DCT Block Operations on Images with Wavelet Transform Analysis

This article outlines a comprehensive image processing workflow through the following key steps: First, we select an input image and divide it into 8×8 pixel blocks. Each block undergoes Discrete Cosine Transform (DCT) processing, which can be implemented using MATLAB's dct2() function or similar libraries. The DCT conversion helps concentrate image energy into fewer coefficients, making it fundamental for compression algorithms. Second, we apply a masking matrix to selectively preserve specific DCT coefficient regions while zeroing out others. This frequency-domain filtering operation is followed by Inverse DCT (IDCT) using idct2() to reconstruct the image. To quantitatively evaluate reconstruction quality, we calculate the Peak Signal-to-Noise Ratio (PSNR) between original and synthesized images, where higher PSNR values indicate better preservation quality. Third, we employ wavelet transform analysis by selecting an appropriate wavelet function (e.g., Haar, Daubechies). The image decomposition using functions like wavedec2() generates multi-resolution coefficients (approximation and detail components). We display these coefficients to observe their hierarchical patterns and statistical distributions. Finally, inverse wavelet transform through waverec2() reconstructs the original image, demonstrating perfect reconstruction capabilities when using orthogonal wavelets. These steps provide detailed insights into image processing techniques, showcasing practical implementation of both DCT-based block processing and wavelet transform methods for image analysis and synthesis.