The phrase "a perceived increase" is correct and usable in written English.
It can be used when discussing an increase that is recognized or believed to exist, even if it may not be objectively measurable.
Example: "The survey indicated a perceived increase in customer satisfaction over the past year."
Alternatives: "an apparent rise" or "a noticeable growth".
In the present study we show that a visual illusion, which induces a perceived increase in a step's riser height, results in increased safety during subsequent step negotiation because of an accompanying increase in toe elevation.
It was a perceived increase in the latter that raised the original question leading to this debate.
It is often implemented when there is a perceived increase risk of self-harm.
The MCC is set to launch a trial with club, university and schools cricket in 2017 to eradicate a perceived increase in excessive sledging and violent behaviour.
Participants using HindSight had fewer collisions, increased their space to other vehicles, experienced reduced cognitive load, and reported a perceived increase in awareness.
Twenty years ago, when I was working at the House of Commons, a perceived increase in threat led to an enormous ratcheting up of security throughout the building.
The decision to significantly expand the infrastructure for monitoring political campaigners was taken in the late 1990s, amid an perceived increase in activity by animal rights and environmental campaigners.
In April the US embassy in Berlin announced a strengthening of security at diplomatic and military facilities in Germany in response to a perceived increased terrorist threat.
SEMS placement for cancers near the upper esophageal sphincter (UES) is controversial because of a perceived increased risk of complications.
Cannulation of the LIJV is associated with a higher complication rate and a perceived increased level of difficulty when compared with cannulation of the RIJV.
"Together with a perceived increased risk of default on the sovereign debt of certain European countries and unprecedented stresses on the financial system within the eurozone, these factors have resulted in significant changes in market conditions including interest rates, foreign exchange rates, credit spreads, and other market factors and consequent changes in asset valuations".
