python复现：PCA-based spatially adaptive denoising of CFA images for single-sensor digital cameras
PCA-based spatially adaptive denoising of CFA images for single-sensor digital cameras
是2009年一篇基于PCA的图像降噪方法，应用在raw图上，下面的代码和
官方 matlab的结果是一致的（因为是逐句翻译的、、、），但是效率很低，优化空间很大，比如取patch的时候重复计算了很多次。
import cv2
import matplotlib.pyplot as plt
import numpy as np
import scipy
import scipy.signal
# 各通道噪声方差
from colour_demosaicing import demosaicing_CFA_Bayer_bilinear
%matplotlib inline
file = r'kodak_fence.tif'
im = cv2.imread(file)
im = im[..., :3]
im = im[..., ::-1]
print(im[100:110,100:110,-1])
[[124 126 128 123 121 121 114 117 122 115]
[127 128 127 123 121 119 119 120 117 117]
[127 127 124 124 121 121 120 118 118 112]
[124 123 119 123 120 121 118 116 117 115]
[120 115 116 119 121 119 116 114 113 111]
[119 120 120 122 120 118 111 113 114 113]
[123 120 121 122 116 115 109 111 118 114]
[125 123 120 119 117 113 114 113 116 114]
[117 119 121 119 120 114 115 113 117 116]
[118 119 120 121 119 118 114 113 118 116]]
im2 = cv2.imread('noise.png')[...,::-1]
im_noise=im2.copy()
print(im2[100:110,100:110,-1])
[[129 127 104 134 132 116 108 108 107 119]
[146 130 134 122 127 128 116 117 123 119]
[118 139 125 128 120 113 125 120 138 121]
[128 133 125 122 116 116 109 114 101 103]
[110 117 115 116 125 121 124 109 118 117]
[118 101 130 126 105 118 122 118 108 104]
[115 116 129 98 119 87 107 106 115 117]
[124 123 114 109 129 111 120 132 114 97]
[121 112 134 102 99 130 124 130 130 102]
[121 112 112 127 106 125 118 98 135 135]]
im.shape
im_clean=im.copy()
bb=1
psnr_noise = 10 * np.log10(255 ** 2 / np.mean((im[bb:-bb,bb:-bb] - im_noise[bb:-bb,bb:-bb]) ** 2, axis=(0,1)))
print(psnr_noise)
[ 29.57315911 29.71359964 30.30441583]
def black_sub(filename, height=800, width=800):
raw_image = np.fromfile(filename, dtype=np.uint16)
print(len(raw_image))
raw_image = raw_image.reshape([height, width])
# black level
black_level = 16
white_level = 1023
normalized_image = raw_image.astype(np.float32) - black_level
# if some values were smaller than black level
normalized_image[normalized_image < 0] = 0
normalized_image = normalized_image / (white_level - black_level)
print(normalized_image.min(), normalized_image.max())
normalized_image = normalized_image * 255
normalized_image2 = np.clip(normalized_image, 0, 255).astype(np.uint8)
return normalized_image2
# filename = r'D:\dataset\dang_yingxiangzhiliangceshi\raw\cap_frame_3641.raw'
# tI = black_sub(filename, height=800, width=800)
# mI=cv2.blur(tI, (30,30))
n, m, ch = im.shape
mI=np.zeros([n, m])
tI=np.zeros([n, m])
# noise grgb
mI[0:n,0:m] = im2[:,:,1]
mI[0:n:2,1:m:2] = im2[0:n:2,1:m:2, 0]
mI[1:n:2,0:m:2] = im2[1:n:2,0:m:2, 2]
tI[0:n,0:m] = im[:,:,1]
tI[0:n:2,1:m:2] = im[0:n:2,1:m:2, 0]
tI[1:n:2,0:m:2] = im[1:n:2,0:m:2, 2]
psnr = 10 * np.log10(255 ** 2 / np.mean(((mI - tI) ** 2)))
print(psnr)
26.7146060444
2. decomposition
def get_gauss(sigma, len):
x = np.arange(-len,len+1)
y = np.arange(-len,len+1)
xx, yy = np.meshgrid(x,y)
z = np.exp(-(xx*xx+yy*yy)/2/(sigma*sigma)) / (2 * np.pi * sigma*sigma)
return z
w = 10
