为什么通过低通滤波器传递图像会产生比原始图像更高的值？

Question

我有一个混合图像，它是由一个图像的低频与另一个图像的高频叠加而成的。我试图通过低通滤波器分离（去杂交）这幅图像，提取低频（两幅图像中的一幅），然后从原始图像中减去低频，得到另一幅图像（高频）

**问题：*当我提取低频时，值都高于原始图像，所以当我从原始图像中减去低频时，剩下的是一堆负值

有人知道为什么我的低通滤波器产生比原始图像更高的频率值吗

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
from numpy.fft import fft2, ifft2, fftshift, ifftshift

# Make Gaussian filter
def makeGaussianFilter(numRows, numCols, sigma, highPass=True):
   centerI = int(numRows/2) + 1 if numRows % 2 == 1 else int(numRows/2)
   centerJ = int(numCols/2) + 1 if numCols % 2 == 1 else int(numCols/2)

   def gaussian(i,j):
      coefficient = np.exp(-1.0 * ((i - centerI)**2 + (j - centerJ)**2) / (2 * sigma**2))
      return 1 - coefficient if highPass else coefficient

   return np.array([[gaussian(i,j) for j in range(numCols)] for i in range(numRows)])

# Filter discrete Fourier transform
def filterDFT(imageMatrix, filterMatrix):
   shiftedDFT = fftshift(fft2(imageMatrix))
   filteredDFT = shiftedDFT * filterMatrix
   return ifft2(ifftshift(filteredDFT))

# Low-pass filter
def lowPass(imageMatrix, sigma):
   n,m = imageMatrix.shape
   return filterDFT(imageMatrix, makeGaussianFilter(n, m, sigma, highPass=False))

# Read in einsteinandwho.png and convert to format that can be displayed by plt.imshow
im3 = mpimg.imread('einsteinandwho.png')
rows = im3.shape[0]
cols = im3.shape[1]
img3 = np.ones((rows, cols, 4))
for i in range(rows):
    for j in range(cols):
        img3[i][j][0:3] = im3[i][j]
        img3[j][j][3] = 1

# Extract low frequencies and convert to format that can be displayed by plt.imshow
lowPassed = np.real(lowPass(im3, 10))
low = np.ones((rows, cols, 4))

for i in range(rows):
    for j in range(cols):
        low[i][j][0:3] = lowPassed[i][j]
        low[j][j][3] = 1

# Remove low frequencies from image
output = img3[:,:,0:3] - low[:,:,0:3]

Answer 1

Does anyone know why my low pass filter is yielding higher frequency values than the original image?

请注意像素值和频率值之间的差异。你看到的是更高的像素值，而不是频率值

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当我运行代码时，我看到高频分量既有负值也有正值，而不是所有负值。预计该图像的平均值为零。零频率分量（也称为DC分量）是设置平均像素值的分量。通过减去低通滤波图像，将零频率设置为0，从而将平均像素值设置为0（低通滤波图像包含零频率的所有功率）