#!/usr/bin/env python
# coding: utf-8

# # Image Compression
# 
# Copyright (C) 2020 Andreas Kloeckner
# 
# <details>
# <summary>MIT License</summary>
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# 
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
# 
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
# </details>

# In[8]:


import numpy as np
import matplotlib.pyplot as pt


# In[9]:


from PIL import Image

with Image.open("andreas.jpeg").resize((500,500)) as img:
    rgb_img = np.array(img)
rgb_img.shape


# In[10]:


img = np.sum(rgb_img, axis=-1)


# In[11]:


pt.imshow(img, cmap="gray")


# In[12]:


u, sigma, vt = np.linalg.svd(img)
sigma

pt.plot(sigma)


# In[13]:


compressed_img = (
    sigma[0] * np.outer(u[:, 0], vt[0])
    + sigma[1] * np.outer(u[:, 1], vt[1])
    + sigma[2] * np.outer(u[:, 2], vt[2])
    + sigma[3] * np.outer(u[:, 3], vt[3])
    + sigma[4] * np.outer(u[:, 4], vt[4])
    + sigma[5] * np.outer(u[:, 5], vt[5])
    )

pt.imshow(compressed_img, cmap="gray")


# In[ ]: