DWT Implementation for Two-Dimensional Wavelet Transform

This demonstration program implements two-dimensional wavelet transform for images using Discrete Wavelet Transform (DWT). The implementation follows these key steps: First, the program loads the original image matrix, typically reading image data from standard formats like JPEG or PNG and converting it to a suitable matrix representation for processing. Next, it performs a two-dimensional wavelet decomposition, breaking down the image into different frequency subbands using DWT algorithms. This decomposition utilizes wavelet filters (such as Haar, Daubechies, or other wavelet families) to separate the image into approximation coefficients (low-frequency components) and detail coefficients (horizontal, vertical, and diagonal high-frequency components) across multiple decomposition levels. Finally, the program visualizes the decomposition results by displaying the wavelet coefficients in each subband and reconstructs the source image through inverse DWT to demonstrate the transform's reversibility. The reconstruction process involves applying inverse wavelet filters to combine the subband coefficients back into the original image format. By employing Discrete Wavelet Transform (DWT), this implementation enables detailed analysis and processing of two-dimensional images. This transformation technique helps capture intricate details and features within images, facilitating better understanding and manipulation of image data for applications like compression, denoising, and feature extraction.