Numpy和Tensorflow傅立叶变换示例：幅值和相位

一、numpy傅立叶变换和反变换

import cv2
import numpy as np
import matplotlib.pyplot as plt

img = cv2.imread('Set5/001_HR.png')
(r, g, b)=cv2.split(img)
img=cv2.merge([b,g,r])
#cv2.imshow("test",img)
#cv2.waitKey(0)
#plt.imshow(img)

#img = cv2.imread('flower.jpg',0) #直接读为灰度图像
f = np.fft.fft2(img)
fshift = np.fft.fftshift(f)
#取绝对值：将复数变化成实数
#取对数的目的为了将数据变化到0-255
s1 = np.log(np.abs(fshift))
plt.subplot(221),plt.imshow(img),plt.title('original')
plt.xticks([]),plt.yticks([])
#---------------------------------------------
# 逆变换--取绝对值就是振幅
f1shift = np.fft.ifftshift(np.abs(fshift))
img_back = np.fft.ifft2(f1shift)
#出来的是复数，无法显示
img_back = np.abs(img_back)
#调整大小范围便于显示
img_back = (img_back-np.amin(img_back))/(np.amax(img_back)-np.amin(img_back))
plt.subplot(222),plt.imshow(img_back,'gray'),plt.title('only Amplitude')
plt.xticks([]),plt.yticks([])
#---------------------------------------------
# 逆变换--取相位
f2shift = np.fft.ifftshift(np.angle(fshift))
img_back = np.fft.ifft2(f2shift)
#出来的是复数，无法显示
img_back = np.abs(img_back)
#调整大小范围便于显示
img_back = (img_back-np.amin(img_back))/(np.amax(img_back)-np.amin(img_back))
plt.subplot(223),plt.imshow(img_back,'gray'),plt.title('only phase')
plt.xticks([]),plt.yticks([])
#---------------------------------------------
# 逆变换--将两者合成看看
s1 = np.abs(fshift) #取振幅
s1_angle = np.angle(fshift) #取相位
s1_real = s1*np.cos(s1_angle) #取实部
s1_imag = s1*np.sin(s1_angle) #取虚部
s2 = np.zeros(img.shape,dtype=complex)
s2.real = np.array(s1_real) #重新赋值给s2
s2.imag = np.array(s1_imag)

f2shift = np.fft.ifftshift(s2) #对新的进行逆变换
img_back = np.fft.ifft2(f2shift)
#出来的是复数，无法显示
img_back = np.abs(img_back)
#调整大小范围便于显示
img_back = (img_back-np.amin(img_back))/(np.amax(img_back)-np.amin(img_back))
plt.subplot(224),plt.imshow(img_back,'gray'),plt.title('another way')
plt.xticks([]),plt.yticks([])

plt.show()

二、tensorflow傅立叶变换示例：幅值和相位

#coding=utf-8
import cv2
import numpy as np
import matplotlib.pyplot as plt
import tensorflow as tf
from skimage import measure
from skimage import img_as_ubyte
# plt显示fft的幅值图
"""
img = cv2.imread('Set5/001_HR.png',0)

f = np.fft.fft2(img)
fshift = np.fft.fftshift(f)
s1 = np.log(np.abs(f))
s2 = np.log(np.abs(fshift))
plt.subplot(121),plt.imshow(s1,'gray'),plt.title('original')
#plt.subplot(122),plt.imshow(s2,'gray'),plt.title('center')

sess = tf.InteractiveSession()
xs = tf.placeholder(dtype=tf.complex64,shape=(img.shape[0],img.shape[1]))
f1=tf.fft2d(xs)
f1_dis=f1.eval(feed_dict={xs:img})
f1shift = np.fft.fftshift(f1_dis)
ss1 = np.log(np.abs(f1_dis))
ss1 = np.float64(ss1)

plt.subplot(122),plt.imshow(ss1,'gray'),plt.title('fft_original')
plt.show()
"""

# plt显示fft的相位图
"""
Ihr = cv2.imread('Set5/003_HR.png',1)
Ilr = cv2.imread('Set5/003_EnhanceNet-PAT.png',1)

ph_out=[]
for i,img in enumerate([Ihr,Ilr]):
    f = np.fft.fft2(img)
    fshift = np.fft.fftshift(f)
    #取绝对值：将复数变化成实数
    #取对数的目的为了将数据变化到较小的范围（比如0-255）
    ph_f = np.angle(f)
    ph_out.append(ph_f)
    ph_fshift = np.angle(fshift)
    index='22'+ str(i+1)
    plt.subplot(int(index)),plt.imshow(ph_f,'gray'),plt.title('original')

    #index = ['22' + str(i * 2 + 1), '22' + str(i * 2 + 2)]
    #plt.subplot(int(index[0])),plt.imshow(ph_f,'gray'),plt.title('original')
    #plt.subplot(int(index[1])),plt.imshow(ph_fshift,'gray'),plt.title('center')

shape = Ihr.shape
sess = tf.InteractiveSession()
xs = tf.placeholder(dtype=tf.complex64, shape=([2, shape[1], shape[0], shape[2]]))

fhr = tf.fft2d(xs[0])
flr = tf.fft2d(xs[1])