f = get_gauss(3, w)
print(f[:10,:10])
[[ 2.64291611e-07 7.59460747e-07 1.95286554e-06 4.49349653e-06
9.25212596e-06 1.70468335e-05 2.81054770e-05 4.14651518e-05
5.47419944e-05 6.46700251e-05]
[ 7.59460747e-07 2.18236448e-06 5.61169806e-06 1.29123819e-05
2.65866421e-05 4.89852888e-05 8.07630877e-05 1.19153063e-04
1.57305015e-04 1.85833918e-04]
[ 1.95286554e-06 5.61169806e-06 1.44298331e-05 3.32026980e-05
6.83644778e-05 1.25960009e-04 2.07672947e-04 3.06388333e-04
4.04491667e-04 4.77850443e-04]
[ 4.49349653e-06 1.29123819e-05 3.32026980e-05 7.63986075e-05
1.57305015e-04 2.89830945e-04 4.77850443e-04 7.04992167e-04
9.30725575e-04 1.09952235e-03]
[ 9.25212596e-06 2.65866421e-05 6.83644778e-05 1.57305015e-04
3.23891607e-04 5.96762985e-04 9.83895828e-04 1.45158148e-03
1.91636740e-03 2.26392058e-03]
[ 1.70468335e-05 4.89852888e-05 1.25960009e-04 2.89830945e-04
5.96762985e-04 1.09952235e-03 1.81280588e-03 2.67450615e-03
3.53086373e-03 4.17122264e-03]
[ 2.81054770e-05 8.07630877e-05 2.07672947e-04 4.77850443e-04
9.83895828e-04 1.81280588e-03 2.98881162e-03 4.40951518e-03
5.82141014e-03 6.87718348e-03]
[ 4.14651518e-05 1.19153063e-04 3.06388333e-04 7.04992167e-04
1.45158148e-03 2.67450615e-03 4.40951518e-03 6.50553684e-03
8.58856282e-03 1.01461881e-02]
[ 5.47419944e-05 1.57305015e-04 4.04491667e-04 9.30725575e-04
1.91636740e-03 3.53086373e-03 5.82141014e-03 8.58856282e-03
1.13385587e-02 1.33949244e-02]
[ 6.46700251e-05 1.85833918e-04 4.77850443e-04 1.09952235e-03
2.26392058e-03 4.17122264e-03 6.87718348e-03 1.01461881e-02
1.33949244e-02 1.58242334e-02]]
w = 10
fmI = cv2.GaussianBlur(mI,(2*w+1,2*w+1),3)
print(fmI[100:110,100:110])
[[ 121.93832694 120.80475462 119.34427302 117.70715601 116.06921131
114.58486129 113.35933285 112.43633939 111.81440447 111.46699312]
[ 121.52631498 120.47457756 119.06497391 117.42939834 115.73886432
114.16113306 112.82476593 111.80118861 111.11348537 110.74756437]
[ 120.87684224 119.92483971 118.59186934 116.98478683 115.2656273
113.61417197 112.18455321 111.07980339 110.35132867 109.99891044]
[ 120.06088905 119.22871398 118.0002417 116.45487617 114.74288424
113.05241178 111.56081857 110.40168771 109.65525121 109.33631585]
[ 119.17015693 118.48072734 117.38722186 115.94233693 114.28226138
112.59720486 111.08110038 109.89275087 109.13933657 108.8525714 ]
[ 118.2985367 117.77233662 116.84362262 115.54084722 113.98304615
112.35314865 110.851063 109.65205922 108.88682568 108.60707037]
[ 117.48539156 117.12919512 116.38418959 115.25858743 113.85106686
112.32643485 110.8775763 109.68491146 108.89737908 108.58942516]
[ 116.73276808 116.52954776 115.9655374 115.0346916 113.81328909
112.43786173 111.08081869 109.91515716 109.10092106 108.73597896]
[ 115.98315995 115.88488868 115.46792689 114.72136547 113.70067514
112.5076856 111.28264307 110.17813221 109.35522429 108.93094655]
[ 115.16712536 115.10319425 114.77481649 114.17840339 113.35413192
112.36733278 111.31740348 110.32423396 109.53731509 109.08319369]]
smI = mI - fmI
print(smI[100:110,100:110])
[[ 29.06167306 12.19524538 -14.34427302 -16.70715601 -10.06921131
