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Super-resolution of 3D Magnetic Resonance Images by Random Shifting and Convolutional Neural Networks
Get PDFEnhancing resolution is a permanent goal in magnetic resonance (MR) imaging, in order to keep improving diagnostic capability and registration methods. Super-resolution (SR) techniques are applied at the postprocessing stage, and their use and development have progressively increased during the last years. In particular, example-based methods have been mostly proposed in recent state-of-the-art works. In this paper, a combination of a deep-learning SR system and a random shifting technique to improve the quality of MR images is proposed, implemented and tested. The model was compared to four competitors: cubic spline interpolation, non-local means upsampling, low-rank total variation and a three-dimensional convolutional neural network trained with patches of HR brain images (SRCNN3D). The newly proposed method showed better results in Peak Signal-to-Noise Ratio, Structural Similarity index, and Bhattacharyya coefficient. Computation times were at the
same level as those of these up-to-date methods. When applied to downsampled MR structural T1 images, the new method also yielded better qualitative results, both in the restored images and in the images of residuals.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
Implicit Resolution
Full text linkLet \Omega be a set of unsatisfiable clauses, an implicit resolution
refutation of \Omega is a circuit \beta with a resolution proof {\alpha} of the
statement "\beta describes a correct tree-like resolution refutation of
\Omega". We show that such system is p-equivalent to Extended Frege. More
generally, let {\tau} be a tautology, a [P, Q]-proof of {\tau} is a pair
(\alpha,\beta) s.t. \alpha is a P-proof of the statement "\beta is a circuit
describing a correct Q-proof of \tau". We prove that [EF,P] \leq p [R,P] for
arbitrary Cook-Reckhow proof system P
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