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Background Magnetic resonance imaging (MRI) is an effective auxiliary diagnostic method in clinical medicine, but it has always suffered from the problem of long acquisition time. Compressed sensing and parallel imaging are two common techniques to accelerate MRI reconstruction. Recently, deep learning provides a new direction for MRI, while most of them require a large number of data pairs for training. However, there are many scenarios where fully sampled k-space data cannot be obtained, which will seriously hinder the application of supervised learning. Therefore, deep learning without fully sampled data is indispensable. Main text In this review, we first introduce the forward model of MRI as a classic inverse problem, and briefly discuss the connection of traditional iterative methods to deep learning. Next, we will explain how to train reconstruction network without fully sampled data from the perspective of obtaining prior information. Conclusion Although the reviewed methods are used for MRI reconstruction, they can also be extended to other areas where ground-truth is not available. Furthermore, we may anticipate that the combination of traditional methods and deep learning will produce better reconstruction results.

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BackgroundMulti-contrast images in magnetic resonance imaging (MRI) provide abundant contrast information reflecting the characteristics of the internal tissues of human bodies, and thus have been widely utilized in clinical diagnosis. However, long acquisition time limits the application of multi-contrast MRI. One efficient way to accelerate data acquisition is to under-sample the k-space data and then reconstruct images with sparsity constraint. However, images are compromised at high acceleration factor if images are reconstructed individually. We aim to improve the images with a jointly sparse reconstruction and Graph-based redundant wavelet transform (GBRWT).MethodsFirst, a sparsifying transform, GBRWT, is trained to reflect the similarity of tissue structures in multi-contrast images. Second, joint multi-contrast image reconstruction is formulated as a ℓ2, 1 norm optimization problem under GBRWT representations. Third, the optimization problem is numerically solved using a derived alternating direction method.ResultsExperimental results in synthetic and in vivo MRI data demonstrate that the proposed joint reconstruction method can achieve lower reconstruction errors and better preserve image structures than the compared joint reconstruction methods. Besides, the proposed method outperforms single image reconstruction with joint sparsity constraint of multi-contrast images.ConclusionsThe proposed method explores the joint sparsity of multi-contrast MRI images under graph-based redundant wavelet transform and realizes joint sparse reconstruction of multi-contrast images. Experiment demonstrate that the proposed method outperforms the compared joint reconstruction methods as well as individual reconstructions. With this high quality image reconstruction method, it is possible to achieve the high acceleration factors by exploring the complementary information provided by multi-contrast MRI.

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