MATLAB Implementation of Wavelet Multi-Scale Decomposition for Image Reconstruction

This program implements wavelet multi-scale decomposition to extract approximation coefficients and detail coefficients for reconstructing the original image. The process is based on principles of signal processing and image analysis, where signals are decomposed into different frequency bands at multiple scales to capture detailed image information. Wavelet multi-scale decomposition serves as an effective technique applicable across multiple domains including image compression, image enhancement, and image restoration. The MATLAB implementation typically involves using wavelet transform functions like wavedec2 for 2D decomposition and waverec2 for reconstruction. The algorithm works by recursively applying wavelet filters to separate image components into approximation coefficients (low-frequency components representing the main structure) and detail coefficients (high-frequency components containing fine details). Key implementation steps include: - Selecting appropriate wavelet basis functions (e.g., Haar, Daubechies) - Specifying decomposition levels using wavelet transform functions - Extracting approximation and detail coefficients from the decomposition structure - Applying reconstruction algorithms to recombine coefficients By extracting and properly recombining these coefficients, we can reconstruct the original image with enhanced clarity and detail resolution. Therefore, wavelet multi-scale decomposition for image reconstruction represents a common and effective methodology that enables better understanding and analysis of image data through multi-resolution analysis. This approach is particularly valuable for applications requiring precise feature extraction and noise reduction in digital image processing.