Multi-contrast reconstruction with Bayesian compressed sensing.
TL;DR: In this article, a hierarchical Bayesian compressed sensing approach is proposed to jointly reconstruct a set of images from undersampled k-space data with higher fidelity than when the images are reconstructed either individually or jointly by a previously proposed algorithm, M-FOCUSS.
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Abstract: Clinical imaging with structural MRI routinely relies on multiple acquisitions of the same region of interest under several different contrast preparations. This work presents a reconstruction algorithm based on Bayesian compressed sensing to jointly reconstruct a set of images from undersampled k-space data with higher fidelity than when the images are reconstructed either individually or jointly by a previously proposed algorithm, M-FOCUSS. The joint inference problem is formulated in a hierarchical Bayesian setting, wherein solving each of the inverse problems corresponds to finding the parameters (here, image gradient coefficients) associated with each of the images. The variance of image gradients across contrasts for a single volumetric spatial position is a single hyperparameter. All of the images from the same anatomical region, but with different contrast properties, contribute to the estimation of the hyperparameters, and once they are found, the k-space data belonging to each image are used independently to infer the image gradients. Thus, commonality of image spatial structure across contrasts is exploited without the problematic assumption of correlation across contrasts. Examples demonstrate improved reconstruction quality (up to a factor of 4 in root-mean-square error) compared to previous compressed sensing algorithms and show the benefit of joint inversion under a hierarchical Bayesian model.
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References
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Stable signal recovery from incomplete and inaccurate measurements
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Atomic Decomposition by Basis Pursuit
TL;DR: This work gives examples exhibiting several advantages over MOF, MP, and BOB, including better sparsity and superresolution, and obtains reasonable success with a primal-dual logarithmic barrier method and conjugate-gradient solver.
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A Wavelet Tour of Signal Processing : The Sparse Way
Stéphane Mallat,Gabriel Peyré +1 more
- 01 Jan 2008
TL;DR: The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications.
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