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frft.py
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import torch
import torch.nn as nn
import math
# core module
class FRFT(nn.Module):
def __init__(self, in_channels, order=0.5):
super(FRFT, self).__init__()
C0 = int(in_channels/3)
C1 = int(in_channels) - 2*C0
self.conv_0 = nn.Conv2d(C0, C0, kernel_size=3, padding=1)
self.conv_05 = nn.Conv2d(2*C1, 2*C1, kernel_size=1, padding=0)
self.conv_1 = nn.Conv2d(2*C0, 2*C0, kernel_size=1, padding=0)
self.conv2 = torch.nn.Conv2d(in_channels, in_channels, kernel_size=3, padding=1)
self.order = nn.Parameter(torch.randn(1))
def dfrtmtrx(self, N, a):
# Approximation order
app_ord = 2
Evec = self.dis_s(N,app_ord).cuda()
Evec = Evec.to(dtype=torch.complex64)
even = 1 - (N%2)
l = torch.tensor(list(range(0,N-1)) + [N-1+even]).cuda()
f = torch.diag(torch.exp(-1j*math.pi/2*a*l))
F = N**(1/2)*torch.einsum("ij,jk,ni->nk", f, Evec.T, Evec)
return F
def dis_s(self, N, app_ord):
app_ord = int(app_ord / 2)
s = torch.cat((torch.tensor([0, 1]), torch.zeros(N-1-2*app_ord), torch.tensor([1])))
S = self.cconvm(N,s) + torch.diag((torch.fft.fft(s)).real);
p = N
r = math.floor(N/2)
P = torch.zeros((p,p))
P[0,0] = 1
even = 1 - (p%2)
for i in range(1,r-even+1):
P[i,i] = 1/(2**(1/2))
P[i,p-i] = 1/(2**(1/2))
if even:
P[r,r] = 1
for i in range(r+1,p):
P[i,i] = -1/(2**(1/2))
P[i,p-i] = 1/(2**(1/2))
CS = torch.einsum("ij,jk,ni->nk", S, P.T, P)
C2 = CS[0:math.floor(N/2+1), 0:math.floor(N/2+1)]
S2 = CS[math.floor(N/2+1):N, math.floor(N/2+1):N]
ec, vc = torch.linalg.eig(C2)
es, vs = torch.linalg.eig(S2)
ec = ec.real
vc = vc.real
es = es.real
vs = vs.real
qvc = torch.vstack((vc, torch.zeros([math.ceil(N/2-1), math.floor(N/2+1)])))
SC2 = P@qvc # Even Eigenvector of S
qvs = torch.vstack((torch.zeros([math.floor(N/2+1), math.ceil(N/2-1)]),vs))
SS2 = P@qvs # Odd Eigenvector of S
idx = torch.argsort(-ec)
SC2 = SC2[:,idx]
idx = torch.argsort(-es)
SS2 = SS2[:,idx]
if N%2 == 0:
S2C2 = torch.zeros([N,N+1])
SS2 = torch.hstack([SS2, torch.zeros((SS2.shape[0],1))])
S2C2[:,range(0,N+1,2)] = SC2;
S2C2[:,range(1,N,2)] = SS2
S2C2 = S2C2[:, torch.arange(S2C2.size(1)) != N-1]
else:
S2C2 = torch.zeros([N,N])
S2C2[:,range(0,N+1,2)] = SC2;
S2C2[:,range(1,N,2)] = SS2
return S2C2
def cconvm(self, N, s):
M = torch.zeros((N,N))
dum = s
for i in range(N):
M[:,i] = dum
dum = torch.roll(dum,1)
return M
def FRFT2D(self, matrix):
N, C, H, W = matrix.shape
h_test = self.dfrtmtrx(H, self.order).cuda()
w_test = self.dfrtmtrx(W, self.order).cuda()
h_test = torch.repeat_interleave(h_test.unsqueeze(dim=0), repeats=C, dim=0)
h_test = torch.repeat_interleave(h_test.unsqueeze(dim=0), repeats=N, dim=0)
w_test = torch.repeat_interleave(w_test.unsqueeze(dim=0), repeats=C, dim=0)
w_test = torch.repeat_interleave(w_test.unsqueeze(dim=0), repeats=N, dim=0)
out = []
matrix = torch.fft.fftshift(matrix, dim=(2, 3)).to(dtype=torch.complex64)
out = torch.matmul(h_test, matrix)
out = torch.matmul(out, w_test)
out = torch.fft.fftshift(out, dim=(2, 3))
return out
def IFRFT2D(self, matrix):
N, C, H, W = matrix.shape
h_test = self.dfrtmtrx(H, -self.order).cuda()
w_test = self.dfrtmtrx(W, -self.order).cuda()
h_test = torch.repeat_interleave(h_test.unsqueeze(dim=0), repeats=C, dim=0)
h_test = torch.repeat_interleave(h_test.unsqueeze(dim=0), repeats=N, dim=0)
w_test = torch.repeat_interleave(w_test.unsqueeze(dim=0), repeats=C, dim=0)
w_test = torch.repeat_interleave(w_test.unsqueeze(dim=0), repeats=N, dim=0)
out = []
matrix = torch.fft.fftshift(matrix, dim=(2, 3)).to(dtype=torch.complex64)
out = torch.matmul(h_test, matrix)
out = torch.matmul(out, w_test)
out = torch.fft.fftshift(out, dim=(2, 3))
return out
def forward(self, x):
N, C, H, W = x.shape
C0 = int(C/3)
x_0 = x[:, 0:C0, :, :]
x_05 = x[:, C0:C-C0, :, :]
x_1 = x[:, C-C0:C, :, :]
# order = 0
x_0 = self.conv_0(x_0)
# order = 0.5
Fre = self.FRFT2D(x_05)
Real = Fre.real
Imag = Fre.imag
Mix = torch.concat((Real, Imag), dim=1)
Mix = self.conv_05(Mix)
Real1, Imag1 = torch.chunk(Mix, 2, 1)
Fre_out = torch.complex(Real1, Imag1)
IFRFT = self.IFRFT2D(Fre_out)
IFRFT = torch.abs(IFRFT)/(H*W)
# order = 1
fre = torch.fft.rfft2(x_1, norm='backward')
real = fre.real
imag = fre.imag
mix = torch.concat((real, imag), dim=1)
mix = self.conv_1(mix)
real1, imag1 = torch.chunk(mix, 2, 1)
fre_out = torch.complex(real1, imag1)
x_1 = torch.fft.irfft2(fre_out, s=(H, W), norm='backward')
output = torch.cat([x_0, IFRFT, x_1], dim=1)
output = self.conv2(output)
return output
#--------------------------------------------------------------------------------------
# your original network
class Net(nn.Module):
def __init__(self):
super(Net, self).__init__()
self.conv1 = nn.Conv2d(C0, C0, kernel_size=3, padding=1)
self.conv2 = nn.Conv2d(C0, C0, kernel_size=3, padding=1)
def forward(self, x):
out1 = self.conv1(x)
out = self.conv2(out1)
return out
#--------------------------------------------------------------------------------------
# plug in our FRFT module and baseline module
class Net(nn.Module):
def __init__(self):
super(Net, self).__init__()
self.conv1 = nn.Conv2d(C0, C0, kernel_size=3, padding=1)
self.conv2 = nn.Conv2d(C0, C0, kernel_size=3, padding=1)
self.FRFT = FRFT(in_channels=C0, order=0.5)
def forward(self, x):
out1 = self.conv1(x) # out1.shape: B, C, H, W
out1 = self.FRFT(out1)
out = self.conv2(out1)
return out