8x8 Block-Based DCT Image Transformation with JPEG Quantization

This program implements discrete cosine transform (DCT) image processing based on 8x8 pixel blocks. The implementation involves dividing the input image into 8x8 blocks and applying 2D-DCT to each block using matrix multiplication operations. After transformation, quantization is performed using JPEG standard quantization matrices, which involves element-wise division of DCT coefficients by corresponding quantization table values. Dequantization is then applied by multiplying the quantized coefficients with the same quantization matrix values. The image reconstruction process employs inverse DCT (IDCT) transformation on each 8x8 block, converting frequency domain coefficients back to spatial domain pixels. The implementation typically uses floating-point calculations for DCT/IDCT and requires proper rounding and clamping to maintain pixel value ranges (0-255 for 8-bit images). For experimental evaluation, a 512×512 pixel image with 8-bit depth per pixel is used as the test subject. The Peak Signal-to-Noise Ratio (PSNR) is calculated to quantify reconstruction quality, comparing the original and reconstructed images using mean squared error computation while considering the maximum possible pixel value (255 for 8-bit images).