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We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRI) from highly undersampled k-space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and the patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailored to the MRI being considered. In addition, we investigate a total variation penalty term in combination with the dictionary learning model, and show how the denoising property of dictionary learning removes dependence on regularization parameters in the noisy setting. We derive a stochastic optimization algorithm based on Markov Chain Monte Carlo (MCMC) for the Bayesian model, and use the alternating direction method of multipliers (ADMM) for efficiently performing total variation minimization. We present empirical results on several MRI, which show that the proposed regularization framework can improve reconstruction accuracy over other methods.
Magnetic resonance image (MRI) reconstruction is a severely ill-posed linear inverse task demanding time and resource intensive computations that can substantially trade off {it accuracy} for {it speed} in real-time imaging. In addition, state-of-the
Compressed sensing for magnetic resonance imaging (CS-MRI) exploits image sparsity properties to reconstruct MRI from very few Fourier k-space measurements. The goal is to minimize any structural errors in the reconstruction that could have a negativ
Compressed sensing MRI is a classic inverse problem in the field of computational imaging, accelerating the MR imaging by measuring less k-space data. The deep neural network models provide the stronger representation ability and faster reconstructio
Compressed sensing (CS) theory assures us that we can accurately reconstruct magnetic resonance images using fewer k-space measurements than the Nyquist sampling rate requires. In traditional CS-MRI inversion methods, the fact that the energy within
Compressed sensing (CS) MRI relies on adequate undersampling of the k-space to accelerate the acquisition without compromising image quality. Consequently, the design of optimal sampling patterns for these k-space coefficients has received significan