MR image reconstruction using the learned data distribution as prior
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MR image reconstruction from undersampled data exploits priors to compensate for missing k-space data. This has previously been achieved by using regularization methods, such as TV and wavelets, or data adaptive methods, such as dictionary learning. We propose to explicitly learn the probability distribution of MR image patches and to constrain patches to have a high probability according to this distribution in reconstruction, effectively employing it as the prior. We use variational autoencoders (VAE) to learn the distribution of MR image patches. This high dimensional distribution is modelled by a latent parameter model of lower dimensions in a non-linear fashion. We develop a reconstruction algorithm that uses the learned prior in a Maximum-A-Posteriori estimation formulation. We evaluate the proposed method with T1 weighted images and compare it to existing alternatives. We also apply our method on images with white matter lesions. Visual evaluation of the samples drawn from the learned model showed that the VAE algorithm was able to approximate the distribution of MR image patches. Furthermore, the reconstruction algorithm using the approximate distribution produced qualitatively better results. The proposed technique achieved RMSE, CNR and CN values of 2.77 ratios of 2 and 3, respectively. It outperformed other evaluated methods in terms of used metrics. In the experiments on images with white matter lesions, the method faithfully reconstructed the lesions. We introduced a novel method for MR reconstruction, which takes a new perspective on regularization by learning priors. Results suggest the method compares favorably against TV and dictionary based methods as well as the neural-network based ADMM-Net in terms of the RMSE, CNR and CN and perceptual image quality and can reconstruct lesions as well.
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