How to restore Aqua MODIS band 06 missing pixels using a nonlinear regression based on Gaussian processes ?: An application based on python and Scikit-Learn.
Author: Benjamin Marchant
(marchant.benjamin01@gmail.com)
(benjamin.marchant@nasa.gov)
v1.0.0
import matplotlib.pyplot as plt
import matplotlib as mpl
import matplotlib.cm as cm
import numpy as np
import warnings
from matplotlib.pyplot import figure
from IPython.core.display import HTML
from pyhdf.SD import SD, SDC
warnings.filterwarnings('ignore')from IPython.core.display import HTML
HTML("""
<style>
.output_png {
display: table-cell;
text-align: center;
vertical-align: middle;
}
</style>
""")myd021km_file = SD('MYD021KM.A2007219.2010.006.2012077031102.hdf', SDC.READ)EV_250_Aggr1km_RefSB = myd021km_file.select('EV_250_Aggr1km_RefSB')
EV_500_Aggr1km_RefSB = myd021km_file.select('EV_500_Aggr1km_RefSB')
EV_1KM_RefSB = myd021km_file.select('EV_1KM_RefSB')
EV_1KM_Emissive = myd021km_file.select('EV_1KM_Emissive')modis_band_dic = {}#print( EV_250_Aggr1km_RefSB.info() )
EV_250_Aggr1km_RefSB_attributes = EV_250_Aggr1km_RefSB.attributes()
EV_250_Aggr1km_RefSB_scales = EV_250_Aggr1km_RefSB_attributes['reflectance_scales']
EV_250_Aggr1km_RefSB_offsets = EV_250_Aggr1km_RefSB_attributes['reflectance_offsets']
#pprint.pprint(EV_250_Aggr1km_RefSB_attributes )
for idx,i in enumerate(EV_250_Aggr1km_RefSB_attributes['band_names'].split(',')):
print(idx,i)
modis_band_dic[i] = [EV_250_Aggr1km_RefSB,idx]0 1
1 2
#print( EV_500_Aggr1km_RefSB.info() )
EV_500_Aggr1km_RefSB_attributes = EV_500_Aggr1km_RefSB.attributes()
EV_500_Aggr1km_RefSB_scales = EV_500_Aggr1km_RefSB_attributes['reflectance_scales']
EV_500_Aggr1km_RefSB_offsets = EV_500_Aggr1km_RefSB_attributes['reflectance_offsets']
#pprint.pprint(EV_500_Aggr1km_RefSB_attributes )
for idx,i in enumerate(EV_500_Aggr1km_RefSB_attributes['band_names'].split(',')):
print(idx,i)
modis_band_dic[i] = [EV_500_Aggr1km_RefSB,idx]0 3
1 4
2 5
3 6
4 7
#print( EV_1KM_RefSB.info() )
EV_1KM_RefSB_attributes = EV_1KM_RefSB.attributes()
EV_1KM_RefSB_scales = EV_1KM_RefSB_attributes['reflectance_scales']
EV_1KM_RefSB_offsets = EV_1KM_RefSB_attributes['reflectance_offsets']
#pprint.pprint(EV_1KM_RefSB_attributes )
for idx,i in enumerate(EV_1KM_RefSB_attributes['band_names'].split(',')):
print(idx,i)
modis_band_dic[i] = [EV_1KM_RefSB,idx]0 8
1 9
2 10
3 11
4 12
5 13lo
6 13hi
7 14lo
8 14hi
9 15
10 16
11 17
12 18
13 19
14 26
print( EV_1KM_Emissive.info() )
EV_1KM_Emissive_attributes = EV_1KM_Emissive.attributes()
EV_1KM_Emissive_scales = EV_1KM_Emissive_attributes['radiance_scales']
EV_1KM_Emissive_offsets = EV_1KM_Emissive_attributes['radiance_offsets']
#pprint.pprint(EV_1KM_Emissive_attributes )
for idx,i in enumerate(EV_1KM_Emissive_attributes['band_names'].split(',')):
print(idx,i)
modis_band_dic[i] = [EV_1KM_Emissive,idx]('EV_1KM_Emissive', 3, [16, 2030, 1354], 23, 8)
0 20
1 21
2 22
3 23
4 24
5 25
6 27
7 28
