Implementation of 2D Discrete Wavelet Transform Using MATLAB

This project presents a MATLAB implementation of Mallat's fast algorithm for 2D discrete wavelet transform, enabling multi-level decomposition and reconstruction of digital images. The implementation leverages MATLAB's built-in wavelet toolbox functions such as wavedec2 for decomposition and waverec2 for reconstruction, while providing custom code for enhanced control over the transformation process. The method finds extensive applications in image processing, where wavelet transformation effectively extracts frequency-domain characteristics from images, facilitating crucial operations like denoising, compression, and feature extraction. Mallat's fast algorithm represents an efficient approach for 2D discrete wavelet transform, significantly reducing computational time through its pyramid-structured processing technique. The implementation includes code for handling multi-scale decomposition where images are progressively broken down into approximation coefficients (low-frequency components) and detail coefficients (horizontal, vertical, and diagonal high-frequency components) at different resolution levels. The reconstruction process reverses this operation using inverse wavelet transforms while maintaining image integrity. Key MATLAB functions utilized include: - dwt2: Single-level 2D discrete wavelet transform - idwt2: Single-level 2D inverse discrete wavelet transform - wavedec2: Multi-level 2D wavelet decomposition - appcoef2/detcoef2: Extraction of approximation and detail coefficients - waverec2: Multi-level 2D wavelet reconstruction The source code has been fully implemented in MATLAB, providing a readily applicable solution for image processing applications with customizable parameters for wavelet types (Daubechies, Haar, etc.) and decomposition levels. The implementation demonstrates proper handling of boundary conditions and coefficient thresholding for practical applications.