Dual-Tree Complex Wavelet Transform - Algorithm Implementation and Function Suite

This comprehensive MATLAB toolkit contains specialized functions for implementing the Dual-Tree Complex Wavelet Transform (DT-CWT) on both one-dimensional and two-dimensional signals. The package employs two parallel wavelet filter banks - one for the real component and another for the imaginary component - using specially designed q-shift filters that maintain approximate Hilbert transform relationships between trees. Key functions include forward and inverse transformation routines with options for multiple decomposition levels, perfect reconstruction capabilities, and directional sensitivity in 2D processing (six distinct subbands at ±15°, ±45°, ±75° orientations). The implementation handles complex coefficient management through separable filtering operations using both low-pass and high-pass filter pairs. This transform excels in applications requiring improved directional analysis compared to standard DWTs, particularly beneficial for image denoising, feature extraction, and compression tasks where phase information and shift-invariance are critical. Researchers can leverage these optimized functions to process signals while maintaining the transform's advantages of reduced aliasing and directional selectivity.