Can one alter their auditory perception? I'm coming from the idea that the way we perceive sound is a reaction to a certain signal, sent to our brain by ears. Of course this feeling intensifies as volume of the sound increases and our ears send us a stronger signal. 

Now here I am wondering if we can augment that signal in our brain, so when the volume stays the same - we will be able to perceive it louder. Can that be done without any kind of chemical or surgical intrusion, just by sheer force of will? Do such perception "controllers" even exist and we just haven't learned to control them?
This question is about auditory system, but since it touches the brain signal interpretation you could explain this from a different perspective (visual or even tactile).

This isn't part of the question, but I also wonder, if previous is possible, than can the same be done to mentally create sounds in your head and hear them as if they were real..?
Imagine a music recording studio, with a band playing in the soundproof room.  Now imagine 2 mic->speaker connections: A mic inside the room records the music, and plays it on a speaker outside, and then another mic records the sound coming out of that speaker, and delivers it to the recording equipment.  You can imagine the loss of quality involved in that set up I'm sure, but bear with me.  Both mic->speaker connections are set to 50% volume.  Say we want to increase the volume: We can increase the volume on either connection (or both).  If we increase the volume to 100% on only one of the 2 connections, then the volume of the recorded sound will increase by approximately the same amount whichever one we choose.  However, increasing the volume of the first connection is better - it results in a better quality recording.  This is because each connection can only lose quality, not add it.

Now, supposing that the first mic->speaker connection represents the auditory nerve (ear -> primary auditory cortex), and the second connection represents "perception" (auditory cortex -> rest of brain), then we can discuss increasing the "volume" at either "connection" via conscious control (I'm assuming that this is what you mean by "force of will").

The auditory nerve passes through the central auditory system, an area of the brain considered unconscious:


  Damage to the Primary Auditory Cortex in humans leads to a loss of any
  awareness of sound, but an ability to react reflexively to sounds
  remains as there is a great deal of subcortical processing in the
  auditory brainstem and midbrain.


In other words, so far as we know, there is no conscious control over this "connection".

Neuroplasticity of "perception" is much greater.  A variety of studies have shown certain improved hearing capabilities in blind people, correlating with how early hearing loss occurs (the earlier the better), and the involvement of neuroplasticity as the visual cortex can be usurped for auditory processing.  Whether or not this corresponds to a change in "volume" is unclear, and this effect does not appear to be "consciously" controlled.

However, more recent research has demonstrated how similar effects can be induced in non-blind adults: Through temporary blindness (as little as 90 minutes with a blindfold).  Corresponding research on mice has shown that this may be the result of increased "volume" in perception:


  The cells fired faster and more powerfully in response to sounds and
  were more sensitive to quiet sounds.


So not exactly "sheer will", but temporary blindness, that you can easily induce on yourself consciously, may improve certain aspects of hearing, possibly including "volume".

Hope this helps.