#fshift_hr, fshift_lr = np.fft.fftshift([fhr_dis,flr_dis])
ph_fhr = tf.cast(tf.angle(fhr),dtype=tf.float64)
ph_flr = tf.cast(tf.angle(flr),dtype=tf.float64)
#ph_fhr = tf.atan2(tf.imag(fhr),tf.real(fhr))
#ph_flr = tf.atan2(tf.imag(flr),tf.real(flr))
ph_fhr, ph_flr = sess.run([ph_fhr,ph_flr],feed_dict={xs:[Ihr, Ilr]})

print ("MSE of  ph_fhr and ph_out[0]:",measure.compare_mse(ph_fhr,ph_out[0]))
print ("MSE of  ph_fhr and ph_flr:",measure.compare_mse(ph_fhr,ph_flr))
plt.show()
"""


# plt显示fft的赋值大小
"""
Ihr = cv2.imread('Set5/003_HR.png',1)
Ilr = cv2.imread('Set5/003_EnhanceNet-PAT.png',1)
nhr = np.fft.fft2(Ihr)
nlr = np.fft.fft2(Ilr)
amp_nhr = np.log(np.abs(nhr))
amp_nlr = np.log(np.abs(nlr))

shape = Ihr.shape
sess = tf.InteractiveSession()
xs = tf.placeholder(dtype=tf.complex64, shape=([2, shape[1], shape[0], shape[2]]))

fhr = tf.fft2d(xs[0])
flr = tf.fft2d(xs[1])
amp_fhr = tf.cast(tf.log(tf.abs(fhr)),dtype=tf.float64)
amp_flr = tf.cast(tf.log(tf.abs(flr)),dtype=tf.float64)
amp_fhr, amp_flr = sess.run([amp_fhr,amp_flr],feed_dict={xs:[Ihr, Ilr]})

print ("MSE of  ph_fhr and ph_out[0]:",measure.compare_mse(amp_fhr,amp_flr))
"""

sess = tf.InteractiveSession()

theta0 = tf.atan2(1.0, 1.0) # pi/4
x0 = tf.constant(1.0)
y  = tf.Variable(0.4)
c  = tf.complex(x0, y)
c = tf.expand_dims(c,0)
c = tf.fft(c)
theta = tf.angle(c)
err = (theta - theta0)**2
optimize = tf.train.GradientDescentOptimizer(1e-1).minimize(err)

sess.run(tf.global_variables_initializer())
for i in range(10000):
    sess.run(optimize)
    if i % 10 == 0:
        print(sess.run(c)) # should go to 1 + 1j

a=tf.constant(1e-8,tf.complex64,tf.shape())

三、numpy相位交换，幅值不变

import cv2
import numpy as np
import matplotlib.pyplot as plt
from skimage import measure
from skimage import img_as_ubyte


#img_flower = cv2.imread('Set5/001_HR.png',1) #直接读为灰度图像
#img_man = cv2.imread('Set5/001_EnhanceNet-E.png',1) #直接读为灰度图像
#img_man = cv2.imread('Set5/004_EnhanceNet-PAT.png',1) #直接读为灰度图像
img_flower = cv2.imread('../../datasets/SuperResolution/EnhanceNet_Urban100/Urban100/039_HR.png',1) #直接读为灰度图像
img_man = cv2.imread('../../datasets/SuperResolution/EnhanceNet_Urban100/Urban100/039_EnhanceNet-E.png',1) #直接读为灰度图像
#img_man = cv2.imread('../../datasets/SuperResolution/EnhanceNet_BSD100\BSD100/043_EnhanceNet-PAT.png',1)

#cv2.imshow("test",img_flower)
#cv2.waitKey(0)
print ("PSNR of  0 and 1:",measure.compare_psnr(img_flower,img_man))

(r, g, b)=cv2.split(img_flower)
img_flower=cv2.merge([b,g,r])
(r, g, b)=cv2.split(img_man)
img_man=cv2.merge([b,g,r])
print ("PSNR of  0 and 1:",measure.compare_mse(img_flower,img_man))