17.41513871 -5.35933285 17.56366061 -5.81440447 -5.46699312]
[ 24.47368502 27.52542244 14.93502609 -13.42939834 11.26113568
-14.16113306 3.17523407 0.19881139 11.88651463 -1.74756437]
[ 6.12315776 -2.92483971 21.40813066 13.01521317 9.7343727
7.38582803 -11.18455321 -13.07980339 -13.35132867 14.00108956]
[ 7.93911095 -17.22871398 6.9997583 -5.45487617 1.25711576
-10.05241178 -2.56081857 -4.40168771 -8.65525121 -14.33631585]
[-14.17015693 -1.48072734 2.61277814 -15.94233693 -4.28226138
-3.59720486 9.91889962 2.10724913 -10.13933657 21.1474286 ]
[ -0.2985367 12.22766338 13.15637738 29.45915278 -8.98304615
-7.35314865 11.148937 -20.65205922 -0.88682568 17.39292963]
[ 4.51460844 0.87080488 -0.38418959 1.74141257 -25.85106686
-25.32643485 -21.8775763 -37.68491146 4.10262092 -36.58942516]
[ 7.26723192 -3.52954776 -1.9655374 6.9653084 15.18671091
-1.43786173 8.91918131 -13.91515716 4.89907894 9.26402104]
[-11.98315995 14.11511132 9.53207311 23.27863453 -7.70067514
17.4923144 10.71735693 8.82186779 5.64477571 -3.93094655]
[ 5.83287464 -5.10319425 -2.77481649 14.82159661 -7.35413192
29.63266722 6.68259652 -22.32423396 25.46268491 -3.08319369]]
plt.figure()
plt.subplot(131)
plt.imshow(mI, cmap='gray')
plt.title("noise")
plt.subplot(132)
plt.imshow(fmI, cmap='gray')
plt.title("filter")
plt.subplot(133)
plt.imshow(np.abs(smI), cmap='gray')
plt.title("detail")
plt.show()
denoiseing
dI=smI.copy();
s=6;#default variable block size
k=34;# training block size,(k-s)/2 should be an even integer%%%%%%%%%
k2=k//2;
#Bayer Pattern: G R; B G
v=12;
vr=13/12;
vb=10/12;
vg=1;
# noise pattern, GRBG的6*6，每个通道的噪声方差乘上一个 1.21倍
c=1.1
D = np.zeros([s,s], dtype=np.float32)
D[:,:] = c*vg*v
D[0:s:2, 1:s:2] = c*vr*v # r
D[1:s:2, 0:s:2] = c*vb*v # b
D=D**2
print(D)
[[ 174.23999 204.49 174.23999 204.49 174.23999 204.49 ]
[ 121. 174.23999 121. 174.23999 121. 174.23999]
[ 174.23999 204.49 174.23999 204.49 174.23999 204.49 ]
[ 121. 174.23999 121. 174.23999 121. 174.23999]
[ 174.23999 204.49 174.23999 204.49 174.23999 204.49 ]
[ 121. 174.23999 121. 174.23999 121. 174.23999]]
def get_pca(X, D):
"""
X : 36 * 100 , fetures * n_samples
D : 36, 每个feature的噪声方差
"""
D = D.reshape(-1)
h, n = X.shape
mx = np.mean(X, 1).reshape(-1, 1)
X = X - mx
convX = X @ X.T / (n-1)
DD = np.diag( D)
convX = convX - DD
convX[convX < 0] = 0.0001
[eig_val, eig_vec] = np.linalg.eigh(convX) # convX * eig_vec = eig_val.reshape(1, -1) * eig_vec
# eig_val是特征值， eig_vec是对应的特征向量，col形式的。
#print('eig_val : ', eig_val,eig_vec, eig_val.shape, eig_vec.shape)
# print(np.sum(convX @ eig_vec - eig_val.reshape(1, -1) * eig_vec <0.01))
# print(eig_vec @ X == X @eig_vec.T)
ind = np.argsort(eig_val)
ind = ind[::-1]
eig_vec = eig_vec[:,ind].T
eig_val = eig_val[ind]
Y = eig_vec @ X
#print('ind:\n',ind, eig_val,eig_vec ,Y)
return Y, eig_vec, eig_val, mx
tttt=0
def pca_cfa(block, D, s):
global tttt
"""
block : 34*34 block, k = 34
D:
s:6 or 8
"""
h, w = block.shape
H = (h-s) // 2 + 1 # 15
W = (w-s) // 2 + 1
L = H*W
X = np.zeros([s*s, L]) # 36*225 : 34*34的block, 6*6的patch, step为2, 一共15*15=225个patch
