Dual-Tree Complex Wavelet Transform Source Code

This section provides detailed technical information about the Dual-Tree Complex Wavelet Transform (DT-CWT). The DT-CWT is an advanced signal processing technique that employs two parallel wavelet filter banks - one for the real component and another for the imaginary component. This dual-tree architecture provides nearly shift-invariant properties and improved directional sensitivity compared to standard wavelet transforms. The implementation typically involves decomposing signals or images into complex wavelet coefficients through a multi-scale pyramid structure. Key algorithmic components include: - Two separate filter trees with carefully designed quadrature mirror filters - Perfect reconstruction conditions ensuring invertible transformations - Directional selectivity with six distinct subbands at each scale for 2D applications Common applications include signal compression through thresholding of insignificant coefficients, noise reduction via coefficient shrinkage methods, and feature extraction for pattern recognition. The transform's computational efficiency stems from its separable filter implementation, allowing O(N) complexity for N-point signals. Typical MATLAB implementations would involve functions for forward/inverse transformation, coefficient thresholding, and multi-scale decomposition visualization.