SVD奇异值分解：压缩图片

import numpy as np
from PIL import Image
# 载入图片
img = np.array(Image.open("./1.png",'r'))
print("img(原图):",img.shape)
# 第一步：通道分离
c_list = [img[...,i] for i in range(img.shape[-1])]
def Compress(x,precent,print_shape=True,print=print):
    """
    作用：对面二维矩阵进行压缩
    x: 二维矩阵
    precent：保留的奇异值的比例, 例如 0.9即保留前90%的奇异值
    print_shape和print: 可忽略，只是方便打印shape的辅助手段。
    """
    if print_shape:
        print = print
    else:
        print = lambda *args,**kwargs:...
    x = np.array(x)
    print("x",x.shape)
    U,Sigma,V_T = np.linalg.svd(x) # 奇异值分解
    print("U,Sigma,V_T:",U.shape,Sigma.shape,V_T.shape)
    # 全零矩阵，大小与目标矩阵相同。
    zeroimg = np.zeros(shape=(U.shape[0],V_T.shape[0]))
    print("zeroimg:",zeroimg.shape)
    assert zeroimg.shape == x.shape
    k = int(len(Sigma)*precent)
    print("k(选取的奇异值数):",k)
    sigma_k = np.eye(k) * Sigma[:k]  
    U_k = U[...,:k]
    V_T_k = V_T[:k,...]
    print("sigma_k,U_k,V_T_k:",sigma_k.shape,U_k.shape,V_T_k.shape)
    x_re = zeroimg + U_k@sigma_k@V_T_k
    x_re = np.clip(x_re,0,255).astype("uint8") # 矩阵数值范围截断为0~255并设值uint8类型   
    print("x_re:",x_re.shape)
    return x_re
img_list = [img]
for i,precent in enumerate([0.1,0.01]):
    print()
    # 第二步：对各个通道矩阵进行压缩
    c_re_list = []
    for j,x in enumerate(c_list):
        x_re = Compress(x,precent,print_shape=True if j==0 else False)
        c_re_list.append(x_re)
    # 第三步 重建图像
    img_re = np.stack(c_re_list,-1)
    print(f"img_re{i}(重建图片{i}):",img_re.shape)
    img_list.append(img_re)
# 可视化
import matplotlib.pyplot as plt
plt.figure(figsize=(20,20))
for i,img in enumerate(img_list,start=1):
    plt.subplot(1,len(img_list),i)
    plt.imshow(img)

输出：