Performing DCT Transformation with Zigzag-Order Coefficient Retention

In this procedure, we begin by loading a 256*256 pixel image and segmenting it into multiple 8x8 pixel blocks. For each block, we implement a Discrete Cosine Transform (DCT) through mathematical operations that convert spatial domain data into frequency components. The transformation employs a cosine basis function decomposition, typically achieved using matrix multiplication with predefined DCT coefficient matrices. Following the DCT, we preserve a selected number of transformation coefficients arranged in zigzag scanning order - a pattern that prioritizes low-frequency components crucial for image quality preservation. The zigzag reordering is algorithmically implemented through index mapping that follows a diagonal traversal pattern across the coefficient matrix. Subsequently, we perform Inverse DCT (IDCT) reconstruction by applying the inverse transformation process to regenerate spatial domain data from the retained coefficients. This reconstruction process involves matrix operations that reverse the frequency-to-spatial conversion. Finally, we compute the signal-to-noise ratio (SNR) between the original and reconstructed images using pixel intensity comparisons, where SNR is calculated as the ratio of signal power to noise power, typically expressed in decibels (dB). This comprehensive workflow demonstrates core image processing techniques while providing quantitative quality assessment of compression and reconstruction effects.