Optimized regularization and CNN-based undersampled magnetic resonance image high-performance reconstruction method
A magnetic resonance image and undersampling technology, which is applied in the field of image processing, can solve the problems of long magnetic resonance imaging time and good reconstruction performance, and achieve the effects of fast imaging time, auxiliary judgment, and reduced scanning time
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[0051] The present invention will be described in detail below with reference to specific embodiments.
[0052] The present invention proposes a high-performance reconstruction method of under-sampling magnetic resonance images based on optimal regularization and CNN, which includes the following steps.
[0053] Step 1: Introduce a general model to solve the most sparse solution of undersampled MR images. The general formula is:
[0054]
[0055] where I∈C N is the reconstructed MR image with N pixels. y∈C M is the acquired undersampled k-space MR image data. K is the observation matrix, expressed as:
[0056] K=MF (2)
[0057] where M is the diagonal matrix of the undersampled mask in K-space and F is the 2D discrete Fourier transform.
[0058] Since the N dimension of the sparse coefficient θ is much larger than the M dimension of the observation matrix K, the reconstruction of the original signal can be regarded as a L0 norm minimization problem of NP, but the non-...
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