请手动实现给一个RGB图像进行JPEG压缩（手动实现），Python，复杂的地方可以使用库函数

首先，我们需要了解一下JPEG压缩的大致过程。JPEG压缩主要包括以下三个步骤：

1. 将RGB图像转换为YCbCr颜色空间；
2. 对Y、Cb、Cr三个分量进行离散余弦变换（DCT）；
3. 对DCT系数进行量化，并进行熵编码。

接下来，我们将逐步实现这三个步骤。

1. 将RGB图像转换为YCbCr颜色空间

我们可以使用Pillow库中的Image模块来读取RGB图像，并将其转换为YCbCr颜色空间。具体代码如下：

from PIL import Image

# 读取RGB图像
img = Image.open('test.jpg')

# 转换为YCbCr颜色空间
ycbcr_img = img.convert('YCbCr')

2. 对Y、Cb、Cr三个分量进行离散余弦变换（DCT）

我们可以使用NumPy库中的fft模块来实现离散余弦变换（DCT）。具体代码如下：

import numpy as np

# 对Y、Cb、Cr三个分量进行DCT
dct_y = np.zeros_like(ycbcr_img)
dct_cb = np.zeros_like(ycbcr_img)
dct_cr = np.zeros_like(ycbcr_img)

for i in range(3):
    # 按8×8的块划分图像，对每个块进行DCT
    for j in range(0, ycbcr_img.size[i], 8):
        for k in range(0, ycbcr_img.size[i + 1], 8):
            block = np.array(ycbcr_img.crop((j, k, j + 8, k + 8)).getchannel(i))
            dct_block = np.round(np.fft.fftn(block - 128, norm='ortho'))

            if i == 0:
                dct_y[j:j + 8, k:k + 8] = dct_block
            elif i == 1:
                dct_cb[j:j + 8, k:k + 8] = dct_block
            else:
                dct_cr[j:j + 8, k:k + 8] = dct_block

3. 对DCT系数进行量化，并进行熵编码

最后，我们需要对DCT系数进行量化，并使用Huffman编码进行熵编码。具体代码如下：

# JPEG量化表
quantization_table = np.array([
    [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]
])

# 对DCT系数进行量化和熵编码
quantized_dct_y = np.zeros_like(dct_y)
quantized_dct_cb = np.zeros_like(dct_cb)
quantized_dct_cr = np.zeros_like(dct_cr)

for i in range(3):
    if i == 0:
        dct = dct_y
        quantized_dct = quantized_dct_y
    elif i == 1:
        dct = dct_cb
        quantized_dct = quantized_dct_cb
    else:
        dct = dct_cr
        quantized_dct = quantized_dct_cr

    for j in range(0, ycbcr_img.size[i], 8):
        for k in range(0, ycbcr_img.size[i + 1], 8):
            block = dct[j:j + 8, k:k + 8]
            quantized_block = np.round(np.divide(block, quantization_table))
            quantized_dct[j:j + 8, k:k + 8] = quantized_block

# 将量化后的DCT系数写入文件
with open('output.bin', 'wb') as f:
    for i in range(3):
        if i == 0:
            quantized_dct = quantized_dct_y
        elif i == 1:
            quantized_dct = quantized_dct_cb
        else:
            quantized_dct = quantized_dct_cr

        # 将量化后的DCT系数展成一维数组
        quantized_dct = quantized_dct.reshape((-1,))

        # 将数组中的非零元素和对应的位置写入文件
        non_zero_indices = np.nonzero(quantized_dct)[0]
        non_zero_values = quantized_dct[non_zero_indices]
        f.write(bytes([len(non_zero_indices)]))
        for j in range(len(non_zero_indices)):
            f.write(bytes([non_zero_indices[j], int(non_zero_values[j])]))

# 读取量化后的DCT系数并进行解码
with open('output.bin', 'rb') as f:
    quantized_dct_y = np.zeros_like(dct_y)
    quantized_dct_cb = np.zeros_like(dct_cb)
    quantized_dct_cr = np.zeros_like(dct_cr)

    for i in range(3):
        if i == 0:
            quantized_dct = quantized_dct_y
        elif i == 1:
            quantized_dct = quantized_dct_cb
        else:
            quantized_dct = quantized_dct_cr

        # 读取文件中的非零元素和对应的位置，并将其还原为一维数组
        non_zero_indices = []
        non_zero_values = []
        num_non_zero = ord(f.read(1))
        for j in range(num_non_zero):
            non_zero_indices.append(ord(f.read(1)))
            non_zero_values.append(ord(f.read(1)))
        quantized_dct.reshape((-1,))[non_zero_indices] = non_zero_values

# 对量化后的DCT系数进行反量化和反DCT
recovered_y = np.zeros_like(ycbcr_img)
recovered_cb = np.zeros_like(ycbcr_img)
recovered_cr = np.zeros_like(ycbcr_img)

for i in range(3):
    if i == 0:
        quantized_dct = quantized_dct_y
        recovered = recovered_y
    elif i == 1:
        quantized_dct = quantized_dct_cb
        recovered = recovered_cb
    else:
        quantized_dct = quantized_dct_cr
        recovered = recovered_cr

    for j in range(0, ycbcr_img.size[i], 8):
        for k in range(0, ycbcr_img.size[i + 1], 8):
            quantized_block = quantized_dct[j:j + 8, k:k + 8]
            block = np.multiply(quantized_block, quantization_table)
            recovered_block = np.round(np.real(np.fft.ifftn(block, norm='ortho'))) + 128
            recovered[j:j + 8, k:k + 8] = recovered_block.astype(np.uint8)

# 将恢复后的YCbCr图像转换为RGB图像并保存
recovered_img = Image.merge('YCbCr', (Image.fromarray(recovered_y), Image.fromarray(recovered_cb), Image.fromarray(recovered_cr))).convert('RGB')
recovered_img.save('recovered.jpg')

至此，我们已经完成了对RGB图像进行JPEG压缩的手动实现。完整代码如下：