写一个在jupyterLab上对一张灰度图像进行基于变换编码的图像压缩代码，并能修改压缩率

好的，以下是一个基于变换编码的图像压缩代码，可以对灰度图像进行压缩，并且可以通过修改 `q` 参数来调整压缩率：

import numpy as np
from scipy.fftpack import dct, idct
from skimage.io import imread, imsave

def compress(img_path, q):
    # 读取灰度图像
    img = imread(img_path, as_gray=True)
    height, width = img.shape
    
    # 将图像分成 8x8 的块
    blocks = np.zeros((height // 8, width // 8, 8, 8))
    for i in range(height // 8):
        for j in range(width // 8):
            blocks[i, j] = img[i*8:(i+1)*8, j*8:(j+1)*8]
    
    # 对每个块进行 DCT 变换并量化
    quantized_blocks = np.zeros_like(blocks)
    for i in range(height // 8):
        for j in range(width // 8):
            dct_block = dct(blocks[i, j], norm='ortho')
            quantized_block = np.round(dct_block / (q*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]
            ])))
            quantized_blocks[i, j] = quantized_block
    
    # 将量化系数输出到文件
    np.save(f'compressed_q{q}.npy', quantized_blocks.reshape(-1, 8, 8))
    
    # 解量化并反DCT变换得到压缩后的图像
    compressed_blocks = np.zeros_like(blocks)
    for i in range(height // 8):
        for j in range(width // 8):
            quantized_block = quantized_blocks[i, j]
            dct_block = quantized_block * (q*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]
            ]))
            compressed_block = idct(dct_block, norm='ortho')
            compressed_blocks[i, j] = compressed_block
    
    # 将压缩后的图像保存到文件
    compressed_img = np.zeros_like(img)
    for i in range(height // 8):
        for j in range(width // 8):
            compressed_img[i*8:(i+1)*8, j*8:(j+1)*8] = compressed_blocks[i, j]
    compressed_img = np.clip(compressed_img, 0, 1)
    imsave(f'compressed_q{q}.png', compressed_img)

这里使用的是基于 DCT 的变换编码方法，具体实现过程如下：

1. 将图像分成 8x8 的块。
2. 对每个块进行 DCT 变换。
3. 进行量化，即将变换系数除以一个量化矩阵，并四舍五入取整。
4. 将量化系数输出到文件。
5. 解量化，即将量化系数乘以量化矩阵。
6. 对每个块进行反DCT变换。
7. 将每个块拼接起来得到压缩后的图像。

其中，量化矩阵可以通过调整 `q` 参数来控制压缩率，`q` 值越大，压缩率越低，图像质量越高。