Two-Dimensional Discrete Wavelet Transform for Image Fusion

This article introduces the implementation of two-dimensional discrete wavelet transform using MATLAB and its application to image fusion. First, let's understand the fundamental concept of discrete wavelet transform. Discrete wavelet transform is a mathematical technique that decomposes signals or images into frequency components at different scales, enabling better analysis of signal characteristics and structural features. This paper provides a detailed explanation of the principles and applications of wavelet transformation.

I will demonstrate how to implement this transform using MATLAB programming tools with specific focus on image fusion applications. Image fusion combines multiple source images into a single composite image to enhance informational content or improve image quality. The implementation utilizes wavelet decomposition to extract different frequency characteristics from input images, followed by fusion rules to combine these features into a new image. This approach yields richer image information, thereby improving both image quality and analytical capabilities.

The technical implementation involves key MATLAB functions such as wavedec2 for 2D wavelet decomposition, wrcoef2 for coefficient reconstruction, and custom fusion rules for combining approximation and detail coefficients. The algorithm typically follows these steps: 1) Decompose source images into wavelet coefficients using multi-level decomposition, 2) Apply fusion rules to combine coefficients (e.g., maximum selection for detail coefficients, averaging for approximation coefficients), 3) Reconstruct the fused image using inverse wavelet transform.

Practical examples and code snippets will be provided to help readers better understand and apply these techniques. The MATLAB code demonstrates how to handle different wavelet families (Daubechies, Symlets, etc.) and adjust decomposition levels according to application requirements. These implementations include error handling for image size compatibility and memory optimization for large datasets.

This comprehensive guide aims to support your learning and research endeavors in digital image processing and multi-sensor data fusion applications.