plt.subplot(221),plt.imshow(img_flower,'gray'),plt.title('001_HR')
plt.xticks([]),plt.yticks([])
plt.subplot(222),plt.imshow(img_man,'gray'),plt.title('001_EnhanceNet-PAT')
plt.xticks([]),plt.yticks([])
#--------------------------------
f1 = np.fft.fft2(img_flower)
f1shift = np.fft.fftshift(f1)
f1_A = np.abs(f1shift) #取振幅
f1_P = np.angle(f1shift) #取相位
#--------------------------------
f2 = np.fft.fft2(img_man)
f2shift = np.fft.fftshift(f2)
f2_A = np.abs(f2shift) #取振幅
f2_P = np.angle(f2shift) #取相位
#---图1的振幅--图2的相位--------------------
img_new1_f = np.zeros(img_flower.shape,dtype=complex)
img1_real = f1_A*np.cos(f2_P) #取实部
img1_imag = f1_A*np.sin(f2_P) #取虚部
img_new1_f.real = np.array(img1_real)
img_new1_f.imag = np.array(img1_imag)
f3shift = np.fft.ifftshift(img_new1_f) #对新的进行逆变换
img_new1 = np.fft.ifft2(f3shift)
#出来的是复数，无法显示
img_new1 = np.abs(img_new1)
#调整大小范围便于显示
img_new1 = (img_new1-np.amin(img_new1))/(np.amax(img_new1)-np.amin(img_new1))
plt.subplot(223),plt.imshow(img_new1,'gray'),plt.title('another way')
plt.xticks([]),plt.yticks([])
#---图2的振幅--图1的相位--------------------
img_new2_f = np.zeros(img_flower.shape,dtype=complex)
img2_real = f2_A*np.cos(f1_P) #取实部
img2_imag = f2_A*np.sin(f1_P) #取虚部
img_new2_f.real = np.array(img2_real)
img_new2_f.imag = np.array(img2_imag)
f4shift = np.fft.ifftshift(img_new2_f) #对新的进行逆变换
img_new2 = np.fft.ifft2(f4shift)
#出来的是复数，无法显示
img_new2 = np.abs(img_new2)
#调整大小范围便于显示
img_new2 = (img_new2-np.amin(img_new2))/(np.amax(img_new2)-np.amin(img_new2))
plt.subplot(224),plt.imshow(img_as_ubyte(img_new2),'gray'),plt.title('another way')
plt.xticks([]),plt.yticks([])
plt._imsave("test.jpg",img_new2)

print ("PSNR of  0 and 4:",measure.compare_mse(img_flower,img_as_ubyte(img_new2)))

plt.show()

四、几个简单的画图函数：

#!/usr/bin/env python
# -*- coding: utf-8 -*-
import numpy as np
from PIL import Image
import matplotlib
import matplotlib.path as path
import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.ticker import MultipleLocator

fig = plt.figure(figsize=(8,6), dpi=72,facecolor="white")
axes = plt.subplot(211, aspect=1, axisbelow=True)

lena = np.array(Image.open("output/001_HR.png"))
im = plt.imshow(lena, origin = 'upper', interpolation='nearest')
axes.set_xticks([])
axes.set_yticks([])

axes = plt.axes([0.05,0.00,0.40,0.50], frameon=False)
patch1 = patches.Circle((.5,.5), radius=.45, transform=axes.transAxes,
                        linewidth=2, facecolor='none', edgecolor='black',zorder=2)
patch2 = patches.Circle((.5,.5), radius=.46, transform=axes.transAxes,
                        linewidth=2, facecolor='white', edgecolor='white',zorder=1)
im = plt.imshow(lena[215:315,285:385], origin = 'upper', zorder=3,
                interpolation='nearest', clip_path=patch1)
axes.set_xticks([])
axes.set_yticks([])
axes.add_patch(patch1)
axes.add_patch(patch2)

plt.show()

#coding=utf-8
import numpy as np
import matplotlib.pyplot as plt

img001_HR = plt.imread('output/001_HR.png',0)
img001_En = plt.imread('output/001_EnhanceNet-PAT.png',0)
img002_HR = plt.imread('output/002_HR.png',0)
img002_En = plt.imread('output/002_EnhanceNet-PAT.png',0)
img003_HR = plt.imread('output/003_HR.png',0)
img003_En = plt.imread('output/003_EnhanceNet-PAT.png',0)
img004_HR = plt.imread('output/004_HR.png',0)
img004_En = plt.imread('output/004_EnhanceNet-PAT.png',0)
img005_HR = plt.imread('output/001_HR.png',0)
img005_En = plt.imread('output/001_EnhanceNet-PAT.png',0)

plt.subplot(521),plt.imshow(img001_HR,'gray'),plt.title('img001_HR')
plt.subplot(522),plt.imshow(img001_En,'gray'),plt.title('img001_En')


plt.subplot(523),plt.imshow(img002_HR,'gray'),plt.title('img002_HR')
plt.subplot(524),plt.imshow(img002_En,'gray'),plt.title('img002_En')

plt.subplot(525),plt.imshow(img003_HR,'gray'),plt.title('img003_HR')
plt.subplot(526),plt.imshow(img003_En,'gray'),plt.title('img003_En')
plt.subplot(527),plt.imshow(img004_HR,'gray'),plt.title('img004_HR')
plt.subplot(528),plt.imshow(img004_En,'gray'),plt.title('img004_En')
"""
plt.subplot(529),plt.imshow(img005_HR,'gray'),plt.title('img005_HR')
#plt.subplot(5210),plt.imshow(img005_En,'gray'),plt.title('img005_En')
"""
plt.show()