Final answer:
The student's question pertains to image compression and reconstruction using Discrete Cosine Transform (DCT), involving the trade-off between compression ratio and image quality. To perform the compression, only the top 10 DCT coefficients are kept for each 8x8 block. This introduces potential image quality loss and an increase in mean square error, both quantified in the task.
Step-by-step explanation:
The student's question involves the process of image compression using Discrete Cosine Transform (DCT) and how it affects the quality of the resulting image. The question asks to divide an image into 8x8 non-overlapping blocks, compute the DCT for each block, and then compress the image by keeping only the top 10 largest magnitude DCT values for each block.
The compression ratio is the measure of how much the image size is reduced, and it can be calculated by comparing the number of bits needed to store the original versus the compressed image. Following compression, an inverse DCT is applied to reconstruct the image, after which the quality of the reconstructed image and the mean square error (MSE) is evaluated.
The mean square error gives us a quantitative measure of the accuracy of the reconstructed image compared to the original. By only keeping the top 10 DCT coefficients, we are significantly reducing the amount of data needed to represent each block. However, since we are discarding many coefficients, this results in lossy compression.
Lossy compression can lead to a decrease in image quality, exhibited by artifacts or blurring of the reconstructed image. High compression ratios typically result in more noticeable image quality degradation. Furthermore, the mean square error will likely increase as the compression ratio goes up, indicating a higher discrepancy between the original and the reconstructed image.