def add_noise(image, epsilon, k): # 添加拉普拉斯噪声 # 进行离散傅里叶变换 f = np.fft.fft2(image) # 将零频率分量移到频谱中心 fshift = np.fft.fftshift(f) rows, cols = image.shape b = laplas(fshift, epsilon, k) # print(b) p = 0.5 noise = np.random.laplace(scale=b, size=(rows, cols)) + np.mean(f) * p # noise = np.random.laplace(0, 1/b, (rows, cols)) image_noise = fshift + noise f_ishift = np.fft.ifftshift(image_noise) # 进行逆离散傅里叶变换 image_back = np.fft.ifft2(f_ishift) image_back = np.real(image_back) return image_back def laplas(FIM, epsilon, k): FIM_k = FIM[:k, :k] # 给定隐私预算 epsilon # 计算给定隐私预算时的拉普拉斯机制的参数的最小值 # 计算每个系数的灵敏度 sensitivity = np.abs(FIM_k) / np.sqrt(epsilon) sensitivity2 = np.abs(FIM) / np.sqrt(epsilon) scale = sensitivity2 / epsilon # 计算拉普拉斯机制的参数 # 计算前 k×k 个 DFT 系数的最大值和最小值之差 delta_f = np.max(np.sqrt(np.real(FIM[:k, :k]) ** 2 + np.imag(FIM[:k, :k]) ** 2)) - np.min( np.sqrt(np.real(FIM[:k, :k]) ** 2 + np.imag(FIM[:k, :k]) ** 2)) # 计算拉普拉斯噪声的尺度参数 c = delta_f / epsilon d = delta_f * math.sqrt(2 * math.log(1.25 / 0.1)) / epsilon # a = np.min(sensitivity) / (epsilon * k**2) return d def add_noisy_image(): # 读取人脸图像 image = cv2.imread("image.jpg", cv2.IMREAD_GRAYSCALE) image = cv2.resize(image, (128, 128), interpolation=cv2.INTER_LINEAR) # 进行离散傅里叶变换 epsilon = 0.3 k = 50 image_back = add_noise(image, epsilon, k) im = cv2.resize(image_back, (47, 62), interpolation=cv2.INTER_LINEAR) # 将图像转换为整型并保存 image_back = np.uint8(im) cv2.imwrite("face_privacy.jpg", image_back) return image_back

将三个函数合并成一个函数如下所示：

import numpy as np
import cv2
import math

def add_noisy_image(image_path, epsilon, k):
    def laplas(FIM, epsilon, k):
        FIM_k = FIM[:k, :k]
        sensitivity = np.abs(FIM_k) / np.sqrt(epsilon)
        sensitivity2 = np.abs(FIM) / np.sqrt(epsilon)
        scale = sensitivity2 / epsilon
        delta_f = np.max(np.sqrt(np.real(FIM[:k, :k]) ** 2 + np.imag(FIM[:k, :k]) ** 2)) - np.min(
            np.sqrt(np.real(FIM[:k, :k]) ** 2 + np.imag(FIM[:k, :k]) ** 2))
        c = delta_f / epsilon
        d = delta_f * math.sqrt(2 * math.log(1.25 / 0.1)) / epsilon
        return d
    
    def add_noise(image, epsilon, k):
        f = np.fft.fft2(image)
        fshift = np.fft.fftshift(f)
        rows, cols = image.shape
        b = laplas(fshift, epsilon, k)
        p = 0.5
        noise = np.random.laplace(scale=b, size=(rows, cols)) + np.mean(f) * p
        image_noise = fshift + noise
        f_ishift = np.fft.ifftshift(image_noise)
        image_back = np.fft.ifft2(f_ishift)
        image_back = np.real(image_back)
        return image_back
    
    image = cv2.imread(image_path, cv2.IMREAD_GRAYSCALE)
    image = cv2.resize(image, (128, 128), interpolation=cv2.INTER_LINEAR)
    image_back = add_noise(image, epsilon, k)
    im = cv2.resize(image_back, (47, 62), interpolation=cv2.INTER_LINEAR)
    image_back = np.uint8(im)
    cv2.imwrite("face_privacy.jpg", image_back)
    return image_back

使用方式：

image_back = add_noisy_image("image.jpg", 0.3, 50)

其中，第一个参数是原始图像的路径，第二个参数是隐私预算 epsilon，第三个参数是前 k 个 DFT 系数的个数。该函数返回添加拉普拉斯噪声后的图像。