validation of a pseudo jpeg compression
If you compute a $8\times 8$ 2D-DCT, and keep the top left corner only, you are keeping a quantity that is proportional to the average of each  $8\times 8$ block.  This is the DC component, similar to the $0$ frequency in a Fourier transform. This works like a JPEG coding with a quantization table looking like:

$$\displaystyle \left( \begin{array}{cccc}
1 &amp; \infty &amp; \cdots &amp; \infty\\
\infty  &amp; \infty  &amp; \cdots &amp; \infty\\
\vdots  &amp; \vdots &amp;  \ddots &amp; \infty\\
\infty  &amp; \infty  &amp; \cdots &amp; \infty
\end{array}\right)$$

Performing the inverse DCT with this "kind of" quantization spreads the average value over the $8\times 8$ block. What you are doing is equivalent to performing a moving average with an $8\times 8$ uniform window and then downsampling by  $8$ in both the $x$ and $y$ directions. You compress by replacing each $64$-pixel  block by its average, resulting (effectively) in a $64$ times smaller image, and you "fake" an original size image by extrapolating the average.

However, you cannot claim a $1/64$ compression yet, because the coefficients you keep are not quantized yet, and are stored for instance on $32$-bit floating point words. Before you go into more advanced coding, you are about at a  $1/16 = 1/64\times 32/8$ compression rate.