8 29
9 30
10 31
11 32
12 33
13 34
14 35
15 36
for key in modis_band_dic:
print(key, modis_band_dic[key][0].info()[0], modis_band_dic[key][1])1 EV_250_Aggr1km_RefSB 0
2 EV_250_Aggr1km_RefSB 1
3 EV_500_Aggr1km_RefSB 0
4 EV_500_Aggr1km_RefSB 1
5 EV_500_Aggr1km_RefSB 2
6 EV_500_Aggr1km_RefSB 3
7 EV_500_Aggr1km_RefSB 4
8 EV_1KM_RefSB 0
9 EV_1KM_RefSB 1
10 EV_1KM_RefSB 2
11 EV_1KM_RefSB 3
12 EV_1KM_RefSB 4
13lo EV_1KM_RefSB 5
13hi EV_1KM_RefSB 6
14lo EV_1KM_RefSB 7
14hi EV_1KM_RefSB 8
15 EV_1KM_RefSB 9
16 EV_1KM_RefSB 10
17 EV_1KM_RefSB 11
18 EV_1KM_RefSB 12
19 EV_1KM_RefSB 13
26 EV_1KM_RefSB 14
20 EV_1KM_Emissive 0
21 EV_1KM_Emissive 1
22 EV_1KM_Emissive 2
23 EV_1KM_Emissive 3
24 EV_1KM_Emissive 4
25 EV_1KM_Emissive 5
27 EV_1KM_Emissive 6
28 EV_1KM_Emissive 7
29 EV_1KM_Emissive 8
30 EV_1KM_Emissive 9
31 EV_1KM_Emissive 10
32 EV_1KM_Emissive 11
33 EV_1KM_Emissive 12
34 EV_1KM_Emissive 13
35 EV_1KM_Emissive 14
36 EV_1KM_Emissive 15
def plot_MODIS_L1(MODIS_band, modis_band_dic):
data_selected_id = modis_band_dic[str(MODIS_band)][0]
band_idx = modis_band_dic[str(MODIS_band)][1]
title = 'MODIS Band' + str(MODIS_band)
figure(num=None, figsize=(12, 10), dpi=80, facecolor='w', edgecolor='k')
data = EV_500_Aggr1km_RefSB.get()
data_selected_band = data[band_idx,:,:]
data_selected_attributes = data_selected_id.attributes()
_FillValue = data_selected_attributes['_FillValue']
_FillValue = 65528 # warning wrong _FillValue stored in attributes
if modis_band_dic[str(MODIS_band)][0].info()[0] == 'EV_1KM_Emissive':
radiance_scales = data_selected_attributes['radiance_scales']
radiance_offsets = data_selected_attributes['radiance_offsets']
data_selected_band[ data_selected_band == _FillValue ] = 0.0
data_selected_band = (data_selected_band - radiance_offsets[band_idx]) * radiance_scales[band_idx]
else:
reflectance_scales = data_selected_attributes['reflectance_scales']
data_selected_band[ data_selected_band == _FillValue ] = 0.0
data_selected_band = data_selected_band * reflectance_scales[band_idx]
cmap = [(0.0,0.0,0.0)] + [(cm.jet(i)) for i in range(1,256)]
cmap = mpl.colors.ListedColormap(cmap)
img = plt.imshow(np.fliplr(data_selected_band), cmap=cmap,interpolation='none', origin='lower')
plt.title(title, fontsize=11)
cbar = plt.colorbar()
cbar.ax.tick_params(labelsize=8)
l = [int(i) for i in np.linspace(0,data_selected_band.shape[1],6)]
plt.xticks(l, [i for i in reversed(l)], rotation=0, fontsize=11 )
l = [int(i) for i in np.linspace(0,data_selected_band.shape[0],9)]
plt.yticks(l, l, rotation=0, fontsize=11 )
plt.xticks(fontsize=11)
plt.yticks(fontsize=11)
plt.show()plot_MODIS_L1(6,modis_band_dic)
plot_MODIS_L1(7,modis_band_dic)
MODIS_band = 6
data_selected_id = modis_band_dic[str(MODIS_band)][0]
band_idx = modis_band_dic[str(MODIS_band)][1]
data = EV_500_Aggr1km_RefSB.get()
data_band_06 = data[band_idx,:,:]
data_selected_attributes = data_selected_id.attributes()
_FillValue = data_selected_attributes['_FillValue']
