简单的基于小波变换的图像压缩（Python）

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2023 沃尔夫数学奖得主，给了杜克大学的Ingrid Daubechies（多贝西）教授

以色列沃尔夫基金会理事会成员 Michael Lin 教授在周二宣布: “Ingrid Daubechies is awarded the Wolf Prize for her work in the creation and development of wavelet theory and modern time frequency analysis。"

多贝西教授在小波理论和调和分析领域做出了重大贡献，她的研究彻底改变了图像和信号的数字处理方式，为数据压缩提供了标准和灵活的算法。多贝西的研究成果带来了多个领域技术的创新，包括医学成像、无线通信，和数字电影，比如：她早期的研究成果被用于图像压缩，JPEG 2000格式图片就是通过Daubechies小波压缩而成，它们也被用于将声音序列压缩成 MP3 文件；在更近的一些应用领域中，它们被用于增强和重建哈勃望远镜早期的图像，检测伪造的文件和指纹等等。

import numpy as np
import matplotlib.pyplot as plt
import os
import cv2
import pywt
import pywt.data
from skimage.data import camera
from skimage.util import random_noise
from skimage import img_as_ubyte
from skimage.metrics import peak_signal_noise_ratio as psnr

print(pywt.wavelist())

['bior1.1', 'bior1.3', 'bior1.5', 'bior2.2', 'bior2.4', 'bior2.6', 'bior2.8', 'bior3.1', 'bior3.3', 'bior3.5', 'bior3.7', 'bior3.9', 'bior4.4', 'bior5.5', 'bior6.8', 'cgau1', 'cgau2', 'cgau3', 'cgau4', 'cgau5', 'cgau6', 'cgau7', 'cgau8', 'cmor', 'coif1', 'coif2', 'coif3', 'coif4', 'coif5', 'coif6', 'coif7', 'coif8', 'coif9', 'coif10', 'coif11', 'coif12', 'coif13', 'coif14', 'coif15', 'coif16', 'coif17', 'db1', 'db2', 'db3', 'db4', 'db5', 'db6', 'db7', 'db8', 'db9', 'db10', 'db11', 'db12', 'db13', 'db14', 'db15', 'db16', 'db17', 'db18', 'db19', 'db20', 'db21', 'db22', 'db23', 'db24', 'db25', 'db26', 'db27', 'db28', 'db29', 'db30', 'db31', 'db32', 'db33', 'db34', 'db35', 'db36', 'db37', 'db38', 'dmey', 'fbsp', 'gaus1', 'gaus2', 'gaus3', 'gaus4', 'gaus5', 'gaus6', 'gaus7', 'gaus8', 'haar', 'mexh', 'morl', 'rbio1.1', 'rbio1.3', 'rbio1.5', 'rbio2.2', 'rbio2.4', 'rbio2.6', 'rbio2.8', 'rbio3.1', 'rbio3.3', 'rbio3.5', 'rbio3.7', 'rbio3.9', 'rbio4.4', 'rbio5.5', 'rbio6.8', 'shan', 'sym2', 'sym3', 'sym4', 'sym5', 'sym6', 'sym7', 'sym8', 'sym9', 'sym10', 'sym11', 'sym12', 'sym13', 'sym14', 'sym15', 'sym16', 'sym17', 'sym18', 'sym19', 'sym20']

path = {'compressed_haar': 'wavelet_compression/compressed_haar.jpg', 'compressed_db1': 'C:/romena/unige/wavelet_compression/compressed_db1.jpg', 'compressed_db2': 'C:/romena/unige/wavelet_compression/compressed_db2.jpg', 'compressed_bior1.3': 'C:/romena/unige/wavelet_compression/compressed_bior1.3.jpg', 'noisy': 'C:/romena/unige/wavelet_compression/noisy.jpeg'}
for i in path:size_img= os.path.getsize(path[i])size_img= size_img/1024print(i +'='+ str(size_img) + 'KB')size_img= 0

Wavelet: haar, Threshold: 5, PSNR: 4.72 dB, CR: 1.16, Size: 71.64 KB
Wavelet: haar, Threshold: 10, PSNR: 4.72 dB, CR: 1.16, Size: 71.64 KB
Wavelet: haar, Threshold: 20, PSNR: 4.72 dB, CR: 1.16, Size: 71.64 KB
Wavelet: db1, Threshold: 5, PSNR: 4.72 dB, CR: 1.16, Size: 71.64 KB
Wavelet: db1, Threshold: 10, PSNR: 4.72 dB, CR: 1.16, Size: 71.64 KB
Wavelet: db1, Threshold: 20, PSNR: 4.72 dB, CR: 1.16, Size: 71.64 KB
Wavelet: db2, Threshold: 5, PSNR: 4.72 dB, CR: 1.05, Size: 78.92 KB
Wavelet: db2, Threshold: 10, PSNR: 4.72 dB, CR: 1.05, Size: 78.92 KB
Wavelet: db2, Threshold: 20, PSNR: 4.72 dB, CR: 1.05, Size: 78.92 KB
Wavelet: coif2, Threshold: 5, PSNR: 4.72 dB, CR: 1.22, Size: 67.99 KB
Wavelet: coif2, Threshold: 10, PSNR: 4.72 dB, CR: 1.22, Size: 67.99 KB
Wavelet: coif2, Threshold: 20, PSNR: 4.72 dB, CR: 1.22, Size: 67.99 KB
Wavelet: custom, Threshold: 5, PSNR: 4.69 dB, CR: 1.31, Size: 63.16 KB
Wavelet: custom, Threshold: 10, PSNR: 4.69 dB, CR: 1.31, Size: 63.16 KB
Wavelet: custom, Threshold: 20, PSNR: 4.69 dB, CR: 1.31, Size: 63.16 KB

担任《Mechanical System and Signal Processing》《中国电机工程学报》《控制与决策》等期刊审稿专家，擅长领域：现代信号处理，机器学习，深度学习，数字孪生，时间序列分析，设备缺陷检测、设备异常检测、设备智能故障诊断与健康管理PHM等。

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