Three-Level Wavelet Transform Decomposition of Images and Extraction of Sub-band Coefficients

This process involves performing a three-level wavelet decomposition on images using wavelet transform, which breaks down the image into different frequency sub-bands and extracts coefficients for each sub-band. Wavelet transform serves as a highly effective signal processing technique for image processing and analysis, capable of capturing detailed texture information and providing multi-scale representations. Through three-level decomposition, we obtain richer image information and enable analysis and processing of details at different scales. In implementation, this typically involves using wavelet decomposition functions (like wavedec2 in MATLAB) to recursively separate approximation and detail coefficients across horizontal, vertical, and diagonal directions at each level, resulting in 10 sub-bands (1 approximation + 9 detail bands) after three iterations. The coefficients can be visualized through coefficient matrices or energy distribution analysis for further processing applications like denoising or compression.