2D Discrete Wavelet Transform MATLAB Implementation

The following MATLAB implementation provides a complete workflow for 2D Discrete Wavelet Transform. The program begins by importing necessary MATLAB libraries and functions, including the Wavelet Toolbox for DWT operations. Users can define their input signal matrix and select appropriate wavelet types (such as Haar, Daubechies, or Symlets) along with decomposition levels. The core implementation utilizes MATLAB's built-in dwt2() function for performing the 2D wavelet decomposition, which returns approximation coefficients (low-frequency components) and detail coefficients (horizontal, vertical, and diagonal high-frequency components). The program handles multi-level decomposition through iterative applications of the transform. Key algorithm aspects include: signal padding handling to maintain matrix dimensions, coefficient thresholding options for denoising applications, and efficient memory management for large 2D datasets. The transform results are stored in structured variables containing both approximation and detailed coefficient matrices. Finally, the implementation includes comprehensive visualization using MATLAB's image processing and plotting functions. This includes subplot arrangements showing original signals, approximation coefficients, and detailed coefficients at different decomposition levels. Additional features include energy distribution analysis and reconstruction verification using idwt2() for transform validation. This implementation serves as an educational resource and practical tool for researchers working on image processing, signal analysis, and wavelet-based applications, providing insights into both theoretical concepts and practical implementation considerations.