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Density is an important characteristic of substances, crucial in determining whether an object sinks or floats in a fluid. Its SI unit is kg/m3, and its cgs unit is g/cm3. The density of an object helps in identifying its composition, and also reveals information about the phase of the matter and its substructure. The densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. However, gases have much lower densities than liquids and...
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Strain-Energy Density01:20

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Understanding the strain energy density in materials under axial load is crucial for evaluating their mechanical behavior and durability. When a rod is subjected to such a load, it elongates and stores energy, known as strain energy, as potential energy within the material. This energy is measured in terms of energy per unit volume.
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Bulk Density of Aggregate01:22

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MR Image Reconstruction Using Deep Density Priors.

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    This study introduces a novel deep learning method for magnetic resonance (MR) image reconstruction. The unsupervised approach uses variational autoencoders (VAE) to improve image quality without paired training data.

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    Area of Science:

    • Medical Imaging
    • Artificial Intelligence
    • Computational Science

    Background:

    • Magnetic resonance (MR) image reconstruction from undersampled data requires prior information to compensate for missing k-space data.
    • Deep learning (DL) methods have been used to learn implicit priors from paired undersampled and fully sampled MR images.
    • Existing DL approaches are sensitive to variations in undersampling patterns and coil configurations.

    Purpose of the Study:

    • To develop an unsupervised deep learning approach for MR image reconstruction using variational autoencoders (VAE).
    • To create a reconstruction algorithm that utilizes an explicit image prior, decoupling it from the encoding process.
    • To eliminate the need for paired training datasets and mitigate sensitivities associated with current DL methods.

    Main Methods:

    • Proposed an unsupervised deep learning framework utilizing variational autoencoders (VAE) to learn the probability distribution of fully sampled MR images.
    • Integrated the learned VAE prior as an explicit term within the MR image reconstruction process.
    • Evaluated the method on T1-weighted images, multi-coil complex MR data from healthy volunteers, and images containing white matter lesions.

    Main Results:

    • The VAE-based prior produced visually high-quality MR image reconstructions with low Root Mean Square Error (RMSE) values.
    • The algorithm outperformed most alternative reconstruction methods on the evaluated datasets.
    • Accurate magnitude and phase reconstruction results were achieved for multi-coil complex data, and lesions were faithfully reconstructed.

    Conclusions:

    • The proposed unsupervised DL method effectively reconstructs MR images using an explicit VAE prior, compensating for undersampled k-space data.
    • This approach offers a robust alternative to paired-data DL methods, avoiding associated sensitivities and improving reconstruction quality.
    • The VAE prior demonstrates significant potential for enhancing MR image reconstruction across various imaging scenarios.