def test_fb_l1_denoising():
n = 1000
# Use a very sparse vector for the test
x = np.zeros((n,1))
x[1,:] = 100
y = x + 0.06 * np.random.randn(n,1)
la = 0.2
prox_f = lambda x,tau: soft_thresholding(x, la*tau)
grad_g = lambda x: x - y
for method in methods:
xRec = forward_backward(prox_f, grad_g, y, 1, method=method)
#TODO ugly test to change
assert_array_almost_equal(x, xRec, decimal=0)
def test_fb_l1_denoising():
n = 1000
# Use a very sparse vector for the test
x = np.zeros((n, 1))
x[1, :] = 100
y = x + 0.06 * np.random.randn(n, 1)
la = 0.2
prox_f = lambda x, tau: soft_thresholding(x, la * tau)
grad_g = lambda x: x - y
for method in methods:
x_rec = forward_backward(prox_f, grad_g, y, 1, method=method)
#TODO ugly test to change
assert_array_almost_equal(x, x_rec, decimal=0)
resy = py - np.roll(py, 1, axis=1)
return -(resx + resy)
# Minimization of F(K*x) + G(x)
K = gradient
K.T = divergence
amp = lambda u: np.sqrt(np.sum(u ** 2, axis=2))
F = lambda u: alpha * np.sum(amp(u))
G = lambda x: 1 / 2 * lin.norm(y - x, 'fro') ** 2
# Proximity operators
normalize = lambda u: u / np.tile(
(np.maximum(amp(u), 1e-10))[:, :, np.newaxis],
(1, 1, 2))
prox_f = lambda u, tau: np.tile(
soft_thresholding(amp(u), alpha * tau)[:, :, np.newaxis],
(1, 1, 2)) * normalize(u)
prox_fs = dual_prox(prox_f)
prox_g = lambda x, tau: (x + tau * y) / (1 + tau)
# context
ctx = Context(full_output=True, maxiter=300)
ctx.callback = lambda x: G(x) + F(K(x))
t1 = time.time()
x_rec, cx = admm(prox_fs, prox_g, K, y, context=ctx)
t2 = time.time()
print("Performed 300 iterations in " + str(t2 - t1) + " seconds.")
py = p[:, :, 1]
resx = px - np.roll(px, 1, axis=0)
resy = py - np.roll(py, 1, axis=1)
return -(resx + resy)
# Minimization of F(K*x) + G(x)
K = gradient
K.T = divergence
amp = lambda u: np.sqrt(np.sum(u ** 2, axis=2))
F = lambda u: alpha * np.sum(amp(u))
G = lambda x: 1 / 2 * lin.norm(y - x, "fro") ** 2
# Proximity operators
normalize = lambda u: u / np.tile((np.maximum(amp(u), 1e-10))[:, :, np.newaxis], (1, 1, 2))
prox_f = lambda u, tau: np.tile(soft_thresholding(amp(u), alpha * tau)[:, :, np.newaxis], (1, 1, 2)) * normalize(u)
prox_fs = dual_prox(prox_f)
prox_g = lambda x, tau: (x + tau * y) / (1 + tau)
callback = lambda x: G(x) + F(K(x))
t1 = time.time()
x_rec, cx = admm(prox_fs, prox_g, K, y, maxiter=300, full_output=1, callback=callback)
t2 = time.time()
print "Performed 300 iterations in " + str(t2 - t1) + " seconds."
pl.subplot(221)
pl.imshow(im, cmap="gray")
pl.title("Original")
pl.axis("off")
resy = py - np.roll(py, 1, axis=1)
return -(resx + resy)
# Minimization of F(K*x) + G(x)
K = gradient
K.T = divergence
amp = lambda u: np.sqrt(np.sum(u**2, axis=2))
F = lambda u: alpha * np.sum(amp(u))
G = lambda x: 1 / 2 * lin.norm(y - x, 'fro')**2
# Proximity operators
normalize = lambda u: u / np.tile(
(np.maximum(amp(u), 1e-10))[:, :, np.newaxis], (1, 1, 2))
prox_f = lambda u, tau: np.tile(
soft_thresholding(amp(u), alpha * tau)[:, :, np.newaxis],
(1, 1, 2)) * normalize(u)
prox_fs = dual_prox(prox_f)
prox_g = lambda x, tau: (x + tau * y) / (1 + tau)
callback = lambda x: G(x) + F(K(x))
t1 = time.time()
x_rec, cx = admm(prox_fs,
prox_g,
K,
y,
maxiter=300,
full_output=1,
callback=callback)
t2 = time.time()