Ridgelet and Curvelet Transform Methods

This article discusses two transformation methods: Ridgelet transform and Curvelet transform. These techniques are widely applied in signal and image processing, particularly in edge detection and compression applications. The Ridgelet transform is a linear multiscale decomposition approach that represents signals or images as sets of local orientation intensity values. From an implementation perspective, Ridgelet transforms typically utilize Radon transform followed by wavelet transform, where the key function involves directional filtering across different scales. The Curvelet transform represents a more advanced method capable of capturing fine details along curves and surfaces, delivering superior performance in image processing tasks. Implementation-wise, Curvelet transform employs multiscale directional filtering through techniques like frequency partitioning and angular decomposition, often implemented using digital Curvelet transform algorithms with wedge-shaped frequency filters. These transformation methods provide deeper insights into signal and image characteristics, offering enhanced information extraction and analytical capabilities for various applications.