High-Quality MATLAB Source Code for Dual-Tree Complex Wavelet Transform (DTCWT)

This article presents a robust MATLAB implementation of the Dual-Tree Complex Wavelet Transform (DTCWT), specifically designed for advanced image processing and multiscale analysis applications. Unlike conventional wavelet transforms, DTCWT employs complex-valued wavelets that deliver superior performance in both efficiency and accuracy. The implementation utilizes two parallel wavelet filter banks with carefully designed frequency responses to achieve approximate analytic properties. Key algorithmic features include: - Implementation of 6-directional selective filters at each scale (except the coarsest level) - Near-perfect shift-invariance through complementary tree structures - Phase information preservation for improved texture analysis The code structure encompasses: 1. Forward transform functions with tree initialization and decomposition routines 2. Inverse transform modules with reconstruction validation checks 3. Multiscale representation handlers for flexible scale configuration 4. Image processing wrappers for seamless integration with existing workflows This implementation demonstrates particular strength in processing images with complex textures and intricate structures, enabling more precise representation of image information across different scales. The code includes comprehensive documentation with examples of filter bank configuration, boundary handling options, and coefficient visualization methods. For researchers and practitioners interested in advanced image processing and multiscale representation techniques, this implementation provides a valuable resource for both educational and practical applications.