图像处理盲卷积算法问题
import numpy as np
import cv2
from scipy.signal import convolve2d
import matplotlib.pyplot as plt
def gaussian_psf(size, sigma):
"""
创建一个高斯点扩散函数（PSF）
参数:
size (int): PSF的大小（必须是奇数）
sigma (float): 高斯分布的标准差
返回:
numpy.ndarray: 高斯PSF
"""
center = size // 2
x = np.arange(0, size) - center
y = np.arange(0, size) - center
x, y = np.meshgrid(x, y)
psf = np.exp(-(x**2 + y**2) / (2 * sigma**2))
psf /= np.sum(psf) # 归一化
return psf
def blind_deconvolution(image, psf_size, iterations=50, regularization=1e-4):
"""
使用盲反卷积算法复原图像
参数:
image (numpy.ndarray): 输入的模糊图像
psf_size (int): PSF的大小
iterations (int): 迭代次数
regularization (float): 正则化参数
返回:
(numpy.ndarray, numpy.ndarray): 复原的图像和估计的PSF
"""
# 初始化原始图像和PSF
estimated_image = np.copy(image)
estimated_psf = np.ones((psf_size, psf_size)) / (psf_size ** 2)
# 迭代过程
for i in range(iterations):
# 固定图像，更新PSF
blurred_estimation = convolve2d(estimated_image, estimated_psf, mode='same')
error = image - blurred_estimation
psf_update = convolve2d(estimated_image, error, mode='same')
estimated_psf += psf_update
estimated_psf = np.clip(estimated_psf, 0, None)
estimated_psf /= np.sum(estimated_psf) # 归一化
# 固定PSF，更新图像
error = image - blurred_estimation
image_update = convolve2d(error, estimated_psf[::-1, ::-1], mode='same')
estimated_image += image_update
estimated_image = np.clip(estimated_image, 0, 1)
# 正则化
estimated_image -= regularization * estimated_image
return estimated_image, estimated_psf
# 示例图像
image = cv2.imread('example_blurred.jpg', cv2.IMREAD_GRAYSCALE) / 255.0 # 归一化
psf_size = 15
# 进行盲反卷积
restored_image, estimated_psf = blind_deconvolution(image, psf_size, iterations=50)
# 显示结果
plt.figure(figsize=(12, 6))
plt.subplot(1, 3, 1)
plt.title('模糊图像')
plt.imshow(image, cmap='gray')
plt.axis('off')
plt.subplot(1, 3, 2)
plt.title('复原图像')
plt.imshow(restored_image, cmap='gray')
plt.axis('off')
plt.subplot(1, 3, 3)
plt.title('估计的PSF')
plt.imshow(estimated_psf, cmap='gray')
plt.axis('off')
plt.show()
我不太明白算法的第47行psf_update = convolve2d(estimated_image, error, mode='valid')，为什么估计图像和error（模糊图像和估计图像的差）的卷积可以代表优化后的PSF呢？这里的PSF是指物理意义上的PSF吗？PSF不应该是图像与模糊图像的反卷积吗？