DN = np.zeros([1, s*s])
k = 0
for i in np.arange(0, s):
for j in np.arange(0, s):
X[k, :] = block[i:(h-s+i+1):2, j:(w-s+j+1):2].reshape([1, L])
DN[0, k] = D[i, j]
k = k + 1
# X是 6*6 * 225
# DN 是 6*6个值,每个值对应的该像素的标准差
# 中间的一个值
q = L // 2 # 112
Xc = X[:, q].reshape(-1, 1) # 36
XC = np.tile(Xc, [1, L]) # 36 * 225
# print(DN, k, X.shape, XC.shape)
E = np.abs(X-XC)
mE = np.mean(E, axis=0) # 每列的均值，相当于求每个patch与中心patch的均值
ind = np.argsort(mE)
num = 100
X = X[:, ind[:num]]
# print('X:',X[:10,:10], DN)
# 到这里选出了100个相似的patch, 从225个里面
Y, P, V, mx = get_pca(X, DN)
#print(Y[:10,:10])
Y1 = np.zeros(Y.shape)
# inverse transform\
# （设置10个为0）
for i in np.arange(0,s*s-8):
y = Y[i,:]
p = P[i,:]
p = p*p
nv = np.sum(p*DN) # p*DN 噪声方差经过 pca转置, P是单位矩阵，类似求均值了，所以sum
if 0==tttt:
print(p.shape, DN.shape, (p*DN).shape,nv.shape)
py = np.mean(y*y) + 0.01
t = max(0, py-nv)
if 0==tttt:
print(py.shape,py, t)
tttt = 1
c = t / py
# print(c) #基本上很小的数，0-0.3之间
Y1[i, :] = 1* Y[i, :]
B = P.T @ Y1 + mx
B = B[:, 0]
B = np.reshape(B, [s, s])
#B = B.T
return B
step = 2
print(n-k,m-k)
for i in np.arange(0, n - k, step):
for j in np.arange(0, m - k, step):
#if i== 50 and j==50:
Block = smI[i:i+k, j:j+k].copy()
db = pca_cfa(Block, D, s)
dI[i+k2-1:i+k2+1, j+k2-1:j+k2+1] = db[2:4, 2:4]
#print(Block[:10,:10])
#print(db)
#print(x[:10.:10])
#print(y[:10.:10])
734 478
(36,) (1, 36) (1, 36) ()
() 167.639940721 0
i
a = n-k
b=i+k-1
c=i+k2-1
db
t = dI[99:110,99:110]
print(i,a,b,c,db,t)
732 734 765 748 [[-25.80532161 11.18396885 21.5562875 15.1691311 15.48400112
29.98028105]
[-26.3432829 21.56501168 -43.50587703 4.79103188 -4.43557792
-7.3855937 ]
[ 17.00578207 57.53942483 28.85620708 29.88176839 15.84105093
13.18102019]
[-25.43627059 22.4839088 16.93029056 14.54577497 -20.64510537
-5.64869904]
[ 0.15234094 -5.87031587 9.84325354 21.98484204 -6.78422562
30.82852626]
[ -2.9422656 -5.54282893 -14.33997315 -2.43183229 -39.36737168
14.82723805]] [[ 2.39425621 -7.50795736 10.1263103 -1.00761166 -14.14296723
4.27147071 9.48992787 -17.40794547 8.14357609 -0.59332369
1.87093838]
[ -5.92387084 31.39388273 14.87143502 -12.58273904 -11.87516387
-2.60759948 8.9776016 -4.55399497 11.75790601 -5.73767096
-6.51739886]
[ 6.10456174 22.48420321 21.68501677 15.79794982 -15.88482472
11.86451625 -9.66591387 3.03897717 2.02633336 12.9747562
1.73978256]
[ -7.54473426 10.60003328 4.92408636 18.46661195 8.99161538
6.65299865 5.16234318 -15.96123275 -7.76966259 -13.20031974
2.27381012]
[-16.26497218 2.37717583 -22.06340946 0.59562629 -5.18313707
4.26679605 -17.48835341 2.85138918 -4.56904362 -9.51967616
-15.8008651 ]
[ 0.70260208 1.76680755 2.85435522 -2.78418131 -7.97310004
-2.99846244 -3.51906016 9.60667614 3.02749668 3.41880403
22.40951242]
[ 2.06235778 -0.97282281 8.61112305 18.59272929 28.4612208
-7.33356166 -5.07142281 11.37647051 -22.11546397 -7.40368596
3.12237772]
[ -6.29088137 2.36391139 -7.30272654 0.05294837 4.31963347
-22.88124845 -27.44595565 -21.358552 -36.03650032 12.40441245
-30.47078166]
[ 6.96705517 4.26531585 3.541887 1.30659318 3.03703037
