def ATBV(x, csmT, VT):
nch = csmT.size(0)
NF = VT.size(1)
tmp1 = torch.zeros((nx, nx, 2)).to(gpu)
atbv = torch.zeros((nx * nx * 2, nbasis)).to(gpu)
x = x.to(gpu)
for i in range(NF):
for j in range(nch):
tmp = x[j, i]
tmp = torch.reshape(tmp, (nx, nx, 2))
tmp1 = tmp1 + sf.pt_cpx_multipy(sf.pt_ifft2c(tmp),
sf.pt_conj(csmT[j]))
tmp2 = VT[:, i].unsqueeze(1)
tmp3 = torch.reshape(tmp1, (nx * nx * 2, 1))
atbv = atbv + tmp3 @ tmp2.T
tmp1 = torch.zeros((nx, nx, 2)).to(gpu)
atbv = atbv * nx
atbv = atbv.permute(1, 0)
atbv = torch.reshape(atbv, (nbasis, nx, nx, 2))
#atbV=atbV.astype(np.complex64)
#atbV=np.fft.fftshift(np.fft.fftshift(atbV,1),2)
#atbV=np.transpose(atbV,[0,2,1])
del tmp, tmp1, tmp2, tmp3
return atbv
def ATBV_NFT(FT, kdata, csmT, VT):
nch = csmT.size(0)
N = csmT.size(1)
nbas = VT.size(0)
tmp1 = torch.zeros((nx, nx, 2)).to(gpu)
atbv = torch.zeros((nx * nx * 2, nbasis)).to(gpu)
x = x.to(gpu)
for i in range(nbas):
for j in range(nch):
tmp2 = VT[:, i].unsqueeze(1)
tmp = torch.diag(tmp2) @ kdata[j, :, :]
tmp = torch.reshape(tmp, (nx, nx, 2))
tmp1[i] = tmp1[i] + sf.pt_cpx_multipy(FT(tmp), sf.pt_conj(csmT[j]))
tmp3 = torch.reshape(tmp1, (nx * nx * 2, 1))
atbv = atbv + tmp3 @ tmp2.T
tmp1 = torch.zeros((nx, nx, 2)).to(gpu)
atbv = atbv * nx
atbv = atbv.permute(1, 0)
atbv = torch.reshape(atbv, (nbasis, nx, nx, 2))
#atbV=atbV.astype(np.complex64)
#atbV=np.fft.fftshift(np.fft.fftshift(atbV,1),2)
#atbV=np.transpose(atbV,[0,2,1])
del tmp, tmp1, tmp2, tmp3
return atbv
def AtAUV(x,csmT,maskT):
atbv=torch.cuda.FloatTensor(nbasis,nx,nx,2).fill_(0)
tmp6=torch.cuda.FloatTensor(nbasis,nx,nx,2).fill_(0)
csmConj=sf.pt_conj(csmT)
for i in range(nch):
tmp1=sf.pt_cpx_multipy(x,csmT[i].repeat(nbasis,1,1,1))
tmp2=sf.pt_fft2c(tmp1)
del tmp1
for k in range(NF1):
tmp3=maskT[k].repeat(nbasis,1,1,1)*tmp2
tmp4=VT[:,k].unsqueeze(1)
tmp3=torch.reshape(tmp3,(nbasis,nx*nx*2))
tmp5=tmp4.T@tmp3#torch.mm(tmp4.T,tmp3)
tmp5=tmp4@tmp5#torch.mm(tmp4,tmp5)
tmp5=torch.reshape(tmp5,(nbasis,nx,nx,2))
tmp6=tmp6+tmp5
del tmp2,tmp3,tmp4,tmp5
tmp1=sf.pt_ifft2c(tmp6)
tmp2=sf.pt_cpx_multipy(csmConj[i].repeat(nbasis,1,1,1),tmp1)
atbv=atbv+tmp2
tmp6=tmp6.fill_(0)
del tmp1,tmp2
x=torch.reshape(x,(nbasis,nx*nx*2))
x=W*x
reg=torch.mm(sT,x)
reg=torch.reshape(reg,(nbasis,nx,nx,2))
atbv=atbv+reg
return atbv
def pt_At(bT,csmT,maskT):
tmp=maskT*bT
tmp=sf.pt_ifft2c(tmp)
csmConj=sf.pt_conj(csmT)
tmp=sf.pt_cpx_multipy(csmConj, tmp)
atbT=torch.sum( tmp ,dim=-4)
return atbT
def pt_At(bT, csmT, maskT):
tmp = maskT * bT
