Principles of Wavelet-Based Image Enhancement with Algorithmic Implementation

This article is tailored for readers new to wavelet theory, focusing on the foundational knowledge of wavelet-based image enhancement principles. We will demonstrate this concept through rigorous high-frequency and low-frequency decomposition and reconstruction methods, avoiding the use of pre-built wavelet toolboxes for demonstration purposes. Additionally, we will delve into relevant concepts of wavelet analysis to facilitate better understanding. The implementation involves manually coding decomposition filters (like Haar or Daubechies filters) for frequency separation, thresholding techniques for enhancement processing, and inverse wavelet transforms for reconstruction. Key algorithmic steps include: 1) Multi-level wavelet decomposition using convolution operations, 2) Coefficient thresholding for noise reduction/enhancement, 3) Reconstruction through inverse filtering operations. This hands-on approach ensures deep understanding of wavelet transform mechanics rather than toolbox abstraction.