MATLAB Source Code for Radon Transform and Inverse Radon Transform

The Radon transform is a mathematical tool widely used in medical imaging, seismic data processing, and other fields, capable of converting two-dimensional image projections into line integrals along different angles. In MATLAB, the implementation of Radon transform and its inverse can help researchers quickly perform image reconstruction or signal analysis.

Radon Transform The core concept of Radon transform involves projecting images or data at various angles. Linear Radon transform is commonly used, performing integration along straight lines, suitable for most standard imaging requirements. Parabolic Radon transform, on the other hand, is applicable to specific scenarios such as seismic wavefield analysis, where integration along parabolic paths better accommodates attenuation characteristics of certain physical models.

In MATLAB, the built-in `radon` function can be used to implement forward Radon transform, allowing users to customize projection angle range and density. For parabolic Radon transform, adjustment of integration paths based on standard Radon transform is required, typically involving additional parameterization processing. Key implementation steps include: specifying theta angles (e.g., theta = 0:179), setting image resolution, and using [R,xp] = radon(I,theta) where R contains projection data and xp represents radial coordinates.

Inverse Radon Transform The inverse Radon transform aims to reconstruct original images or signals from projection data. MATLAB's `iradon` function supports Filtered Back Projection (FBP) algorithm, suitable for inverse linear Radon transform. For inverse parabolic Radon transform, custom reconstruction algorithms such as least squares inversion or iterative methods may be necessary to adapt to nonlinear integration paths. Code implementation typically involves: specifying filter types (e.g., 'Ram-Lak', 'Shepp-Logan'), interpolation methods, and using I = iradon(R,theta) with optional output scaling parameters.

Choosing Between Linear and Parabolic Radon Transform Users can select transform types based on specific requirements: Linear Radon transform is suitable for standard tomography or simple projection reconstruction problems, offering high computational efficiency. Parabolic Radon transform is more appropriate for processing signals with parabolic trajectories, such as seismic wavefield separation or data enhancement for specific physical models.

During MATLAB implementation, users can adapt to different transform requirements by adjusting parameters or writing custom functions, thereby improving flexibility and accuracy in data processing. Algorithm optimization may include parallel processing for large datasets or implementing regularization techniques for ill-posed inverse problems.