Enable DSR factors (Nvidia)/VSR (AMD) in graphics card control panel if you have lower than 4K display. Set DSR smoothness to 15%.

Download ReShade: https://reshade.me/

Download ReShade preset: https://drive.google.com/file/d/1bayDe4s2caVhKAGPh3HIWNsU8577dsJ7/view?usp=sharing

Download Flawless Widescreen: https://www.flawlesswidescreen.org/

Open regedit: https://support.microsoft.com/en-us/windows/how-to-open-registry-editor-in-windows-10-deab38e6-91d6-e0aa-4b7c-8878d9e07b11

RUN THE GAME AT LEAST ONCE and go straight to the video settings menu.
Set resolution to 3840x2160.
Check all other boxes except Depth of Field (DOF) and Distortion. Leave those off.
Set the brightness so that the left symbol is completely invisible and the center one is quite dim.
Apply and quit out of the game.

Go to regedit and find: HKEY_CURRENT_USER\Software\Activision\Singularity
Look for: MaxAnisotropy
right click and select modify, choose decimal type and change to 16
You will notice other settings you can change here, the following is a list of changes I made to my install which did not result in any issues:
AmbientOcclusion (1)
MotionBlur (0)
MinShadowResolution (128)
MaxShadowResolution (2048)

Double click on reshade executable. Direct it at ...\steamapps\common\Singularity\Binaries\Singularity.exe. Select DX9 rendering API. Choose sweetfx and quint shader packs. When installed click on edit reshade settings and check the 'skip tutorial' box. Put the ReShadePreset.ini into the same folder:
(...\steamapps\common\Singularity\Binaries)

Install Flawless Widescreen, or load it up. Look for the entry for Singularity, set the resolution at 3840x2160 and go to next step. Make sure the 'Fix Enabled' box is ticked. Don't mess with the FOV fine tuning yet. You can minimize Flawless Widescreen and it will stay in the Quick Launch area. FOV fix won't work if it's completely shut down.

Load up the game and check that the reshade is working by pressing Home key and looking at the overlay. Go to the settings tab to set a key for toggling the effect. I'll probably come back and update the reshade preset as I play through the game but it's a pretty simple filter and a similar or better effect can be easily achieved by tinkering with same or other shaders.

I'll post some screenshots and video when I get a chance.

Enjoy the game!