标题
爱尔兰（伽马）噪声
爱尔兰噪声的PDF是
P
(
z
)
=
{
a
b
z
b
−
1
(
b
−
1
)
!
e
−
a
z
,
z
≥
0
0
,
z
<
0
(5.7)
P(z) = \begin{cases} \frac{a^bz^{b-1}}{(b-1)!}e^{-az}, & z\geq 0 \\ 0, & z < 0 \end{cases} \tag{5.7}
P
(
z
)
=
{
(
b
−
1
)
!
a
b
z
b
−
1
e
−
a
z
,
0
,
z
≥
0
z
<
0
(
5
.
7
)
a
>
b
a > b
a
>
b
,
b
b
b
是一个正整数，”!”是阶乘
均值和方差为
z
ˉ
=
b
a
(5.8)
\bar{z} = \frac{b}{a} \tag{5.8}
z
ˉ
=
a
b
(
5
.
8
)
σ
2
=
b
a
2
(5.9)
\sigma^2 = \frac{b}{a^2} \tag{5.9}
σ
2
=
a
2
b
(
5
.
9
)
仅当分母 为伽马函数
Γ
(
b
)
\Gamma(b)
Γ
(
b
)
时这称为
伽马密度
当
b
=
1
b=1
b
=
1
时，为指数噪声
def ireland_pdf(z, a=2, b=1):
"""
create ireland PDF, math $$P(z) = \begin{cases} \frac{a^bz^{b-1}}{(b-1)!}e^{-az}, & z\geq 0 \\ 0, & z < 0 \end{cases}$$
param: z: input grayscale value of iamge
param: a: float, a > b
param: b: uint,
"""
ireland = (a**b * z**(b-1) / np.math.factorial(b - 1)) * np.exp(- a *z)
ireland = np.where(z >= 0, ireland, 0)
return ireland
更正下面代码，如果之前已经复制的，也请更正
def add_gamma_noise(img, scale=1):
"""
add gamma noise for image
param: img: input image, dtype=uint8
param: mean: noise mean
param: sigma: noise sigma
return: image_out: image with gamma noise
"""
# image = np.array(img/255, dtype=float) # 这是有错误的，将得不到正确的结果，修改如下
image = np.array(img, dtype=float)
noise = np.random.gamma(shape=1, scale=scale, size=image.shape)
image_out = image + noise
image_out = np.uint8(normalize(image_out)*255)
return image_out
# 爱尔兰(伽马)噪声
a = 2.1
b = 2
z = np.linspace(0, 10, 200)
z_ = b / a
sigma = b / a**2
print(f"z_ -> {z_}, sigma -> {sigma}")
ireland = ireland_pdf(z, a=a, b=b)
plt.figure(figsize=(9, 6))
plt.plot(z, ireland)
plt.show()
z_ -> 0.9523809523809523, sigma -> 0.4535147392290249
# 伽马噪声
img_ori = cv2.imread("DIP_Figures/DIP3E_Original_Images_CH05/Fig0503 (original_pattern).tif", 0)
# img_ori = np.ones((512, 512)) * 128
img_gamma = add_gamma_noise(img_ori, scale=20)
plt.figure(figsize=(9, 6))
plt.subplot(121), plt.imshow(img_ori, 'gray', vmin=0, vmax=255), plt.xticks([]), plt.yticks([])
plt.subplot(122), plt.imshow(img_gamma, 'gray', vmin=0, vmax=255), plt.xticks([]), plt.yticks([])
plt.tight_layout()
plt.show()
hist, bins = np.histogram(img_gamma.flatten(), bins=255, range=[0, 255], density=True)
bar = plt.bar(bins[:-1], hist[:])