tmp = sf.pt_ifft2c(tmp)
csmConj = sf.pt_conj(csmT)
for i in range(NF):
tmp1 = sf.pt_cpx_multipy(csmConj, tmp[i])
atbT[i] = torch.sum(tmp1, dim=-4)
return atbT
def AtAUV(x, csmT, maskT1, VT):
# atbv=torch.zeros(nbasis,nx,nx,2)
# atbv=atbv.to(gpu)
# tmp2=torch.zeros(nbasis,nch,nx,nx,2)
# tmp2=tmp2.to(gpu)
#tmp6=torch.zeros(nbasis,nx,nx,2)
#tmp6=tmp6.to(gpu)
nch = csmT.size(0)
NF = maskT1.size(0)
atbv = torch.cuda.FloatTensor(nbasis, nx, nx, 2).fill_(0)
tmp6 = torch.cuda.FloatTensor(nbasis, nx, nx, 2).fill_(0)
csmConj = sf.pt_conj(csmT)
for i in range(nch):
#tmp=csmT[i,:,:,:]
#tmp=tmp.repeat(nbasis,1,1,1)
tmp1 = sf.pt_cpx_multipy(x, csmT[i].repeat(nbasis, 1, 1, 1))
tmp2 = sf.pt_fft2c(tmp1)
del tmp1
for k in range(NF):
#tmp=maskT[k,:,:,:]
#tmp=tmp.repeat(nbasis,1,1,1).to(gpu)
tmp3 = maskT1[k].unsqueeze(2).repeat(nbasis, 1, 1, 2) * tmp2
#tmp3=tmp3.to(gpu,dtype)
tmp4 = VT[:, k].unsqueeze(1)
tmp3 = torch.reshape(tmp3, (nbasis, nx * nx * 2))
tmp5 = tmp4.T @ tmp3 #torch.mm(tmp4.T,tmp3)
#tmp5=torch.matmul(tmp3.permute(1,2,3,0),tmp4)
#tmp5=torch.matmul(tmp5,tmp4.T)
tmp5 = tmp4 @ tmp5 #torch.mm(tmp4,tmp5)
tmp5 = torch.reshape(tmp5, (nbasis, nx, nx, 2))
#tmp5=tmp5.permute(3,0,1,2)
tmp6 = tmp6 + tmp5
del tmp2, tmp3, tmp4, tmp5
tmp1 = sf.pt_ifft2c(tmp6)
#tmp=csmConj[i,:,:,:]
#tmp=tmp.repeat(nbasis,1,1,1).to(gpu)
tmp2 = sf.pt_cpx_multipy(csmConj[i].repeat(nbasis, 1, 1, 1), tmp1)
atbv = atbv + tmp2
#tmp6=torch.zeros(nbasis,nx,nx,2)
#tmp6=tmp6.to(gpu)
tmp6 = tmp6.fill_(0)
del tmp1, tmp2
x = torch.reshape(x, (nbasis, nx * nx * 2))
#x=W*x
#reg=torch.mm(sT,x)
#reg=torch.reshape(reg,(nbasis,nx,nx,2))
#atbv=atbv+reg
del x
return atbv
def reg_term(u1, D):
u = torch.reshape(u1, (nbasis, nx * nx * 2))
x = torch.mm(D.T, u)
u2 = torch.mm(D, x)
u2 = torch.reshape(u2, (nbasis, nx, nx, 2))
return u2
#%%
lam2 = 1e-3
cgIter = 1
cgTol = 1e-15
out_iter = 3
cgIter1 = 10
epochs = 400
csmConj = sf.pt_conj(csmT)
res = torch.cuda.FloatTensor(nbasis, nbasis, nx * nx * 2).fill_(0)
for k in range(NF):
tmp3 = maskT[k].repeat(nbasis, 1) #*tmp2
tmp = torch.diag_embed(VT[:, k]) @ tmp3 #np.tile(maskTst[i],(nbasis,1)))
#tmp1=torch.diag_embed(VT[:,i])
tmp = tmp.unsqueeze(0)
tmp = tmp.repeat(nbasis, 1, 1)
tmp = torch.reshape(tmp, (nbasis, nbasis * nx * nx * 2))
tmp1 = torch.diag_embed(VT[:, k]) @ tmp
tmp1 = torch.reshape(tmp1, (nbasis, nbasis, nx * nx * 2))
#tmp1=np.matmul(np.expand_dims(tmp,axis=0).T,np.expand_dims(V[:,i],axis=1).T)
#tmp7=tmp1.sum(axis=0)
#tmp1=tmp1.sum(axis=1)
res = res + tmp1