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Related Concept Videos

Convolution Properties II01:17

Convolution Properties II

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The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
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Convolution Properties I01:20

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Convolution computations can be simplified by utilizing their inherent properties.
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Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
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Convolution: Math, Graphics, and Discrete Signals01:24

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In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
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Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction.

Chen Qin, Jo Schlemper, Jose Caballero

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    |August 7, 2018
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    This study introduces a novel deep learning model for faster dynamic cardiac magnetic resonance imaging (dMRI). The convolutional recurrent neural network reconstructs high-quality dMRI images from undersampled data, improving both accuracy and speed.

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    Area of Science:

    • Medical Imaging
    • Machine Learning
    • Signal Processing

    Background:

    • Accelerating dynamic magnetic resonance imaging (dMRI) presents an ill-posed inverse problem, crucial for both signal processing and machine learning.
    • Exploiting temporal correlations in MR sequences is key to resolving aliasing artifacts in accelerated dMRI.
    • Traditional methods rely on iterative optimization algorithms, while deep learning offers a promising alternative for inverse problems.

    Purpose of the Study:

    • To develop a novel convolutional recurrent neural network (CRNN) for reconstructing high-quality cardiac MR images from highly undersampled k-space data.
    • To jointly leverage temporal sequence dependencies and the iterative nature of traditional optimization algorithms for enhanced reconstruction.
    • To improve the efficiency and accuracy of dynamic MRI reconstruction.

    Main Methods:

    • Proposed a unique CRNN architecture that embeds traditional iterative algorithm structures.
    • Utilized recurrent hidden connections to model the recurrence of iterative reconstruction stages.
    • Employed bidirectional recurrent hidden connections across time sequences to learn spatio-temporal dependencies.

    Main Results:

    • The proposed CRNN effectively learns temporal dependence and iterative reconstruction processes with a minimal number of parameters.
    • Achieved superior reconstruction accuracy compared to current MR reconstruction methods.
    • Demonstrated significant improvements in reconstruction speed.

    Conclusions:

    • The novel CRNN architecture offers an effective solution for accelerated dynamic MRI reconstruction.
    • The method successfully integrates deep learning with iterative optimization principles for improved performance.
    • This approach holds potential for faster and more accurate cardiac MRI acquisition.