def forward(self, x, weights):
r"""Solve the total variation problem and return the solution.
Arguments
---------
x: :class:`torch:torch.Tensor`
A tensor with shape ``(n,)`` holding the input signal.
weights: :class:`torch:torch.Tensor`
The edge weights.
Shape ``(n-1,)``, or ``(1,)`` if all weights are equal.
Returns
-------
:class:`torch:torch.Tensor`
The solution to the total variation problem, of shape ``(m, n)``.
"""
self.equal_weights = weights.size() == (1, )
if self.equal_weights:
opt = tv1_1d(x.numpy().ravel(), weights.numpy()[0], **self.tv_args)
else:
opt = tv1w_1d(x.numpy().ravel(),
weights.numpy().ravel(), **self.tv_args)
opt = torch.Tensor(opt).view_as(x)
self.save_for_backward(opt)
return opt
def solve_and_refine(x, w, equal_weights=True, **tv_args):
if equal_weights:
opt = tv1_1d(x.reshape(-1), w[0], **tv_args)
else:
opt = tv1w_1d(x.reshape(-1), w.reshape(-1), **tv_args)
return opt
def test_tv1w_1d():
methods = ('tautstring', 'pn')
for _ in range(20):
dimension = np.random.randint(1e1, 1e3)
x = 100 * np.random.randn(dimension)
w = 20 * np.random.rand(dimension - 1)
solutions = [tv1w_1d(x, w, method=method) for method in methods]
for i in range(len(solutions) - 1):
assert np.allclose(solutions[i], solutions[i + 1])
def test_tv1w_1d_uniform_weights_small_input():
for _ in range(1000):
dimension = np.random.randint(2, 4)
x = 100 * np.random.randn(dimension)
w1 = np.random.rand()
w = np.ones(dimension - 1) * w1
solw = tv1w_1d(x, w)
sol = tv1_1d(x, w1)
assert np.allclose(solw, sol)
def test_tv1w_1d():
methods = ('tautstring', 'pn')
for _ in range(20):
dimension = np.random.randint(1e1, 1e3)
x = 100*np.random.randn(dimension)
w = 20*np.random.rand(dimension-1)
solutions = [tv1w_1d(x, w, method=method) for method in methods]
for i in range(len(solutions)-1):
assert np.allclose(solutions[i], solutions[i+1])
def test_tv1w_1d_uniform_weights_small_input():
for _ in range(1000):
dimension = np.random.randint(2, 4)
x = 100*np.random.randn(dimension)
w1 = np.random.rand()
w = np.ones(dimension-1) * w1
solw = tv1w_1d(x, w)
sol = tv1_1d(x, w1)
assert np.allclose(solw, sol)
def prox(Z, s):
"""total variation prox operator on row dimension
"""
return ptv.tv1w_1d(Z.T, s * w).reshape(shape).T
N = 1000
s = np.zeros((N, 1))
s[N / 4:N / 2] = 1
s[N / 2:3 * N / 4] = -1
s[3 * N / 4:-N / 8] = 2
# Introduce noise
n = s + 0.5 * randn(*shape(s))
# Generate weights
lam = np.linspace(0, 2, N - 1)
# Filter using weighted TV-L1
print('Filtering signal with weighted TV-L1...')
start = time.time()
f = ptv.tv1w_1d(n, lam)
end = time.time()
print('Elapsed time ' + str(end - start))
# Plot results
plt.subplot(4, 1, 1)
plt.title('Weighted TVL1 filtering')
plt.plot(s)
plt.ylabel('Original')
grid(True)
plt.subplot(4, 1, 2)
plt.plot(n)
plt.ylabel('Noisy')
grid(True)
### Weighted TV-L1 filtering
# Generate impulse (blocky) signal
s = _blockysignal()
# Introduce noise
n = s + 0.5*np.random.randn(*np.shape(s))
# Generate weights
lam = np.linspace(0,2,N-1)
# Filter using weighted TV-L1
print('Filtering signal with weighted TV-L1...')
start = time.time()
f = ptv.tv1w_1d(n, lam)
end = time.time()
print('Elapsed time ' + str(end-start))
# Plot results
plt.subplot(4, 1, 1)
plt.title('Weighted TVL1 filtering')
plt.plot(s)
plt.ylabel('Original')
plt.grid(True)
plt.subplot(4, 1, 2)
plt.plot(n)
plt.ylabel('Noisy')
plt.grid(True)