Room correction, DSP for dummies.

@recluse -- if you want to experiment on a relatively low cost basis, here's an option for you.

Buy a Raspberry Pi 3B+ or 4 ($30 or $40) along with a HiFiBerry DAC+DSP Hat (under $100 and fits on the RPI). A case for the boards, a power supply and an SD card might be another $25.  The needed HiFiBerry OS system is a free download.  Finally, you'll need a measurement microphone with a USB connection; there are a number of options for $100, give or take. 

Set up the RPi/DAC card and use it as a player into a line-level input on your stereo. The HiFiBerry OS has an option where, using the measurement microphone, it will measure the frequency response of your speakers in your room.  Once done that'll show you a graph of the response and give you options to make corrections -- bass only or several broader choices. 

The OS also has the option to do custom equalizations if you have others ideas in mind. 

Obviously this is something that requires a LOT of experimentation, but it gives an effective way to investigate your DSP options without throwing down big bucks. 

dsyckx, check out my system page and you will see an advanced DSP system at work.

Same with my page.

Erik, the best room correction systems merely create a mirror image filter to the speakers frequency response in a given room and give you the arrival time of each individual speaker. Some will also calculate the delays required to make the sound of each speaker get to the microphone at the exact same time. After that all the choices are yours. Unfortunately a large proportion of clients had no idea what to do with those choices and made a f---ing mess out of it. So manufacturers started making those decisions for people such as with DEQX and Anthem units but even with these units if you care to dog deeper you can wrestle control away from them. Most are not so inclined.
You can not just ignore the room. You still have to block early reflections and set up subwoofers correctly. The filters can only do so much. 
IMHO you can not get to the seventh level without correction but you have to do everything else with it or it is just a waste. 

Room control does not "release the speaker from the room." Nothing does that. It helps to blend them together to get to the right result along with sensible acoustic measures such as sound deadening in the right locations. It's most important function is to make the frequency response of both channels exactly identical. This is the way you get the best imaging. Next is to tailor the system frequency response to specific situations. There is not one setting that suits all. I have 14 different settings in memory which I use regularly. Some of them I have shown on my system page which you should visit if you have an interest in this.
The best room control system available today is by Trinnov. Lyngdorf's room perfect is a simplified bastardized version of the system Radomir Bozevic developed for TACT 25 years ago. It is room control for dummies. But, Lyngdorf survived and Radomir did not. The dummies far out number the digital electronics engineers. If only Radomir had come up with better instruction manuals.