MATLAB Implementation of Radon Transform with Ridgelet Applications

The Radon transform serves as a fundamental mathematical tool in image processing and computer vision, primarily employed for image reconstruction from projection data. In MATLAB, this transform can be efficiently implemented using the built-in radon() function which computes line integrals along specified angles. The inverse Radon transform for reconstruction is achieved through the iradon() function, typically utilizing filtered backprojection algorithms. The ridgelet transform represents an advanced mathematical technique particularly effective for image processing tasks. It excels in directional feature detection, making it ideal for edge identification in images with linear structures. For signal processing, ridgelet transforms demonstrate robust noise reduction capabilities by leveraging sparse representations in the Radon domain. MATLAB implementations often involve applying wavelet transforms to Radon transform coefficients, requiring custom coding since no direct built-in function exists. Both transforms constitute essential components in modern image processing toolkits. They prove particularly valuable when handling complex imagery or signal datasets where traditional Fourier-based methods may underperform. Key implementation considerations include parameter optimization for projection angles in Radon transforms and scale-direction tuning for ridgelet transforms to achieve optimal results across various applications.