实现图像的一阶、二阶、三阶、四阶DPCM编码和解码恢复图像的代码

以下是Python代码实现图像的一阶、二阶、三阶、四阶DPCM编码和解码恢复图像的过程：

import cv2
import numpy as np

def dpcm_encode(img, order):
    rows, cols = img.shape
    # 定义预测值和误差值矩阵
    pred = np.zeros((rows, cols))
    error = np.zeros((rows, cols))

    # 一阶DPCM编码
    if order == 1:
        for i in range(rows):
            for j in range(cols):
                if j == 0:
                    pred[i][j] = img[i][j]
                else:
                    pred[i][j] = img[i][j-1]
                error[i][j] = img[i][j] - pred[i][j]

    # 二阶DPCM编码
    elif order == 2:
        for i in range(rows):
            for j in range(cols):
                if j == 0:
                    pred[i][j] = img[i][j]
                elif j == 1:
                    pred[i][j] = img[i][j-1]
                else:
                    pred[i][j] = 2*img[i][j-1] - img[i][j-2]
                error[i][j] = img[i][j] - pred[i][j]

    # 三阶DPCM编码
    elif order == 3:
        for i in range(rows):
            for j in range(cols):
                if j == 0:
                    pred[i][j] = img[i][j]
                elif j == 1:
                    pred[i][j] = img[i][j-1]
                elif j == 2:
                    pred[i][j] = 2*img[i][j-1] - img[i][j-2]
                else:
                    pred[i][j] = 3*img[i][j-1] - 3*img[i][j-2] + img[i][j-3]
                error[i][j] = img[i][j] - pred[i][j]

    # 四阶DPCM编码
    elif order == 4:
        for i in range(rows):
            for j in range(cols):
                if j == 0:
                    pred[i][j] = img[i][j]
                elif j == 1:
                    pred[i][j] = img[i][j-1]
                elif j == 2:
                    pred[i][j] = 2*img[i][j-1] - img[i][j-2]
                elif j == 3:
                    pred[i][j] = 3*img[i][j-1] - 3*img[i][j-2] + img[i][j-3]
                else:
                    pred[i][j] = 4*img[i][j-1] - 6*img[i][j-2] + 4*img[i][j-3] - img[i][j-4]
                error[i][j] = img[i][j] - pred[i][j]

    return pred, error

def dpcm_decode(pred, error, order):
    rows, cols = pred.shape
    img = np.zeros((rows, cols))

    # 一阶DPCM解码
    if order == 1:
        for i in range(rows):
            for j in range(cols):
                if j == 0:
                    img[i][j] = pred[i][j] + error[i][j]
                else:
                    img[i][j] = pred[i][j-1] + error[i][j]

    # 二阶DPCM解码
    elif order == 2:
        for i in range(rows):
            for j in range(cols):
                if j == 0:
                    img[i][j] = pred[i][j] + error[i][j]
                elif j == 1:
                    img[i][j] = pred[i][j-1] + error[i][j]
                else:
                    img[i][j] = 2*pred[i][j-1] - pred[i][j-2] + error[i][j]

    # 三阶DPCM解码
    elif order == 3:
        for i in range(rows):
            for j in range(cols):
                if j == 0:
                    img[i][j] = pred[i][j] + error[i][j]
                elif j == 1:
                    img[i][j] = pred[i][j-1] + error[i][j]
                elif j == 2:
                    img[i][j] = 2*pred[i][j-1] - pred[i][j-2] + error[i][j]
                else:
                    img[i][j] = 3*pred[i][j-1] - 3*pred[i][j-2] + pred[i][j-3] + error[i][j]

    # 四阶DPCM解码
    elif order == 4:
        for i in range(rows):
            for j in range(cols):
                if j == 0:
                    img[i][j] = pred[i][j] + error[i][j]
                elif j == 1:
                    img[i][j] = pred[i][j-1] + error[i][j]
                elif j == 2:
                    img[i][j] = 2*pred[i][j-1] - pred[i][j-2] + error[i][j]
                elif j == 3:
                    img[i][j] = 3*pred[i][j-1] - 3*pred[i][j-2] + pred[i][j-3] + error[i][j]
                else:
                    img[i][j] = 4*pred[i][j-1] - 6*pred[i][j-2] + 4*pred[i][j-3] - pred[i][j-4] + error[i][j]

    return img

# 测试代码
img = cv2.imread('test.png', cv2.IMREAD_GRAYSCALE)
cv2.imshow('Original Image', img)

# 一阶DPCM编码和解码
pred_1, error_1 = dpcm_encode(img, 1)
img_1 = dpcm_decode(pred_1, error_1, 1)
cv2.imshow('1st Order DPCM Image', img_1.astype(np.uint8))

# 二阶DPCM编码和解码
pred_2, error_2 = dpcm_encode(img, 2)
img_2 = dpcm_decode(pred_2, error_2, 2)
cv2.imshow('2nd Order DPCM Image', img_2.astype(np.uint8))

# 三阶DPCM编码和解码
pred_3, error_3 = dpcm_encode(img, 3)
img_3 = dpcm_decode(pred_3, error_3, 3)
cv2.imshow('3rd Order DPCM Image', img_3.astype(np.uint8))

# 四阶DPCM编码和解码
pred_4, error_4 = dpcm_encode(img, 4)
img_4 = dpcm_decode(pred_4, error_4, 4)
cv2.imshow('4th Order DPCM Image', img_4.astype(np.uint8))

cv2.waitKey(0)
cv2.destroyAllWindows()

请注意，此代码仅供参考，实际应用中可能需要进行更多的优化和改进。