15.66634705 -2.43022019 6.90065626 -13.58299795 5.86283103
10.24549084]
[ 8.18625562 -4.30581833 7.32269359 9.17154543 21.27121419
-2.85394241 19.95621912 7.63124297 3.05477624 4.34158611
-9.33247657]
[ -4.23236535 10.92552271 -9.23752909 -0.75844497 16.45297477
-4.0952441 29.42888478 7.88977393 -17.74546651 23.72911602
-0.42439872]]
ddI = dI.copy()
ddI = ddI + fmI
plt.figure(figsize=(20,15))
plt.subplot(131)
plt.imshow(mI,cmap='gray')
plt.subplot(132)
plt.imshow(tI,cmap='gray')
plt.subplot(133)
plt.imshow(ddI,cmap='gray')
plt.show()
bb = 20
psnr = 10 * np.log10(255 ** 2 / np.mean(((ddI[bb:-bb,bb:-bb] - tI[bb:-bb,bb:-bb]) ** 2)))
print(psnr)
psnr = 10 * np.log10(255 ** 2 / np.mean(((mI[bb:-bb,bb:-bb] - tI[bb:-bb,bb:-bb]) ** 2)))
print(psnr)
27.4094591896
26.7145989939
print(ddI.min(),ddI.max(),ddI.mean())
#
im_noise_bayer2rgb = demosaicing_CFA_Bayer_bilinear(mI, "GRBG")
im_noise_bayer2rgb2 = np.clip(im_noise_bayer2rgb,0,255).astype(np.uint8)
rgb = demosaicing_CFA_Bayer_bilinear(ddI, "GRBG")
rgb2 = np.clip(rgb,0,255).astype(np.uint8)
print(rgb2.max(),rgb2.min())
plt.figure(figsize=(20,15))
plt.subplot(131)
plt.imshow(im_noise_bayer2rgb2)
plt.subplot(132)
plt.imshow(im2)
plt.subplot(133)
plt.imshow(rgb2)
plt.show()
bb = 1
psnr = 10 * np.log10(255 ** 2 / np.mean(((im[bb:-bb,bb:-bb] - rgb2[bb:-bb,bb:-bb]) ** 2)))
print(psnr)
psnr_noise = 10 * np.log10(255 ** 2 / np.mean(((im[bb:-bb,bb:-bb] - im2[bb:-bb,bb:-bb]) ** 2)))
print(psnr_noise)
bb = 1
psnr = 10 * np.log10(255 ** 2 / np.mean(((im[bb:-bb,bb:-bb] - rgb2[bb:-bb,bb:-bb]) ** 2), axis=(0,1)))
print(psnr)
psnr_noise = 10 * np.log10(255 ** 2 / np.mean(((im[bb:-bb,bb:-bb] - im_noise[bb:-bb,bb:-bb]) ** 2), axis=(0,1)))
print(psnr_noise)
-13.911260205 273.354212873 112.224014452
255 0
30.3929142051
29.8523440731
[ 30.19659709 30.45414954 30.53523719]
[ 29.57315911 29.71359964 30.30441583]
bayer_diff_noise = np.abs(im_noise_bayer2rgb-im2)
bayer_diff_noise2 = np.clip(bayer_diff_noise,0,255).astype(np.uint8)+40
plt.figure(figsize=(20,15))
plt.imshow(bayer_diff_noise2)
plt.show()
bayer_diff_denoise = np.abs(im_noise_bayer2rgb-rgb2)
bayer_diff_denoise2 = np.clip(bayer_diff_noise,0,255).astype(np.uint8)+40
plt.figure(figsize=(20,15))
plt.imshow(bayer_diff_denoise2)
plt.show()
q = np.random.randn(18,6)
conv = q.T@q
[eig_val, eig_vec] = np.linalg.eigh(conv)
# convX * eig_vec = eig_val.reshape(1, -1) * eig_vec
# eig_val是特征值， eig_vec是对应的特征向量，col形式的。
print('eig_val : ', eig_val,eig_vec, eig_val.shape, eig_vec.shape)
print(np.sum(conv @ eig_vec - eig_val.reshape(1, -1) * eig_vec <0.01))
print(eig_vec @ conv - (conv @eig_vec.T).T)
print(q @ eig_vec.T , (eig_vec.T @ q.T).T)
print(eig_vec @ conv)
eig_val : [ 3.00685873 6.20435828 11.58297164 13.42519523 17.63008572
43.47319024] [[ 0.08787425 -0.32322719 0.68824544 -0.17445992 0.61739305 -0.05010059]
[ 0.20655283 -0.32032156 -0.31217256 -0.10821841 0.05036977 -0.86199187]
[-0.39190487 -0.22314618 -0.36999561 -0.7642356 0.15395569 0.22794997]
[-0.02485003 0.34875418 -0.446504 0.2923101 0.76925841 0.03440172]
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