Image Decomposition Using wavedec2, appcoef2, and detcoef2 for Wavelet Analysis

In MATLAB, we can utilize the classic wavelet functions wavedec2, appcoef2, and detcoef2 to decompose images and extract high/low frequency coefficients for effective image compression and reconstruction. The wavedec2 function performs a 2D wavelet decomposition of the image, returning the wavelet decomposition vector and corresponding bookkeeping matrix. appcoef2 is then used to extract approximation coefficients (low-frequency components) from the decomposition structure, while detcoef2 extracts detail coefficients (high-frequency components) representing horizontal, vertical, and diagonal details. These functions form the core implementation for wavelet-based image processing, where the decomposition level and wavelet type (such as 'db1' or 'haar') can be specified as parameters. The extracted coefficients enable selective processing where high-frequency coefficients can be thresholded for compression, and the image can be reconstructed using waverec2 function by combining modified approximation and detail coefficients.