FDK算法实现锥束CT重建，给出python代码，输入为1880张RAW格式锥束投影图像，重建出三维模型并显示，已知SOD、SDD

由于FDK算法实现锥束CT重建需要用到大量的数学知识，这里给出一个简单的Python代码示例供参考：

import numpy as np
import matplotlib.pyplot as plt
import scipy.ndimage

def fdk_reconstruction(projections, angles, SOD, SDD, output_size):
    num_projections = projections.shape[0]
    height, width = projections.shape[1], projections.shape[2]
    output_depth, output_height, output_width = output_size

    # Calculate the center of rotation
    mid_index = width // 2
    center = np.array([mid_index] * num_projections)

    # Calculate the projection positions
    positions = (np.arange(width) - center[:, np.newaxis]) * SDD / SOD + center[:, np.newaxis]

    # Convert angles to radians
    angles = np.deg2rad(angles)

    # Initialize the output volume
    reconstruction = np.zeros(output_size)

    # Create an array of z positions
    zs = np.arange(output_depth) - (output_depth - 1) / 2

    # Calculate the step size for each projection
    step_size = SDD / SOD / output_height

    # Loop over each projection
    for i in range(num_projections):
        # Calculate the sine and cosine of the angle
        sin_theta = np.sin(angles[i])
        cos_theta = np.cos(angles[i])

        # Calculate the x and y positions of the projection
        xs = positions[i] * cos_theta
        ys = positions[i] * sin_theta

        # Create a grid of x and y coordinates
        x_grid, y_grid = np.meshgrid(np.arange(output_width), np.arange(output_height))

        # Calculate the distance between each pixel and the projection line
        distance = (xs[:, np.newaxis, np.newaxis] - x_grid[np.newaxis, :, :]) ** 2 + \
                   (ys[:, np.newaxis, np.newaxis] - y_grid[np.newaxis, :, :]) ** 2 + \
                   (zs[i] - output_depth / 2) ** 2
        distance = np.sqrt(distance)

        # Calculate the angles between each pixel and the projection line
        beta = np.arccos((xs[:, np.newaxis, np.newaxis] - x_grid[np.newaxis, :, :]) / distance)
        beta[np.isnan(beta)] = 0

        # Calculate the weighted sum of the projections
        reconstruction += np.sum(projections[i] * np.sin(beta) / distance * step_size, axis=0)

    # Smooth the reconstruction using a Gaussian filter
    reconstruction = scipy.ndimage.filters.gaussian_filter(reconstruction, sigma=1)

    return reconstruction

# Load the projections and angles
projections = np.load('projections.npy')
angles = np.load('angles.npy')

# Set the SOD and SDD
SOD = 1000
SDD = 1500

# Set the output size
output_size = (512, 512, 512)

# Reconstruct the volume
reconstruction = fdk_reconstruction(projections, angles, SOD, SDD, output_size)

# Display the reconstructed volume
plt.imshow(reconstruction[:, :, 256], cmap='gray')
plt.show()

请注意，这是一个简单的示例，实际上FDK算法实现锥束CT重建涉及到许多细节和优化，需要根据具体的应用场景进行调整和改进。