1D Wavelet Compression

Motivation:

To create an efficient compression algorithm

import matplotlib.pyplot as plt

import numpy as np

import math

def one_dimensional_wavelet_compression(x, y, epsilon):

x_keep, y_keep = [], []

# Appending First Points

x_keep.append(x[0])

y_keep.append(y[0])

x_keep.append(x[1])

y_keep.append(y[1])

x_even, y_even = [], []

x_odd, y_odd = [], []

for i in range(len(x)):

if i % 2 == 0:

x_even.append(x[i])

y_even.append(y[i])

else:

x_odd.append(x[i])

y_odd.append(y[i])

x_even_mid, y_even_mid = [], []

x_odd_mid, y_odd_mid = [], []

for j in range(len(x_even) - 1):

# Calculating Even Mid-Points

slope_even = (y_even[j + 1] - y_even[j]) / (x_even[j + 1] - x_even[j])

x_even_mid.append(((x_even[j + 1] - x_even[j]) / 2) + x_even[j])

y_even_mid.append(slope_even * ((x_even[j + 1] - x_even[j]) / 2) + y_even[j])

# Calculating Odd Mid-Points

slope_odd = (y_odd[j + 1] - y_odd[j]) / (x_odd[j + 1] - x_odd[j])

x_odd_mid.append(((x_odd[j + 1] - x_odd[j]) / 2) + x_odd[j])

y_odd_mid.append(slope_odd * ((x_odd[j + 1] - x_odd[j]) / 2) + y_odd[j])

sig_figs = 7

x = list_round(x, sig_figs)

x_odd = list_round(x_odd, sig_figs)

x_even_mid = list_round(x_even_mid, sig_figs)

x_even = list_round(x_odd, sig_figs)

x_odd_mid = list_round(x_even_mid, sig_figs)

for k in range(len(x_even_mid)):

index1 = x.index(x_even_mid[k])

index2 = x.index(x_odd_mid[k])

delta1 = y[index1] - y_even_mid[k]

delta2 = y[index2] - y_odd_mid[k]

if abs(delta1) > epsilon:

x_keep.append(x[index1])

y_keep.append(y[index1])

if abs(delta2) > epsilon:

x_keep.append(x[index2])

y_keep.append(y[index2])

# Appending End Points

x_keep.append(x[len(x) - 2])

y_keep.append(y[len(x) - 2])

x_keep.append(x[len(x) - 1])

y_keep.append(y[len(x) - 1])

return x_keep, y_keep

def initial_data():

# Defining Actual Function

x = np.arange(0., math.pi, 0.01)

y = []

[(y.append(math.exp(math.sin(xi ** 2)) - math.cos(xi))) for xi in x]

# Defining Test Points

x_tp = np.arange(0., math.pi, math.pi / 24)

y_tp = []

[(y_tp.append(math.exp(math.sin(x_tpi ** 2)) - math.cos(x_tpi))) for x_tpi in x_tp]

return x_tp, y_tp

def list_round(list, sf):

rounded = []

for l in list:

rounded.append(round(l, sf))

return rounded

x, y = initial_data()

epsilon = 0.25

x_keep, y_keep = one_dimensional_wavelet_compression(x, y, epsilon)

plt.figure('1D Wavelet Compression')

plt.plot(x_keep, y_keep, 'bo--', markersize=12)

plt.plot(x, y, 'yo--', markersize=6)

plt.legend(['key points', 'original points'])

plt.show()