MATLAB Code Implementation for Wavelet Decomposition

This text demonstrates the application of MATLAB's wavelet decomposition technique for image processing. Wavelet decomposition is a method that breaks down signals or images into sub-signals or sub-images at different frequency bands. By performing a 3-level wavelet decomposition on an image, we can extract more detailed structural information and frequency components. The implementation typically involves using MATLAB's Wavelet Toolbox functions like wavedec2 for 2D wavelet decomposition, which returns approximation coefficients and detailed coefficients (horizontal, vertical, diagonal) at each level. The reconstruction process utilizes the waverec2 function to synthesize the decomposed wavelet coefficients back into an approximate reconstruction of the original image. This approach finds applications in image processing, signal analysis, and data compression, where it helps in feature extraction, noise reduction, and efficient data representation through multi-resolution analysis.