_FillValue = 65528 # warning wrong _FillValue stored in attributes
reflectance_scales = data_selected_attributes['reflectance_scales']
data_band_06[ data_band_06 == _FillValue ] = 0.0
data_band_06 = data_band_06 * reflectance_scales[band_idx]
data_band_6_vmin = np.min(data_band_06)
data_band_6_vmax = np.max(data_band_06)
data_shape = data_band_06.shape
#print(np.where(data_band_06[:,0]==0.0))
#print(np.where(data_band_06[:,0]==0.0)[0].shape)
nb_missing_rows = np.where(data_band_06[:,0]==0.0)[0].shape[0]
band_06_missing_data_idx = np.where(data_band_06==0.0)
print('data_shape --> ', data_shape)
print('nb_missing_rows --> ', nb_missing_rows)
print('number of missing data --> ', nb_missing_rows * data_shape[1])
print('Fraction of missing data --> ', 100.0 * nb_missing_rows * data_shape[1] / ( data_shape[0] * data_shape[1] ))
#for i in range(100):
# print(i,data_band_6[i,0])
nbx = 25
x = np.arange(nbx)
figure(num=None, figsize=(8, 6), dpi=80, facecolor='w', edgecolor='k')
plt.scatter(x,data_band_06[0:nbx,0])
plt.xlabel('MODIS AlongTrack First 25 Index')
plt.xlim(0,nbx)
plt.show()
plt.close()data_shape --> (2030, 1354)
nb_missing_rows --> 812
number of missing data --> 1099448
Fraction of missing data --> 40.0
MODIS_band = 7
data_selected_id = modis_band_dic[str(MODIS_band)][0]
band_idx = modis_band_dic[str(MODIS_band)][1]
data = EV_500_Aggr1km_RefSB.get()
data_band_07 = data[band_idx,:,:]
data_selected_attributes = data_selected_id.attributes()
_FillValue = data_selected_attributes['_FillValue']
_FillValue = 65528 # warning wrong _FillValue stored in attributes
reflectance_scales = data_selected_attributes['reflectance_scales']
data_band_07[ data_band_07 == _FillValue ] = 0.0
data_band_07 = data_band_07 * reflectance_scales[band_idx]
a_idx = np.where(data_band_06[:,0]!=0.0)[0]
A = data_band_06[a_idx].ravel()
B = data_band_07[a_idx].ravel()
figure(num=None, figsize=(8, 6), dpi=80, facecolor='w', edgecolor='k')
plt.scatter(A[0:1000],B[0:1000])
plt.xlabel('MODIS Band 06')
plt.ylabel('MODIS Band 07')
plt.show()
plt.close()
i_start = 0
j_start = 0
cmap = [(0.0,0.0,0.0)] + [(cm.jet(i)) for i in range(1,256)]
cmap = mpl.colors.ListedColormap(cmap)
figure(num=None, figsize=(8, 6), dpi=80, facecolor='w', edgecolor='k')
#img = plt.imshow(np.fliplr(data_band_6[0:12,0:12]), cmap=cmap,
# interpolation='none', origin='lower')
img = plt.imshow(data_band_06[i_start:i_start+12,j_start:j_start+12], cmap=cmap,
interpolation='none', origin='lower')
cbar = plt.colorbar()
cbar.ax.tick_params(labelsize=8)
plt.title('Band 06', fontsize=10)
plt.show()
figure(num=None, figsize=(8, 6), dpi=80, facecolor='w', edgecolor='k')
cmap = [(cm.jet(i)) for i in range(1,256)]
cmap = mpl.colors.ListedColormap(cmap)
img = plt.imshow(data_band_07[i_start:i_start+12,j_start:j_start+12], cmap=cmap,
interpolation='none', origin='lower')
plt.title('Band 07', fontsize=10)
cbar = plt.colorbar()
