Somebody else just asked me about this today, so I did a search......getting excited....the answer is a very big YES !

You need a program called RetroArch, which is sort of a front end for different emulator 'Cores', the core for the PS1 is called Beetle PSX HW.
Most of the cores are preloaded with the program, you just have to check that they are up to date.
http://www.retroarch.com/index.php?page=platforms

So how good can you get PS1 games looking on a 4K screen?
Checkout just how stunningly good this emulation of FFVII is, I was absolutely blown away when I first saw this.
Make sure you have a blank piece of A4 paper and a pen with you when you watch this video, as the as the video plays the guy gives the various settings he has used to get the results, you'll see them typed up on the top right of the screen.



Also see this forum where I first heard about it.
https://www.resetera.com/threads/ps1...-ffvii.109469/

I'm going to be trying this stuff over the weekend.