def image_formation():
Ncopy = 1000
use_sPCA = False
image_idx = 0
SNR = .1
r_max = 64
seed = 0
Coeff, Freqs, rad_freqs, Mean, Phi_ns, sigma, Coeff_raw, rotations = make_data(
Ncopy=Ncopy, SNR=SNR, seed=seed, image_idx=image_idx, sPCA=use_sPCA)
image0 = recover_image(Coeff_raw, Phi_ns, Freqs, r_max, Mean)
Rl = np.expand_dims(np.exp(1j * 2 * np.pi * 45 / 360 * Freqs), axis=-1)
Coeff_rotated = Coeff_raw * Rl
image_rotated = recover_image(Coeff_rotated, Phi_ns, Freqs, r_max, Mean)
image_rotated_noisy = recover_image(np.expand_dims(Coeff[:, 0], axis=-1),
Phi_ns, Freqs, r_max, Mean)
plt.subplot(131)
plt.imshow(image0, cmap='gray')
plt.axis('off')
plt.subplot(132)
plt.imshow(image_rotated, cmap='gray')
plt.axis('off')
plt.subplot(133)
plt.imshow(image_rotated_noisy, cmap='gray')
plt.axis('off')
plt.savefig('mra_2d_observations_model.png')
plt.savefig('mra_2d_observations_model.eps')
plt.clf()
def ppm_em_experiment(seed, image_idx, SNR, Ncopy, Ndir, use_sPCA,
use_signal_prior, gamma, BW, path_learning, P):
Coeff, Freqs, rad_freqs, Mean, Phi_ns, sigma, Coeff_raw, rotations = make_data(
Ncopy=Ncopy, SNR=SNR, seed=seed, image_idx=image_idx, sPCA=use_sPCA)
image0 = recover_image(Coeff_raw, Phi_ns, Freqs, r_max, Mean)
TT = time()
Coeff_s, est_rotations = synchronize_2d(Coeff, Freqs, Ndir)
t_synch = time() - TT
x_s = np.expand_dims(np.mean(Coeff_s, axis=-1), axis=-1)
x = align_image(x_s, Coeff_raw, Freqs)
imager = recover_image(x, Phi_ns, Freqs, r_max, Mean)
err_synch = np.sqrt(
np.sum(np.sum((image0 - imager)**2, axis=-1), axis=0) /
np.sum(np.sum(image0**2, axis=-1), axis=0))
x, num_iter_synch_em, t_synch_em = EM_General_Prior(Coeff,
Freqs,
sigma,
Ndir,
1 / Ndir * np.ones(
(Ndir, 1)),
Ndir,
0,
Coeff_raw,
use_signal_prior,
uniform=False)
x = align_image(x, Coeff_raw, Freqs)
imager = recover_image(x, Phi_ns, Freqs, r_max, Mean)
err_synch_em = np.sqrt(
np.sum(np.sum((image0 - imager)**2, axis=-1), axis=0) /
np.sum(np.sum(image0**2, axis=-1), axis=0))
results = pd.DataFrame()
results = results.append(
{
'use_signal_prior': use_signal_prior,
'use_sPCA': use_sPCA,
'seed': seed,
'SNR': SNR,
'sigma': sigma,
'N': Ncopy,
'L': Coeff.shape[0],
'image_idx': image_idx,
'err': err_synch_em,
'num_iter': num_iter_synch_em,
'BW': BW,
'gamma': gamma,
't': t_synch + t_synch_em,
't_synch': t_synch,
't_em': t_synch_em,
'err_synch': err_synch
},
ignore_index=True)
return results
def draw_from_prior():
Ncopy = 10000
use_sPCA = True
image_idx = 0
SNR = 10
filename = 'E70s.mat'
r_max = 64
seed = 0
Coeff, Freqs, rad_freqs, Mean, Phi_ns, sigma, Coeff_raw, rotations = make_data(
Ncopy=Ncopy, SNR=SNR, seed=seed, image_idx=image_idx, sPCA=use_sPCA)
data_prior = np.expand_dims(4 * np.exp(-np.asarray(Freqs) / 8), axis=-1)
Gamma_a = np.diag(np.abs(data_prior[:, 0])**2)
np.random.seed(10)
for i in range(9):
x = 1 / np.sqrt(2) * (
np.random.multivariate_normal(np.zeros(
(Freqs.shape[0], )), Gamma_a) +
1j * np.random.multivariate_normal(np.zeros(
(Freqs.shape[0], )), Gamma_a))
Coeff_raw = np.expand_dims(x, axis=-1)
image0 = recover_image(Coeff_raw, Phi_ns, Freqs, r_max, Mean)
plt.subplot('33%d' % (i + 1))
plt.imshow(image0, cmap='gray')
plt.axis('off')
plt.savefig('draw_from_prior.png')
plt.savefig('draw_from_prior.eps')
plt.clf()
def synchronize_and_match_experiment(seed, image_idx, SNR, Ncopy, Ndir,
use_sPCA, P):