cbar.ax.tick_params(labelsize=8)
plt.show()
plt.close()
#data_sample = data_band_6[0:12,0:12]
data_sample = np.copy(data_band_06[i_start:i_start+12,j_start:j_start+12])
X = np.stack((np.where(data_sample!=0.0)[0],np.where(data_sample!=0.0)[1]), axis=-1)
Y = data_sample[np.where(data_sample!=0.0)[0],np.where(data_sample!=0.0)[1]]
y_min = np.min(Y)
y_max = np.max(Y)
x1_min = np.min(X[:,0]) # Data Scaling
x1_max = np.max(X[:,0]) # Data Scaling
X = X.astype('float64')
X[:,0] = (1.0*X[:,0]-x1_min) / (x1_max-x1_min)
x2_min = np.min(X[:,1])
x2_max = np.max(X[:,1])
X[:,1] = (1.0*X[:,1]-x2_min) / (x2_max-x2_min)
X_dim1 = X.shape[0]
sigma_n = 0.00
#X = X[:,:,np.newaxis]
#X1 = X[:,0,:]
#X2 = X[:,1,:]
X1 = X[:,0]
X2 = X[:,1]
print(X.shape)
print(Y.shape)
print(X1.shape)(96, 2)
(96,)
(96,)
from sklearn.metrics import accuracy_score, log_loss
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF
from sklearn.gaussian_process.kernels import DotProduct, ConstantKernel as C
from sklearn import preprocessing
%%time
kernel = C(1.0, (0.1, 10.0)) * RBF([0.2,0.2], (1e-2, 1e2))
gp = GaussianProcessRegressor(kernel=kernel, n_restarts_optimizer=20)
model = gp.fit(X,Y)CPU times: user 2.42 s, sys: 22.4 ms, total: 2.44 s
Wall time: 1.25 s
%%time
l1 = 0.2
l2 = 0.2
sigma_f = 0.01
kernel = C( 0.01, ( 0.01, 0.01)) * RBF([0.2,0.2], (0.2, 0.2))
gp = GaussianProcessRegressor(kernel=kernel, n_restarts_optimizer=20)
model = gp.fit(X,Y)CPU times: user 78.7 ms, sys: 1.56 ms, total: 80.3 ms
Wall time: 41.7 ms
- [AttributeError while adding colorbar in matplotlib](https://stackoverflow.com/questions/2643953/attributeerror-while-adding-colorbar-in-matplotlib/51622063)
- [matplotlib and subplots properties](https://stackoverflow.com/questions/38662667/matplotlib-and-subplots-properties)%%time
X1_new, X2_new = np.meshgrid(np.arange(0, 12, 1.0), np.arange(0, 12, 1.0))
X1_new= (1.0*X1_new-x1_min) / (x1_max-x1_min) # data scaling
X2_new= (1.0*X2_new-x2_min) / (x2_max-x2_min) # data scaling
print(X1_new.shape)
X_new = np.stack((X1_new.ravel(),X2_new.ravel()), axis=-1)
print(X_new.shape)
Y_new = model.predict(X_new)
fig, axs = plt.subplots(1,2,gridspec_kw={'hspace': 0.3},figsize=(14,14))
(ax1, ax2) = axs
img = ax1.imshow(data_sample, cmap=cmap,
interpolation='none', origin='lower')
ax1.set_xlabel(r'$x_1$')
ax1.set_ylabel(r'$x_2$')
ax1.set_title('MODIS Band 06', fontsize=10)
plt.colorbar(img, ax=ax1, shrink=0.35)
img = ax2.imshow(Y_new.reshape(12,12).T, interpolation='nearest',
origin='lower', cmap=cm.jet, vmin=0.0, vmax=y_max)
ax2.set_xlabel(r'$x_1$')
ax2.set_ylabel(r'$x_2$')
ax2.set_title('MODIS Band 06 (Restored)', fontsize=10)
plt.colorbar(img, ax=ax2, shrink=0.35)
plt.title('MODIS Band 06 (Restored)', fontsize=10)
plt.show()(12, 12)
(144, 2)
CPU times: user 522 ms, sys: 8.78 ms, total: 531 ms
Wall time: 373 ms
X1_new, X2_new = np.meshgrid(np.arange(0, 11, 0.5), np.arange(0, 11, 0.5))
X1_new= (1.0*X1_new-x1_min) / (x1_max-x1_min) # data scaling
