Non-local low-rank constrained self-calibration parallel magnetic resonance imaging reconstruction method
A magnetic resonance imaging, low-rank constraint technology, applied in the field of self-calibration parallel magnetic resonance imaging reconstruction, can solve problems such as image quality needs to be improved, and achieve the effect of improving quality
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[0056] Embodiment 1: The present invention is an efficient reconstruction method proposed based on the SPIRiT framework.
[0057] suppose represents the multi-coil image to be reconstructed, Represents undersampled k-space data. N represents the number of pixels of the single-coil image to be reconstructed, M represents the number of k-space undersampled projection data of the single-coil image, and C is the number of coils. Each column of X and Y is obtained by stacking single coil images column by column. The undersampled k-space data Y of the multi-coil image is given by:
[0058] Y=AX (1)
[0059] Among them, the matrix Represents an operator for undersampling projection on multi-coil data X, is an undersampling operator, is the Fourier transform.
[0060] SPIRiT performs consistency between each point of the image grid and its entire neighborhood points (whether they are acquired or not), and the calibration consistency formula for all k-space positions is: ...
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