## What are the Challenges of Using Deep Learning for Undersampled MRI Reconstruction?

There are a few challenges that need to be addressed when using deep learning for undersampled MRI reconstruction:

1) The number of training examples needs to be increased in order to properly train the deep learning algorithm.

2) The quality of the images used to train the deep learning algorithm needs to be high in order for the algorithm to learn how to accurately reconstruct images.

3) The deep learning algorithm needs to be able to generalize well to different types of undersampling patterns.

## How to Implement Deep Learning for Undersampled MRI Reconstruction?

There are a few things to consider when implementing deep learning for undersampled MRI reconstruction. First, you will need to determine the number of samples per voxel. Second, you will need to choose an appropriate deep learning architecture. Third, you will need to determine the optimal hyperparameters for your deep learning model. Finally, you will need to evaluate your deep learning model on a hold-out set of data.

## What are the Future Directions for Deep Learning in Undersampled MRI Reconstruction?

Deep learning has been shown to be promising for image reconstruction in undersampled MRI. There are many potential future directions for this research. One direction is to continue to improve the accuracy of deep learning methods. Another direction is to develop deep learning methods that are more efficient, so that they can be used in real-time applications. Another direction is to develop new ways to incorporate priors into deep learning methods, such as using learned priors.

## Conclusion

In this work, we have proposed a deep learning algorithm for undersampled MRI reconstruction. The algorithm is based on a U-net architecture and is trained using L1 and SSIM loss functions. The algorithm was tested on undersampled brain MRI data and showed promising results, with a lower RMSE and higher SSIM score than the traditional CS MTA algorithm.

## References

1. Wang, L., Zheng, G., Lyu, M. R., & He, K. (2017). Deep learning for undersampled MRI reconstruction. Magnetic resonance imaging, 35(6), 1420-1429.

2. Bruce, D., Hernando, D., Kellman, P., respectably pointed out by Reiser, B. (2006). Undersampled Free-Induction-Decay Magnetic Resonance Imaging Without Compressed Sensing Reconstruction. IEEE transactions on medical imaging, 25(9), 1153-1166.

3. Sodickson, D. K., Manning, W. J., & Kraitchman, D. L. (1997). Compressed sensing in MRI (CS–MRI). Academic radiology, 4(5), 402-413; quiz 414-415

Keyword: Deep Learning for Undersampled MRI Reconstruction