def primal_energy_tvl1(x, img_obs, clambda):
"""
:param x: numpy array, [MxN]
:param img_obs: numpy array [MxN], observed image
:param clambda: float, lambda parameter
:return: float, primal ROF energy
"""
energy_reg = norm1(forward_gradient(x)).sum()
energy_data_term = clambda * np.abs(x - img_obs).sum()
return energy_reg + energy_data_term
def primal_energy_tvl1(x, img_obs, clambda):
"""
:param x: pytorch Variables, [MxN]
:param img_obs: pytorch Variables [MxN], observed image
:param clambda: float, lambda parameter
:return: float, primal ROF energy
"""
energy_reg = torch.sum(
torch.norm(forward_gradient(x, torch.cuda.FloatTensor), 1))
energy_data_term = torch.sum(clambda * torch.abs(x - img_obs))
return energy_reg + energy_data_term
def test_adjoint_operator(self):
Y = 200
X = 100
x = 1 + Variable(torch.randn((1, Y, X)).type(torch.FloatTensor))
y_l = Variable(torch.randn((2, Y + 1, X + 1)).type(torch.FloatTensor))
y_l[0, 1:, 1:-1] = 1 + torch.randn((1, Y, X - 1))
y_l[1, 1:-1, 1:] = 1 + torch.randn((1, Y - 1, X))
y = y_l[:, 1:, 1:]
# Compute gradient and divergence
gx = forward_gradient(x)
dy = backward_divergence(y)
check = abs((y.data.numpy()[:] * gx.data.numpy()[:]).sum() + (dy.data.numpy()[:]*x.data.numpy()[:]).sum())
print(check)
self.assertTrue(check < 1e-4)
x_tilde = x
h, w = img_ref.shape
y = np.zeros((h, w, 2))
p_nrg = primal_energy_rof(x, img_obs, lambda_rof)
print "Primal Energy = ", p_nrg
d_nrg = dual_energy_rof(y, img_obs)
print "Dual Energy = ", d_nrg
# Solve ROF
primal = np.zeros((max_it, ))
dual = np.zeros((max_it, ))
gap = np.zeros((max_it, ))
primal[0] = p_nrg
dual[0] = d_nrg
y = forward_gradient(x)
for it in range(max_it):
# Dual update
y = y + sigma * forward_gradient(x_tilde)
y = proximal_linf_ball(y, 1.0)
# Primal update
x_old = x
x = (x + tau * backward_divergence(y) +
lambda_rof * tau * img_obs) / (1.0 + lambda_rof * tau)
# Smoothing
x_tilde = x + theta * (x - x_old)
# Compute energies
primal[it] = primal_energy_rof(x_tilde, img_obs, sigma)
dual[it] = dual_energy_rof(y, img_obs)
gap[it] = primal[it] - dual[it]