# 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 * np.linalg.norm(y-x,'fro') ** 2
# Proximity operators
normalize = lambda u : u/np.tile(
(np.maximum(amp(u), 1e-10))[:,:,np.newaxis],
(1,1,2))
proxF = lambda u,tau : np.tile(
soft_thresholding(amp(u), alpha*tau)[:,:,np.newaxis],
(1,1,2) )* normalize(u)
proxFS = dual_prox(proxF)
proxG = lambda x,tau : (x + tau*y) / (1+tau)
callback = lambda x : G(x) + F(K(x))
t1 = time.time()
xRec, cx = pp.admm(proxFS, proxG, K, y,
maxiter=300, full_output=1, callback=callback)
t2 = time.time()
print "Performed 300 iterations in " + str(t2-t1) + " seconds."
plt.subplot(221)
imgplot = plt.imshow(im)
imgplot.set_cmap('gray')
plt.title('Original')
# 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.")
plt.subplot(221)
plt.imshow(im, cmap='gray')
# 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."
