手动实现对图像的DCT变换和IDCT变换pyhon

DCT变换和IDCT变换是图像压缩中的基本算法之一，下面是手动实现对图像的DCT变换和IDCT变换的Python代码：

import numpy as np

def dct2(block):
    """Perform 2D DCT on a block of size NxN."""
    N = block.shape[0]
    dct = np.zeros((N, N))
    for k in range(N):
        for l in range(N):
            alpha_k = np.sqrt(1/N) if k == 0 else np.sqrt(2/N)
            alpha_l = np.sqrt(1/N) if l == 0 else np.sqrt(2/N)
            sum = 0
            for m in range(N):
                for n in range(N):
                    sum += block[m, n] * np.cos((2*m+1)*k*np.pi/(2*N)) * np.cos((2*n+1)*l*np.pi/(2*N))
            dct[k, l] = alpha_k * alpha_l * sum
    return dct

def idct2(dct):
    """Perform 2D IDCT on a block of size NxN."""
    N = dct.shape[0]
    block = np.zeros((N, N))
    for m in range(N):
        for n in range(N):
            sum = 0
            for k in range(N):
                for l in range(N):
                    alpha_k = np.sqrt(1/N) if k == 0 else np.sqrt(2/N)
                    alpha_l = np.sqrt(1/N) if l == 0 else np.sqrt(2/N)
                    sum += alpha_k * alpha_l * dct[k, l] * np.cos((2*m+1)*k*np.pi/(2*N)) * np.cos((2*n+1)*l*np.pi/(2*N))
            block[m, n] = sum
    return block

其中，`dct2`函数实现对输入图像块的DCT变换，`idct2`函数实现对输入DCT系数块的IDCT变换。由于DCT变换和IDCT变换都是线性的，因此这两个函数可以分别作用于图像的每个块和DCT系数的每个块，实现对整张图像的DCT变换和IDCT变换。