Two-Dimensional Discrete Wavelet Transform for Image Decomposition, Reconstruction, and Error Analysis

This code provides implementation for two-dimensional discrete wavelet transform decomposition, image reconstruction, and error image generation. The implementation focuses on wavelet-based image processing techniques suitable for applications such as image compression, denoising, and feature extraction. The algorithm performs wavelet decomposition by applying filter banks in both horizontal and vertical directions, separating the image into four subbands: approximation coefficients (LL), horizontal details (LH), vertical details (HL), and diagonal details (HH). This multi-resolution analysis enables extraction of image details and features at different frequency scales. For reconstruction, the inverse discrete wavelet transform is applied using synthesis filter banks to combine the subband images back into the original image space. The implementation includes proper upsampling and filtering operations to ensure accurate reconstruction. The error analysis component calculates the pixel-wise difference between the original and reconstructed images, generating an error image that quantifies reconstruction accuracy. This error metric is particularly useful for evaluating compression quality and transformation fidelity. Key functions include wavelet family selection (Daubechies, Haar, etc.), decomposition level specification, and thresholding options for compression applications. The code serves as an educational tool for understanding wavelet transforms' role in digital image processing while providing practical implementation for real-world applications.