Ridgelet Multiscale Transform

This project implements a ridgelet-based multiscale image processing algorithm using MATLAB programming. The implementation includes core functionalities for image decomposition, reconstruction, and compression. Through the ridgelet transform, images are decomposed into subbands at different scales and orientations, effectively extracting local feature information from the image data. The algorithm utilizes directional filtering and radon transform operations to capture linear singularities in images. The inverse ridgelet transform reconstructs the decomposed subbands back into the original image, maintaining image fidelity through proper coefficient reassembly. For compression applications, the implementation leverages the sparse representation property of ridgelet transforms, where significant coefficients are preserved while discarding negligible ones, thereby reducing storage requirements. Key MATLAB functions include directional filter banks for multiscale decomposition and thresholding techniques for coefficient selection. This ridgelet-based approach enables efficient image processing while preserving critical image information, making it suitable for applications requiring optimal balance between compression efficiency and image quality retention. The implementation demonstrates practical applications in medical imaging and texture analysis where directional features are paramount.