MATLAB Code Implementation of Radon Transform

The Radon transform is a mathematical tool widely used in image processing, particularly significant in motion blur handling. It effectively captures linear features in images by projecting them along different angles. In MATLAB, implementing the Radon transform primarily relies on the built-in `radon` function, which performs projection transformation on input image matrices. By setting different angle parameters, we can obtain projection data of the image in various directions. The function syntax is typically `R = radon(I, theta)`, where `I` is the input grayscale image and `theta` specifies the projection angles (either a scalar or vector). For motion blur scenarios, the Radon transform helps analyze blur direction and intensity. First, perform Radon transform on the blurred image and observe the distribution characteristics of projection data to determine the motion trajectory of the blur. Then, using inverse Radon transform (typically implemented through filtered back-projection algorithm) can attempt to restore the original image. The back-projection algorithm reconstructs images by smearing projection values back along their original paths and applying filtration to reduce artifacts. In practical applications, it's often necessary to combine denoising and optimization algorithms to improve the quality of restored images. MATLAB's `iradon` function executes inverse Radon transform, but careful selection of filters (e.g., Ram-Lak, Shepp-Logan, or Cosine filters) and interpolation methods is crucial for optimal results. The basic implementation follows `IR = iradon(R, theta, filter, interpolation)` where proper parameter tuning significantly affects reconstruction accuracy.