基于短时傅里叶变换的音频数字水印

有关音频文件数字水印的参考材料相对较少，在短暂的尝试后，通过模仿图像文件dwt算法的嵌入方式，使用librosa库中短时傅里叶变换函数完成了水印嵌入及提取。过程简洁，代码量极少。美中不足的是由于音频文件数据类型为complex64而图像文件数据类型为uint8，嵌入过程中会不可避免的存在部分数据丢失，且该方法暂无理论支撑。

嵌入部分

import librosa
import matplotlib.pyplot as plt
import soundfile
import cv2
y, sr = librosa.load("C:\\Users\\split.wav")
waterImg = cv2.imread("C:\\Users\\logo.bmp", 0)

# stft 短时傅立叶变换
a = librosa.stft(y)
w = a.shape[0]
h = a.shape[1]


waterImg = cv2.resize(waterImg, (h, w))
print(type(a[0][2]))
key = 0.001 #嵌入强度
r_a = key * waterImg + a

# istft 逆短时傅立叶变换
b = librosa.istft(r_a)
soundfile.write("C:\\Users\\new.wav", b, sr)

频谱图对比（key=0.25时，原音频与嵌入后）

提取部分

import librosa
import numpy as np
from PIL import Image

y1, sr1 = librosa.load("C:\\Users\\split.wav")
y2, sr2 = librosa.load("C:\\Users\\new.wav")
a = librosa.stft(y1)
r_a = librosa.stft(y2)
key = 0.001
waterImg = (r_a-a)/key
waterImg = np.array(waterImg, dtype='uint8')


waterImg = Image.fromarray(waterImg)
waterImg = waterImg.resize((100, 100), Image.ANTIALIAS) 
waterImg = waterImg.convert("L")
waterImg.save('C:\\Users\\57882\\Desktop\\audio.bmp') 

提取图像处理

二值化

import cv2
from PIL import Image
import numpy as np

Img_path = 'C:\\Users\\audio.bmp'

Img = Image.open(Img_path)
Img = Img.convert('L')

threshold = 2 #我这里设的阈值为2
table = []
for i in range(256):
    if i < threshold:
        table.append(0)
    else:
        table.append(255)

waterImg = Img.point(table, '1')
waterImg.save('C:\\Users\\57882\\Desktop\\2valuelogo.bmp')

图像增强与反相

import cv2
import numpy as np
# 反相
def reverse(img):
    gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
    dst = 255 - gray
    return dst

image = cv2.imread("C:\\Users\\2valuelogo.bmp")

kernel = np.array([[0, -1, 0], [-1, 5, -1], [0, -1, 0]], np.float32)
dst = cv2.filter2D(image, -1, kernel=kernel)
dst = reverse(dst)
cv2.imwrite('C:\\Users\\newpic.bmp', dst)

结果示例：（水印图像100*100）

提取图像：

 

二值化（阈值=2）

 

 

图像增强，反相

 

 

水印原图

 

 

 2022.3.16更新

使用二值化图像，并通过在复数的虚部中嵌入信息，减少信息丢失。

嵌入部分

import librosa
import cv2
import soundfile
import numpy as np

y, sr = librosa.load('C:\\Users\\57882\\split.wav')
waterImg = cv2.imread('C:\\Users\\2value.bmp', 0)

stft = librosa.stft(y, n_fft=2048, hop_length=None, win_length=None, window='hann', center=True, pad_mode='reflect')

w = int(stft.shape[0])
h = int(stft.shape[1])

key1 = 0.025
waterImg = cv2.resize(waterImg, (h, w))
Img = np.array(waterImg, dtype='complex64')
for i in range(w):
    for j in range(h):
        Img[i][j] = complex(0, int(waterImg[i][j])*key1)

key2 = 0.02
stft_new = key2 * Img + stft
Y = librosa.istft(stft_new)
soundfile.write("C:\\Users\\new1.wav", Y, sr)

提取部分

import librosa
import numpy as np
from PIL import Image

Y, Sr = librosa.load('C:\\Users\\new1.wav')
y, sr = librosa.load('C:\\Users\\split.wav')
stft1 = librosa.stft(Y, n_fft=2048, hop_length=None, win_length=None, window='hann', center=True, pad_mode='reflect')
stft2 = librosa.stft(y, n_fft=2048, hop_length=None, win_length=None, window='hann', center=True, pad_mode='reflect')
w = stft1.shape[0]
h = stft1.shape[1]

key2 = 0.02
key1 = 0.025
Img = (stft1 - stft2)/key2
Img = np.imag(Img)
Img = np.array((Img/key1), dtype='uint8')
waterImg = Image.fromarray(Img)
waterImg = waterImg.resize((100, 100), Image.ANTIALIAS)
waterImg = waterImg.convert("L")
waterImg.save('C:\\Users\\audionew.bmp')

结果示例

 

 图像增强及反相后