Question: Why are rebreathers used for underwater photography and covert work?
About the article "Scuba diving", section "Rebreather".

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Media Diving is a term used to describe divers engaged in underwater photography and underwater cinematography outside of normal recreational interests.
Media Diving is often carried out in support of television documentaries, such as the BBC series Planet Earth or Hollywood blockbusters, with feature films such as Titanic and The Perfect Storm featuring underwater photography or footage.
Media divers are normally highly trained camera operators who use diving as a method to reach their workplace, although some underwater photographers may start as recreational divers and move on to make a living from their hobby.
Equipment in this field is varied with scuba and surface supplied equipment used, depending on requirements, but rebreathers are often used for wildlife related work as they are normally quiet, release few or no bubbles and allow the diver a lengthy bottom time with a reduced risk of frightening off the subject at hand. 
Less common are closed circuit (CCR) and semi-closed (SCR) rebreathers, which unlike open-circuit sets that vent off all exhaled gases, process all or part of each exhaled breath for re-use by removing the carbon dioxide and replacing the oxygen used by the diver.
Rebreathers release little or no gas bubbles into the water, and use much less stored gas volume, for an equivalent depth and time because exhaled oxygen is recovered; this has advantages for research, military, photography, and other applications.
Rebreathers are more complex and more expensive than open-circuit scuba, and special training and correct maintenance are required for them to be safely used, due to the larger variety of potential failure modes.
In a closed-circuit rebreather the oxygen partial pressure in the rebreather is controlled, so it can be maintained at a safe continuous maximum, which reduces the inert gas (nitrogen and/or helium) partial pressure in the breathing loop.
Minimising the inert gas loading of the diver's tissues for a given dive profile reduces the decompression obligation.
This requires continuous monitoring of actual partial pressures with time and for maximum effectiveness requires real-time computer processing by the diver's decompression computer.
Decompression can be much reduced compared to fixed ratio gas mixes used in other scuba systems and, as a result, divers can stay down longer or require less time to decompress.
A semi-closed circuit rebreather injects a constant mass flow of a fixed breathing gas mixture into the breathing loop, or replaces a specific percentage of the respired volume, so the partial pressure of oxygen at any time during the dive depends on the diver's oxygen consumption and/or breathing rate.
Planning decompression requirements requires a more conservative approach for a SCR than for a CCR, but decompression computers with a real time oxygen partial pressure input can optimise decompression for these systems.
Because rebreathers produce very few bubbles, they do not disturb marine life or make a diver’s presence known at the surface; this is useful for underwater photography, and for covert work.
The closed-circuit type filters, supplements, and recirculates exhaled gas: see rebreather for more information.
It is used when a longer-duration supply of breathing gas is needed, such as in mine rescue and in long tunnels, and going through passages too narrow for a big open-circuit air cylinder.
Before open-circuit SCBA's were developed, most industrial breathing sets were rebreathers, such as the Siebe Gorman Proto, Siebe Gorman Savox, or Siebe Gorman Salvus.
An example of modern rebreather SCBAs would be the SEFA.
Rebreathers used underwater have the advantage of not releasing tell-tale bubbles, making it more difficult to detect divers involved in covert operations (see frogman). 
Breathing sets.
Frogmen's breathing sets on covert operations should have particular features.
Some are needed because they may need to swim fast and far.
Some are needed to avoid detection.
Sometimes patrol divers may have to be sent down to find or arrest submerged suspect divers.
For reasons stated in Anti-frogman techniques#Sending other frogmen against them, underwater fights between divers are much rarer in reality than in fiction, and thus suitability of the frogman's kit for "diver to diver combat" is less important than some other features when designing it; but the point is considered here for completeness.
USA frogmen's rebreathers tended to have the breathing bag on the back before enclosed backpack-box rebreathers became common. 
 "For the construction and design of rebreathers, see Rebreather."
Rebreather diving is underwater diving using rebreathers which recirculate the air already used by the diver after replacing oxygen used by the diver and removing the carbon dioxide metabolic product.
Rebreather diving is used by recreational, military and scientific divers where it has advantages over open circuit scuba, and surface supply of breathing gas is impracticable.
Rebreathers are generally used for scuba applications, but are also occasionally used for bailout systems for surface supplied diving.