Wavelet Decomposition and Reconstruction of 2D Images

This document provides an in-depth exploration of wavelet decomposition and reconstruction for 2D images, accompanied by graphical visualizations of the process. Wavelet decomposition represents a multiresolution analysis technique that decomposes images into frequency bands at different scales. This approach enables better understanding of image details and structures, significantly benefiting image processing and analysis applications. The implementation typically involves using wavelet transform functions (such as wavedec2 and waverec2 in MATLAB) to perform multi-level decomposition and reconstruction, where approximation coefficients and detail coefficients (horizontal, vertical, diagonal) are computed at each decomposition level. Through detailed explanations and graphical illustrations in this document, we aim to enhance your understanding and practical application of wavelet decomposition and reconstruction techniques, including code implementation strategies for handling different wavelet families and decomposition levels.