In [43]:

    

# System imports
import numpy as np
import math

class Jpeg:
    PI_DIV_16 = math.pi / 16
    INV_SQRT_2 = 1 / math.sqrt(2)
    
    def __init__(self, number_of_cells, quantisation_matrix):
        self.number_of_cells = number_of_cells
        self.quantisation_matrix = quantisation_matrix
        self.output = np.zeros(shape=(self.number_of_cells, self.number_of_cells))
        self.compression_factor = 0
    
    def compress(self, input_, compression_factor):
        self.compression_factor = compression_factor
        
        for u in range(0, self.number_of_cells):
            cu = self.INV_SQRT_2 if u == 0 else 1
            
            for v in range(0, self.number_of_cells):
                cv = self.INV_SQRT_2 if v == 0 else 1
                sum_ = 0
                
                for x in range(0, self.number_of_cells):
                    cos1 = math.cos(self.PI_DIV_16 * u * (2 * x + 1))
                    
                    for y in range(0, self.number_of_cells):
                        cos2 = math.cos(self.PI_DIV_16 * v * (2 * y + 1))
                        sum_ = sum_ + input_[x, y] * cos1 * cos2
                
                sum_ = self.compression_factor * cu * cv * sum_ / self.quantisation_matrix[u, v]
                self.output[u, v] = sum_
                
        return self.output
    
    def decompress(self, input_):
        # Clear output matrix
        self.output = np.zeros(shape=(self.number_of_cells, self.number_of_cells))
        
        for x in range(0, self.number_of_cells):
            for y in range(0, self.number_of_cells):
                sum_ = 0
                
                for u in range(0, self.number_of_cells):
                    cu = self.INV_SQRT_2 if u == 0 else 1
                    cos1 = math.cos(self.PI_DIV_16 * u * (2 * x + 1))
                    
                    for v in range(0, self.number_of_cells):
                        cv = self.INV_SQRT_2 if v == 0 else 1
                        cos2 = math.cos(self.PI_DIV_16 * v * (2 * x + 1))
                        sum_ = sum_ + cu * cv * input_[u, v] * cos1 * cos2 * self.quantisation_matrix[u, v]
                
                sum_ = sum_ * self.compression_factor
                self.output[x, y] = sum_
        
        return self.output


    

In [45]:

    

import scipy.misc as misc
import matplotlib.pyplot as plt

source_matrix = np.matrix(
    '100 100 100 100 100 100 100 100 ;'
    '100 100 100 100 100 100 100 100 ;'
    '100 100 100 100 100 100 100 100 ;'
    '100 100 100 100 100 100 100 100 ;'
    '0 0 0 0 0 0 0 0 ;'
    '0 0 0 0 0 0 0 0 ;'
    '0 0 0 0 0 0 0 0 ;'
    '0 0 0 0 0 0 0 0'
)

quantisation_matrix = np.matrix(
    '16 11 10 16 24 40 51 61 ;'
    '12 12 14 19 26 58 60 55 ;'
    '14 13 16 24 40 57 69 56 ;'
    '14 17 22 29 51 87 80 62 ;'
    '18 22 37 56 68 109 103 77 ;'
    '24 35 55 64 81 104 113 92 ;'
    '49 64 78 87 103 121 120 101 ;'
    '72 92 95 98 112 100 103 99'
)

jpeg = Jpeg(8, quantisation_matrix)
output = jpeg.compress(source_matrix, 1)
output_reconstructed = jpeg.decompress(output)

plt.imshow(source_matrix)
plt.title('Source matrix (weird colors..)')
plt.show()

plt.imshow(output)
plt.title('Ouput of compression')
plt.show()

plt.imshow(output_reconstructed)
plt.title('Ouput after reconstruction')
plt.show()


    

In [ ]:

    

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