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lena_dct_exp1.py
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from PIL import Image
import numpy as np
from scipy import fftpack
def dct2d(data):
return fftpack.dct(fftpack.dct(data, norm='ortho').T, norm='ortho').T
def idct2d(data):
return fftpack.idct(fftpack.idct(data, norm='ortho').T, norm='ortho').T
def matrix_select(data, side):
x, y = data.shape
result = np.zeros(data.shape)
for i in range(int(x/side)):
for j in range(int(y/side)):
result[i,j] = data[i,j]
return result
img = Image.open('lena_grayscale.png')
data = np.array(img, dtype=np.float)
print('orig img', data)
dct = dct2d(data)
Image.fromarray(dct.clip(0, 255).astype('uint8')).save('lena_1ddct.png')
Image.fromarray(dct.clip(0, 255).astype('uint8')).save('lena_2ddct.png')
idct = idct2d(dct)
Image.fromarray(idct.clip(0, 255).astype('uint8')).save('lena_1ddct_1didct.png')
Image.fromarray(idct.clip(0, 255).astype('uint8')).save('lena_2ddct_2didct.png')
mse = np.mean((data - idct) ** 2)
psnr = 10 * np.log10(255.0 ** 2 / mse)
print('psnr 2ddct:', psnr)
# 1/side^2 coefs
def full_compress(side):
idct_4 = np.zeros(data.shape)
dct_4 = matrix_select(dct,side)
idct_4 = idct2d(dct_4)
Image.fromarray(idct_4.clip(0, 255).astype('uint8')).save('lena_2ddct_%d_2didct.png' % (side ** 2))
mse = np.mean((data - idct_4) ** 2)
psnr = 10 * np.log10(255.0 ** 2 / mse)
full_compress(2) # 1/4
full_compress(4) # 1/16
full_compress(8) # 1/64
x, y = data.shape
idct_8x8 = np.zeros(data.shape)
idct_8x8_4 = np.zeros(data.shape)
idct_8x8_16 = np.zeros(data.shape)
idct_8x8_64 = np.zeros(data.shape)
for i in range(int(x/8)):
for j in range(int(y/8)):
submatrix = data[i*8:(i+1)*8, j*8:(j+1)*8]
dct = dct2d(submatrix)
Image.fromarray(dct.clip(0, 255).astype('uint8')).save('lena_2ddct_8x8/lena_2ddct_%d_%d.png' % (i, j))
idct = idct2d(dct)
idct_8x8[i*8:(i+1)*8, j*8:(j+1)*8] = idct
# 1/4 coefs
dct_4 = matrix_select(dct,2)
Image.fromarray(dct_4.clip(0, 255).astype('uint8')).save('lena_2ddct_8x8_4/lena_2ddct_%d_%d.png' % (i, j))
idct = idct2d(dct_4)
idct_8x8_4[i*8:(i+1)*8, j*8:(j+1)*8] = idct
# 1/16 coefs
dct_16 = matrix_select(dct,4)
Image.fromarray(dct_16.clip(0, 255).astype('uint8')).save('lena_2ddct_8x8_16/lena_2ddct_%d_%d.png' % (i, j))
idct = idct2d(dct_16)
idct_8x8_16[i*8:(i+1)*8, j*8:(j+1)*8] = idct
# 1/64 coefs
dct_64 = matrix_select(dct,8)
Image.fromarray(dct_64.clip(0, 255).astype('uint8')).save('lena_2ddct_8x8_64/lena_2ddct_%d_%d.png' % (i, j))
idct = idct2d(dct_64)
idct_8x8_64[i*8:(i+1)*8, j*8:(j+1)*8] = idct
Image.fromarray(idct_8x8.clip(0, 255).astype('uint8')).save('lena_2ddct_8x8_2didct.png')
mse = np.mean((data - idct_8x8) ** 2)
psnr = 10 * np.log10(255.0 ** 2 / mse)
print('psnr 2ddct 8x8:', psnr)
Image.fromarray(idct_8x8_4.clip(0, 255).astype('uint8')).save('lena_2ddct_8x8_4_2didct.png')
mse = np.mean((data - idct_8x8_4) ** 2)
psnr = 10 * np.log10(255.0 ** 2 / mse)
print('psnr 2ddct 8x8 1/4:', psnr)
Image.fromarray(idct_8x8_16.clip(0, 255).astype('uint8')).save('lena_2ddct_8x8_16_2didct.png')
mse = np.mean((data - idct_8x8_16) ** 2)
psnr = 10 * np.log10(255.0 ** 2 / mse)
print('psnr 2ddct 8x8 1/16:', psnr)
Image.fromarray(idct_8x8_64.clip(0, 255).astype('uint8')).save('lena_2ddct_8x8_64_2didct.png')
mse = np.mean((data - idct_8x8_64) ** 2)
psnr = 10 * np.log10(255.0 ** 2 / mse)
print('psnr 2ddct 8x8 1/64:', psnr)
def dct1d_compress(ratio):
rows = fftpack.dct(data, norm='ortho')
# assuming data.shape[0] == data.shape[1]
rows = rows[0:x,0:(int(x/ratio))]
dct = fftpack.dct(rows.T, norm='ortho')
dct = dct[0:(int(x/ratio)),0:(int(x/ratio))].T
dct_full = np.zeros(data.shape)
dct_full[0:(int(x/ratio)),0:(int(x/ratio))] = dct
idct = idct2d(dct_full)
Image.fromarray(idct.clip(0, 255).astype('uint8')).save('lena_1ddct_%d.png' % ratio)
mse = np.mean((data - idct) ** 2)
psnr = 10 * np.log10(255.0 ** 2 / mse)
print('psnr 1ddct 1/%d:' % (ratio ** 2), psnr)
dct1d_compress(2)
dct1d_compress(4)
dct1d_compress(8)