I'm making a coffe table with an LED intergrated in it
...
I want this table to be driven by a computer which uploads to arduino which reads from serial and it saves the picture somehow and display it on the table.
Does "LED" mean a TFT display like a small GLCD or LED 8*8 matrix or bigass flat screen like the size of the table?
What is the source of picture to display? What resolution in pixels are you planning to work with?
Mang GLCD libraries have example routines to read BMP from SD cards and displaying on small screens. One could run an algorithm against the BMP stream to remap to a LED matrix.... This is in theory and the algorithm would need to manage grayscaling too. This concept should work but I know of no example code to bootstrap a prototype.
Your write up does a poor job at describing what you wish to do... No product models, no links, no expectation of costs, ... Etc. You need to be specific.
Ray