postgis - Retrieve polygon smallest MBR

I have a postgis table containing polygons. I want to transform my polygons to 4 points polygons : retrieve the smallest MBR.

Here comes an illustration of what I want :

My original polygon is in pink color. I guess, it will be quite easy to get the MBR (with ST_Envelope and BBox function) But is there an easy way to get what I want?

Any ideas? Many thanks