Keeping your LED cool with PWM
You can indeed achieve higher brightness by PWMing an LED. You can also (sometimes) achieve better power efficiency. But those things are usually mutually exclusive.

If you turn an LED on for 50% of the time, and off for the other 50%, you will decrease its perceived brightness by about half. This creates a lower brightness with less power consumption (provided you are providing it the same current).

The same goes for the other way. You can provide a higher current in a short PWM cycle to achieve higher brightness. Keep in mind that this usually uses more power and can shorten the life of the LED. The extent of these drawbacks depends on how much current you are applying to the LED and for how long (depends on the PWM cycle you decide to use).

If you look at a data sheet for a 1 Watt LED you will see there is a DC forward current and a Pulsed Current.

Your specifications will likely differ but for this LED:


DC Forward Current: 350ma
Pulsed Forward Current: 700ma


The manufacturer also specifies a Typical Period (TP) of 100uS and a duty cycle of 0.005.
This means that 1 cycle takes 100 microseconds and the LED is on for 0.5% (0.005 x 100).
That means that if implemented as the specification says the LED will be on for 0.5us then off for 99.5us. 

The most useful thing is that it keeps the LED cool. The LED is turned on for a small period and off for a larger period while it cools down.

To achieve what you want, higher brightness, you can certainly over power the LED at small duty cycle. Just be aware of the consequences of more heat and potentially less life time.

To tell how much current you should apply to achieve your desired results, you should be able to look at your LED Spec sheet. It should have a graph of current (ma) against luminosity (lumens).
In general you can see what the apparent brightness is with:
Apparent Brightness = Luminosity x Duty Cycle