print(r'Noise level: {0:.2e}'.format(noise_level))
print(r'Minimum approximation error |a - Gb|_2: {0:.2e}'.format(min_error))
# reconstruct Diracs' locations tk
z = np.roots(c_opt)
z = z / np.abs(z)
tk_recon = np.real(tau * 1j / (2 * np.pi) * np.log(z))
tk_recon = np.sort(tk_recon - np.floor(tk_recon / tau) * tau)
# reconstruct amplitudes ak
Phi_recon = periodicSinc(
np.pi * B * (np.reshape(t_samp, (-1, 1), order='F') -
np.reshape(tk_recon, (1, -1), order='F')), B * tau)
ak_recon = np.real(linalg.lstsq(Phi_recon, y_ell)[0])
# location estimation error
t_error = distance(tk_recon, tk)[0]
# plot reconstruction
plt.close()
fig = plt.figure(num=1, figsize=(5.5, 2.5), dpi=90)
# sub-figure 1
ax1 = plt.axes([0.125, 0.59, 0.85, 0.31])
markerline211_1, stemlines211_1, baseline211_1 = \
ax1.stem(tk, ak, label='Original Diracs')
plt.setp(stemlines211_1, linewidth=1.5, color=[0, 0.447, 0.741])
plt.setp(markerline211_1,
marker='^',
linewidth=1.5,
markersize=8,
markerfacecolor=[0, 0.447, 0.741],
mec=[0, 0.447, 0.741])
plt.setp(baseline211_1, linewidth=0)
Ihat_omega_ell_noisy,
K_est,
tau1,
tau2,
sympy.Rational(15, 12),
sympy.Rational(15, 12),
omega_ell,
M_N[0],
M_N[1],
noise_level,
max_ini,
stop_cri,
num_rotation=12)
# calculate reconstruction error
r_est_error, index = distance(xk + 1j * yk,
xk_recon + 1j * yk_recon)
xk = xk[index[:, 0]]
yk = yk[index[:, 0]]
alpha_k = alpha_k[index[:, 0]]
xk_recon = xk_recon[index[:, 1]]
yk_recon = yk_recon[index[:, 1]]
alpha_k_recon = np.real(alpha_k_recon[index[:, 1]])
# order the results for the ease of comparison
ind_order = np.argsort(xk)
fri_recon_all[realisations, :] = np.hstack(
(np.reshape(xk_recon[ind_order], (1, K), order='F'),
np.reshape(yk_recon[ind_order], (1, K), order='F'),
np.reshape(alpha_k_recon[ind_order], (1, K), order='F'),
np.reshape(r_est_error, (1, 1), order='F')))
print('Position estimation error: {0:.2e}\n').format(r_est_error)
P = 5
noise = np.random.randn(L) + 1j * np.random.randn(L)
noise = noise / linalg.norm(noise) * linalg.norm(Xomega_ell) * 10**(-P /
20.)
Xomega_ell_noisy = Xomega_ell + noise
# noise energy, in the noiseless case 1e-14 is considered as 0
noise_level = np.max([1e-14, linalg.norm(noise)])
max_ini = 50 # maximum number of random initialisations
tk_ref, ak_recon, Xomega_Uniform_ref = \
dirac_recon_irreg_fourier(Xomega_ell_noisy, K, tau, omega_ell, M,
noise_level, max_ini, stop_cri,
interp_kernel)
# location estimation error
t_error = distance(tk_ref, tk)[0]
# plot reconstruction
plt.close()
fig = plt.figure(num=1, figsize=(5, 4), dpi=90)
subplt_height = 0.2
subplt_width = 0.87
subplt_left_corner = 0.115
# sub-figure 1
ax1 = plt.axes([subplt_left_corner, 0.71, subplt_width, subplt_height])
markerline311_1, stemlines311_1, baseline311_1 = ax1.stem(
tk, ak, label='Original Diracs')
plt.setp(stemlines311_1, linewidth=1.5, color=[0, 0.447, 0.741])
plt.setp(markerline311_1,
marker='^',
noise_level = np.max([1e-10, linalg.norm(noise)])
taus = np.array([tau1, tau2])
omega_ell = np.column_stack((omega_ell_x, omega_ell_y))
tic = time.time()
num_rotation = 12
xk_recon, yk_recon, alpha_k_recon = \
recon_2d_dirac(Ihat_omega_ell_noisy, K_est, tau1, tau2,
sympy.Rational(15, 12), sympy.Rational(15, 12),
omega_ell, M, N, noise_level,
max_ini, stop_cri, num_rotation)
toc = time.time()
print('Average time: {0:.2f}[sec]'.format((toc - tic) / num_rotation))
# calculate reconstruction error
r_est_error = distance(xk + 1j * yk, xk_recon + 1j * yk_recon)[0]
print('Position estimation error: {0:.2e}\n'.format(r_est_error))
# plot results
file_name_loc = (r'./result/TSP_eg4_K_{0}_L_{1}_' +
r'noise_{2}dB_locations.' +
fig_format).format(repr(K), repr(L), repr(P))
plot_2d_dirac_loc(xk_recon, yk_recon, alpha_k_recon, xk, yk, alpha_k, K, L, P, tau1, tau2,
save_figure=True, fig_format=fig_format, file_name=file_name_loc)
file_name_spec = (r'./result/TSP_eg4_K_{0}_L_{1}_' +
r'noise_{2}dB_spectrum').format(repr(K), repr(L), repr(P))
plot_2d_dirac_spec(xk_recon, yk_recon, alpha_k_recon, Ihat_omega_ell_noisy, Ihat_omega_ell,
omega_ell_x, omega_ell_y, M, N, P, L,
save_figure=True, fig_format=fig_format,
file_name=file_name_spec,
show_dirty_img=True, dirty_img=dirty_img)