X2_new= (1.0*X2_new-x2_min) / (x2_max-x2_min) # data scaling
print(X1_new.shape)
X_new = np.stack((X1_new.ravel(),X2_new.ravel()), axis=-1)
print(X_new.shape)
Y_new = model.predict(X_new)
fig, axs = plt.subplots(1,2,gridspec_kw={'hspace': 0.3},figsize=(14,14))
(ax1, ax2) = axs
img = ax1.imshow(data_sample, cmap=cmap,
interpolation='none', origin='lower')
ax1.set_xlabel(r'$x_1$')
ax1.set_ylabel(r'$x_2$')
ax1.set_title('MODIS Band 06', fontsize=10)
plt.colorbar(img, ax=ax1, shrink=0.35)
img = ax2.imshow(Y_new.reshape(22,22).T, interpolation='nearest',
origin='lower', cmap=cm.jet, vmin=0.0, vmax=y_max)
ax2.set_xlabel(r'$x_1$')
ax2.set_ylabel(r'$x_2$')
ax2.set_title('MODIS Band 06 (Restored)', fontsize=10)
plt.colorbar(img, ax=ax2, shrink=0.35)
plt.title('MODIS Band 06 (Restored)', fontsize=10)
plt.show()(22, 22)
(484, 2)
X1_new, X2_new = np.meshgrid(np.arange(0, 10, 0.25), np.arange(0, 10, 0.25))
X1_new= (1.0*X1_new-x1_min) / (x1_max-x1_min) # data scaling
X2_new= (1.0*X2_new-x2_min) / (x2_max-x2_min) # data scaling
print(X1_new.shape)
X_new = np.stack((X1_new.ravel(),X2_new.ravel()), axis=-1)
print(X_new.shape)
Y_new = model.predict(X_new)
fig, axs = plt.subplots(1,2,gridspec_kw={'hspace': 0.3},figsize=(14,14))
(ax1, ax2) = axs
img = ax1.imshow(data_sample, cmap=cmap,
interpolation='none', origin='lower')
ax1.set_xlabel(r'$x_1$')
ax1.set_ylabel(r'$x_2$')
ax1.set_title('MODIS Band 06', fontsize=10)
plt.colorbar(img, ax=ax1, shrink=0.35)
img = ax2.imshow(Y_new.reshape(40,40).T, interpolation='nearest',
origin='lower', cmap=cm.jet, vmin=0.0, vmax=y_max)
ax2.set_xlabel(r'$x_1$')
ax2.set_ylabel(r'$x_2$')
ax2.set_title('MODIS Band 06 (Restored)', fontsize=10)
plt.colorbar(img, ax=ax2, shrink=0.35)
plt.title('MODIS Band 06 (Restored)', fontsize=10)
plt.show()(40, 40)
(1600, 2)
%%time
#X_new = np.stack((np.where(data_sample==0.0)[0],np.where(data_sample==0.0)[1]), axis=-1)
X1_new_unscaled = np.where(data_sample==0.0)[0]
X2_new_unscaled = np.where(data_sample==0.0)[1]
X1_new = (1.0*X1_new_unscaled-x1_min) / (x1_max-x1_min) # data scaling
X2_new = (1.0*X2_new_unscaled-x2_min) / (x2_max-x2_min) # data scaling
X1_new_dim = X1_new.shape
X_new = np.stack((X1_new.ravel(),X2_new.ravel()), axis=-1)
print(X_new.shape)
Y_new = model.predict(X_new)
print(Y_new.shape)
data_band_06[X1_new_unscaled+i_start,X2_new_unscaled+j_start] = Y_new
fig, axs = plt.subplots(1,2,gridspec_kw={'hspace': 0.3},figsize=(14,14))
(ax1, ax2) = axs
img = ax1.imshow(data_sample, cmap=cmap,
interpolation='none', origin='lower')
ax1.set_xlabel(r'$x_1$')
ax1.set_ylabel(r'$x_2$')
ax1.set_title('MODIS Band 06', fontsize=10)
plt.colorbar(img, ax=ax1, shrink=0.35)
img = ax2.imshow(data_band_06[i_start:i_start+12,j_start:j_start+12], cmap=cmap,
interpolation='none', origin='lower',vmin=0.0)
ax2.set_xlabel(r'$x_1$')
ax2.set_ylabel(r'$x_2$')
ax2.set_title('MODIS Band 06 (Restored)', fontsize=10)
