CBCT图像的反投影python'

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import numpy as np
import scipy.ndimage as ndi

def back_projection(sinogram, theta):
    """
    Back projection algorithm for CT reconstruction.
    Args:
        sinogram: 2D array, sinogram data
        theta: 1D array, angle values in radians
    Returns:
        2D array, reconstructed image
    """
    # Determine the shape of the sinogram and the size of the output image
    num_angles, num_detectors = sinogram.shape
    output_size = num_detectors

    # Create empty output image
    output_image = np.zeros((output_size, output_size))

    # Loop over all angles
    for i in range(num_angles):
        # Calculate the sinogram row for the current angle
        sinogram_row = sinogram[i, :]

        # Calculate the angle of the current projection
        angle = theta[i]

        # Create an empty image for the current projection
        projection_image = np.zeros((output_size, output_size))

        # Loop over all detectors
        for j in range(num_detectors):
            # Calculate the x and y coordinates of the current detector
            x = j - num_detectors / 2
            y = output_size / 2

            # Calculate the x and y coordinates of the current point on the projection
            x_proj = x * np.cos(angle) + y * np.sin(angle)
            y_proj = -x * np.sin(angle) + y * np.cos(angle)

            # Round the x and y coordinates to the nearest integer
            x_proj = int(round(x_proj))
            y_proj = int(round(y_proj))

            # Add the value of the sinogram row to the projection image
            projection_image[y_proj, x_proj] = sinogram_row[j]

        # Apply a smoothing filter to the projection image
        projection_image = ndi.gaussian_filter(projection_image, sigma=1)

        # Add the projection image to the output image
        output_image += projection_image

    return output_image