Coeff, Freqs, rad_freqs, Mean, Phi_ns, sigma, Coeff_raw, rotations = make_data(
Ncopy=Ncopy, SNR=SNR, seed=seed, image_idx=image_idx, sPCA=use_sPCA)
image0 = recover_image(Coeff_raw, Phi_ns, Freqs, r_max, Mean)
TT = time()
Coeff_s, est_rotations = synchronize_and_match_2d(Coeff,
Freqs,
P=P,
L=Ndir)
t_synch = time() - TT
h, bin_edges = np.histogram((est_rotations - rotations) % 360,
bins=np.arange(-0.5, 360 + 0.5))
measured_rho = np.expand_dims(h / np.sum(h), axis=-1)
x_s = np.expand_dims(np.mean(Coeff_s, axis=-1), axis=-1)
x = align_image(x_s, Coeff_raw, Freqs)
imager = recover_image(x, Phi_ns, Freqs, r_max, Mean)
err_synch = np.sqrt(
np.sum(np.sum((image0 - imager)**2, axis=-1), axis=0) /
np.sum(np.sum(image0**2, axis=-1), axis=0))
print('#### synchronize and match ####')
print('e = %f' % err_synch)
results = pd.DataFrame()
results = results.append(
{
'use_sPCA': use_sPCA,
'seed': seed,
'SNR': SNR,
'sigma': sigma,
'N': Ncopy,
'L': Coeff.shape[0],
'image_idx': image_idx,
'rho': measured_rho,
'err': err_synch,
'num_iter': 0,
't': t_synch
},
ignore_index=True)
return results
def known_rotations_experiment(seed, image_idx, SNR, Ncopy, Ndir, use_sPCA):
Coeff, Freqs, rad_freqs, Mean, Phi_ns, sigma, Coeff_raw, rotations = make_data(
Ncopy=Ncopy, SNR=SNR, seed=seed, image_idx=image_idx, sPCA=use_sPCA)
image0 = recover_image(Coeff_raw, Phi_ns, Freqs, r_max, Mean)
est_rotations = rotations
Coeff_s = np.zeros_like(Coeff)
for i in range(Ncopy):
Coeff_s[:, i] = Coeff[:, i] * np.exp(
-1j * 2 * np.pi * est_rotations[i] / 360 * Freqs)
t_synch = 0
h, bin_edges = np.histogram((est_rotations - rotations) % 360,
bins=np.arange(-0.5, 360 + 0.5))
measured_rho = np.expand_dims(h / np.sum(h), axis=-1)
x_s = np.expand_dims(np.mean(Coeff_s, axis=-1), axis=-1)
x = align_image(x_s, Coeff_raw, Freqs)
imager = recover_image(x, Phi_ns, Freqs, r_max, Mean)
err_synch = np.sqrt(
np.sum(np.sum((image0 - imager)**2, axis=-1), axis=0) /
np.sum(np.sum(image0**2, axis=-1), axis=0))
print('#### oracle ####')
print('e = %f' % err_synch)
results = pd.DataFrame()
results = results.append(
{
'use_sPCA': use_sPCA,
'seed': seed,
'SNR': SNR,
'sigma': sigma,
'N': Ncopy,
'L': Coeff.shape[0],
'image_idx': image_idx,
'rho': measured_rho,
'err': err_synch,
'num_iter': 0,
't': t_synch
},
ignore_index=True)
return results
def standard_em_experiment(seed, image_idx, SNR, Ncopy, Ndir, use_sPCA,
use_signal_prior):
Coeff, Freqs, rad_freqs, Mean, Phi_ns, sigma, Coeff_raw, rotations = make_data(
Ncopy=Ncopy, SNR=SNR, seed=seed, image_idx=image_idx, sPCA=use_sPCA)
image0 = recover_image(Coeff_raw, Phi_ns, Freqs, r_max, Mean)
x, num_iter_em_uniform, t_em_uniform = EM_General_Prior(Coeff,
Freqs,
sigma,
Ndir,
1 / Ndir * np.ones(
(Ndir, 1)),
Ndir,
0,
Coeff_raw,
use_signal_prior,
uniform=True)
x = align_image(x, Coeff_raw, Freqs)
imager = recover_image(x, Phi_ns, Freqs, r_max, Mean)
err_em_uniform = np.sqrt(
np.sum(np.sum((image0 - imager)**2, axis=-1), axis=0) /
np.sum(np.sum(image0**2, axis=-1), axis=0))
results = pd.DataFrame()
results = results.append(
{
'use_signal_prior': use_signal_prior,
'use_sPCA': use_sPCA,
'seed': seed,
'SNR': SNR,
'sigma': sigma,
'N': Ncopy,
'L': Coeff.shape[0],
'image_idx': image_idx,
'err': err_em_uniform,
'num_iter': num_iter_em_uniform,
't': t_em_uniform
},
ignore_index=True)
return results