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import torch
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import torch_dct as dct
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from torchvision.transforms import functional as F
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def flip_odd_lines(matrix):
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"""
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Flip odd lines of a matrix
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"""
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matrix = matrix.clone()
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matrix[..., 1::2, :] = matrix[..., 1::2, :].flip(-1)
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return matrix
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rotate = lambda m, r: torch.rot90(m, r, [-2, -1])
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sequency_vec = lambda m: flip_odd_lines(rotate(m, 0)).flatten(start_dim= m.dim()-2)
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sequency_mat = lambda v, s: rotate(flip_odd_lines(v.unflatten(-1, s)), 0)
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def modulo(x, L):
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positive = x > 0
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x = x % L
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x = torch.where( ( x == 0) & positive, L, x)
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return x
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def center_modulo(x, L):
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return modulo(x + L/2, L) - L/2
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def unmodulo(psi):
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psi = torch.nn.functional.pad(psi, (1,1), mode='constant', value=0)
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psi = torch.diff(psi, 1)
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psi = dct.dct(psi, norm='ortho')
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N = psi.shape[-1]
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k = torch.arange(0, N)
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denom = 2*( torch.cos( torch.pi * k / N ) - 1 )
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denom[0] = 1.0
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denom = denom.unsqueeze(0).unsqueeze(0) + 1e-7
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psi = psi / denom
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psi[..., 0] = 0.0
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psi = dct.idct(psi, norm='ortho')
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return psi
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RD = lambda x, L: torch.round( x / L) * L
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def hard_thresholding(x, t):
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return x * (torch.abs(x) > t)
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def stripe_estimation(psi, t=0.15):
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dx = torch.diff(psi, 1, dim=-1)
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dy = torch.diff(psi, 1, dim=-2)
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dx = hard_thresholding(dx, t)
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dy = hard_thresholding(dy, t)
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dx = F.pad(dx, (1, 0, 1, 0))
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dy = F.pad(dy, (0, 1, 0, 1))
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rho = torch.diff(dx, 1, dim=-1) + torch.diff(dy, 1, dim=-2)
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dct_rho = dct.dct_2d(rho, norm='ortho')
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MX = rho.shape[-2]
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NX = rho.shape[-1]
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I, J = torch.meshgrid(torch.arange(0, MX), torch.arange(0, NX), indexing="ij")
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I = I.to(rho.device)
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J = J.to(rho.device)
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denom = 2 * (torch.cos(torch.pi * I / MX ) + torch.cos(torch.pi * J / NX ) - 2)
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denom = denom.unsqueeze(0).unsqueeze(0)
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denom = denom.to(rho.device)
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dct_phi = dct_rho / denom
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dct_phi[..., 0, 0] = 0
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phi = dct.idct_2d(dct_phi, norm='ortho')
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phi = phi - torch.min(phi)
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return phi
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def recons(m_t, DO=1, L=1.0, vertical=False, t=0.3):
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if vertical:
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m_t = m_t.permute(0, 1, 3, 2)
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shape = m_t.shape[-2:]
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modulo_vec = sequency_vec(m_t)
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res = center_modulo( torch.diff(modulo_vec, n=DO), L) - torch.diff(modulo_vec, n=DO)
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bl = res
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for i in range(DO):
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bl = unmodulo(bl)
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bl = RD(bl, L)
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x_est = bl
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x_est = sequency_mat(x_est, shape)
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x_est = x_est + m_t
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if vertical:
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x_est = x_est.permute(0, 1, 3, 2)
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stripes = stripe_estimation(x_est, t=t)
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x_est = x_est - stripes
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x_est = x_est - x_est.min()
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x_est = x_est / x_est.max()
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return x_est |
