Slice grappa with even and odd kernels

Author: Zimu Huo

Date: 05.2022

See the figure 2 in [1]. Slice grappa with even and odd kernels is tailored to the SMS with EPI, as there are imperfections exist in the EPI phase correction. One kernel used for even lines and one kernel used for odd lines.

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References

[1] 
Author:  Peter J Koopmans
Title: Two-dimensional-NGC-SENSE-GRAPPA for fast, ghosting-robust reconstruction of in-plane and slice-accelerated blipped-CAIPI echo planar imaging
Link: https://pubmed.ncbi.nlm.nih.gov/26932565/

[2] 
Author:  Setsompop K et al. 
Title: Improving diffusion MRI using simultaneous multi-slice echo planar imaging
Link: https://pubmed.ncbi.nlm.nih.gov/22732564/

import sys
sys.path.insert(1, '../')
import matplotlib.pyplot as plt
import numpy as np
from scipy import io
import util.simulator as simulate
from util.coil import *
from util.fft import *
import util.mask as undersample
from util.spsg2k import *
import math

numSlice = 4
R = 4
slice1 = np.load("../lib/slice1_grappa1.npy")
slice2 = np.load("../lib/slice2_grappa1.npy")
slice3 = np.load("../lib/slice3_grappa1.npy")
slice4 = np.load("../lib/slice4_grappa1.npy")
data = np.concatenate((slice1[...,None], slice2[...,None], slice3[...,None], slice4[...,None]), -1)[...,:numSlice]
data = data[...,:numSlice]
rawImage = ifft2c(data)
fovHeight, fovWidth, numCoil, _ = rawImage.shape

rawData = np.zeros(rawImage.shape, dtype = complex)
for sli in range (numSlice):
    rawData[:,:,:,sli] = fft2c(rawImage[:,:,:,sli])

cycle = np.arange(0,1,1/numSlice) * 2* np.pi
numAccq = int(numSlice*fovHeight/R)

shift = cycle*numAccq/(2*np.pi)
dataR = fft2c(simulate.multiSliceCAIPI(rawImage, cycle, R))

ncx = 32
ncy = 32
acsshift = cycle*int(numSlice* ncy/R)/(2*np.pi)
acsK = simulate.acs(rawData, (ncy, ncx))
acsIm = ifft2c(acsK)
calib = fft2c(simulate.singleSliceFov(acsIm,acsshift))

recon = spsg2k(dataR, calib, kh = 3, kw = 3)

fig = plt.figure(figsize=(8, 6), dpi=80)
plt.subplot(211)
plt.imshow(np.abs(stitch(rsos(rawImage), 1)), cmap = "gray")
plt.subplot(212)
plt.imshow(np.abs(stitch(rsos(ifft2c(recon)),1)), cmap = "gray")

<matplotlib.image.AxesImage at 0x7ff182772c10>

reconshift = cycle*int(numSlice* fovHeight/R)/(2*np.pi) 
recon1 = simulate.singleSliceFov(ifft2c(recon), - reconshift)
fig = plt.figure(figsize=(8, 6), dpi=80)
plt.subplot(211)
plt.imshow(np.abs(stitch(rsos(rawImage), 1)), cmap = "gray")
plt.subplot(212)
plt.imshow(np.abs(stitch(rsos((recon1)),1)), cmap = "gray")

<matplotlib.image.AxesImage at 0x7ff1763339a0>