plt.colorbar(img, ax=ax2, shrink=0.35)
plt.title('MODIS Band 06 (Restored)', fontsize=10)
plt.show()(48, 2)
(48,)
CPU times: user 322 ms, sys: 6.04 ms, total: 328 ms
Wall time: 332 ms
%%time
MODIS_band = 6
data_selected_id = modis_band_dic[str(MODIS_band)][0]
band_idx = modis_band_dic[str(MODIS_band)][1]
data = EV_500_Aggr1km_RefSB.get()
data_band_06 = data[band_idx,:,:]
data_selected_attributes = data_selected_id.attributes()
_FillValue = data_selected_attributes['_FillValue']
_FillValue = 65528 # warning wrong _FillValue stored in attributes
reflectance_scales = data_selected_attributes['reflectance_scales']
data_band_06[ data_band_06 == _FillValue ] = 0.0
data_band_06 = data_band_06 * reflectance_scales[band_idx]
data_shape = data_band_06.shape
i_start = 0
j_start = 0
for i_start in np.arange(0,data_shape[0],10):
if i_start > data_shape[0] - 10: i_start = data_shape[0] - 10
print(i_start)
for j_start in np.arange(0,data_shape[1],12):
if j_start > data_shape[1] - 12: j_start = data_shape[1] - 12
#print(i_start,j_start)
data_sample = data_band_06[i_start:i_start+12,j_start:j_start+12]
X = np.stack((np.where(data_sample!=0.0)[0],np.where(data_sample!=0.0)[1]), axis=-1)
Y = data_sample[np.where(data_sample!=0.0)[0],np.where(data_sample!=0.0)[1]]
x1_min = np.min(X[:,0])
x1_max = np.max(X[:,0])
X = X.astype('float64')
X[:,0] = (1.0*X[:,0]-x1_min) / (x1_max-x1_min)
x2_min = np.min(X[:,1])
x2_max = np.max(X[:,1])
X[:,1] = (1.0*X[:,1]-x2_min) / (x2_max-x2_min)
X_dim1 = X.shape[0]
X1 = X[:,0]
X2 = X[:,1]
X = np.stack((X1,X2), axis=-1)
#print(X.shape)
#print(Y.shape)
model = gp.fit(X,Y)
X1_new_unscaled = np.where(data_sample==0.0)[0]
X2_new_unscaled = np.where(data_sample==0.0)[1]
#print(X1_new_unscaled)
X1_new = (1.0*X1_new_unscaled-x1_min) / (x1_max-x1_min) # data scaling
X2_new = (1.0*X2_new_unscaled-x2_min) / (x2_max-x2_min) # data scaling
X_new = np.stack((X1_new,X2_new), axis=-1)
Y_new = model.predict(X_new)
data_band_06[X1_new_unscaled+i_start,X2_new_unscaled+j_start] = Y_new0
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CPU times: user 27min 23s, sys: 13.5 s, total: 27min 36s
Wall time: 14min 22s
data_band_06[data_band_06<0.0] = 0.0
figure(num=None, figsize=(12, 10), dpi=80, facecolor='w', edgecolor='k')
cmap = [(0.0,0.0,0.0)] + [(cm.jet(i)) for i in range(1,256)]
cmap = mpl.colors.ListedColormap(cmap)
img = plt.imshow(np.fliplr(data_band_06), cmap=cmap,
interpolation='none', origin='lower', vmin=data_band_6_vmin, vmax=data_band_6_vmax)
plt.xticks([0,250,500,750,1000,1250],
['0','250','500', '750', '1000','1250'], rotation=0, fontsize=8 )
plt.yticks([0,250,500,750,1000,1250,1500,1750,2000],
['0','250','500', '750', '1000','1250','1500','1750','2000'],
rotation=0, fontsize=8 )
plt.title('AQUA MODIS L1 Band07 \n 2007-08-07; 20h10', fontsize=10)
cbar = plt.colorbar()
cbar.ax.tick_params(labelsize=8)
plt.title('AQUA MODIS C6 L1: Band 06', fontsize=10)
plt.show()
plt.close()