I think you need to be more specific.

Tell us about your current level of understanding about the topic (DCT). How much do you know about JPEG/JFIF? Can you write a simple software decoder for JPEG?

And one more thing. Maybe I underestimated you. But have you ever used hex editor before? I bring this issue up because I've seen beginners not knowing anything about bytes and what makes up a file. To study a file format, you should start by opening the file you want to study in a hex editor.

Back to the "project". It seems to me like your project explores the mathematics and algorithms of DCT, which I think can make your project stand out from others. The common people might do something like application of image compression in some kind of innovative system, which they do not need to know about how image compression is achieved.

Now the bad news is you stand a very low chance to succeed. I assume you are trying to optimize DCT algorithms to run faster. But this has already been done by many people from the world, eg. Chen. Or maybe you want to refer to JPEG, then make some modification and improvement to suit a particular application?

Or this image compression is just a small part of your project? If this is the case, why not just use a JPEG library? But why do I see the word "DCT"?

So you have to show your instructor that you can write a program that compresses images with the usage of DCT? And actually what are the main objectives of your project?

It is a long way to go. Start by analyzing JPEG file, then write a decoder for JPEG.