I've done something which is not exactly the jpeg algorithm. What I've done is that given an image $I$ of $N\times N$ size, I have computed the DCT of individual $8\times 8$ blocks.
Once this has been done, I have imposed that the top leftmost corner is left intact but the other elements be equalled to zero.
Then i compute the inverse-DCT on that block and use it to reconstruct my image.
The algorithm seems to work giving the following results
Given that I've ignored lots of steps in the jpeg algorithm (all the things related to huffman encoding, quantization matrix etc) why is this simple algorithm working?