MATLAB Implementation of 2D Discrete Wavelet Transform for Image Processing

Using two-dimensional discrete wavelet transform (2D DWT), an image can be decomposed into different frequency subbands and subsequently reconstructed to recover the original image. This process leverages wavelet properties to extract various frequency components from the image, enabling detailed analysis and processing of image data. The implementation typically involves using MATLAB's wavelet toolbox functions such as wavedec2 for decomposition and waverec2 for reconstruction. During decomposition, the image is separated into approximation coefficients (low-frequency components) and detail coefficients (horizontal, vertical, and diagonal high-frequency components) through filtering and downsampling operations. Through image decomposition and reconstruction, we can obtain richer image information and perform various image processing and enhancement operations. The 2D DWT algorithm employs filter banks with quadrature mirror filters that maintain perfect reconstruction properties when certain conditions are met. Key parameters include wavelet type selection (e.g., Haar, Daubechies), decomposition level specification, and thresholding techniques for denoising applications. Therefore, two-dimensional discrete wavelet transform serves as a powerful image processing tool that helps researchers better understand and manipulate image data through multi-resolution analysis, with applications in compression, denoising, and feature extraction.