At night, when I want to take photos, I usually use LiveView to focus instead of the optical viewfinder. So I set my camera on a tripod, go to LiveView and use manual focusing to get the focus. But the problem here is that what appears on the LCD screen is very noisy, so the subject isn't very clear and hence is difficult to focus.
How can I reduce the noise? Can the LCD refresh rate be lowered so that it produce a brighter and less noisy image?
I use a Canon 650D.
Your LCD only outputs data from camera sensor. It could be possible to tweak software so sensor would capture more exposed scene, but at the cost of low framerate ( because exposure would have to be longer ) . If there is not much light, camera software can only incease ISO, which is artificially increasing sensitivity of sensor, hence producing noise, while still trying to keep framerate high. If somebody managed to hack it, result would be blurry 'live view' which is kind of oxymoron.
(Edit) Conclusion: it is possible if you can directly control your camera sensor.
As martinerk0 said, you could have less noise by increasing the exposure time of the live view at the cost of a low frame rate. But to do that, you have to hack the software.
What you can do instead of hacking the software (and what you are probably already doing), is take a picture with no noise, see the result, correct... and so on, by trial and error.
It is nearly the same thing as dramatically decreasing the framerate of the live view, but you have to do it manually.
The Magic Lantern custom firmware allows you to adjust the gain of the live view display (without affecting exposure of the image when you take the photo)
It may only allow you to increase gain (probably the opposite of what you want) however there are also options for turning live view exposure simulation on / off, which may achieve what you want.
If you have automatic white balance enabled, you can try using something like a "daylight" setting instead. This should result in less blue channel gain (and noise) when the scene is lit by incandescent (or other "warm") sources... at the cost of displaying the scene as very yellow, obviously.
This has the possible side benefit of giving you a more accurate histogram for shooting RAW and "exposing to the right". If you aren't shooting RAW, you would probably want to change back to the desired white balance after focusing, which may not be terribly convenient.
This may not be the answer you are looking for, thinking outside the box, (the box being the camera) may help you overcome the situation and obtain the image you want if no other option is found on time.
I use a Canon 50D and when I face similar situations, I add to the equipment a small but powerful L.E.D. torch or flashlight. It is small, powered by 3 AAA batteries.
What I do is illuminate part of the subject for focusing purposes. I do it either for live view manual focusing or even to enable auto focus on very low light situations. This can be done from the camera's position, but you can also have a friend stand close do the subject and illuminate it for you while you focus. Just tell them to hide (and turn of the light) before shooting
Of course, there are subjects that are too far away to use this trick, so depending on what is it I have two alternatives.
For starry skies or cityscapes, I use one of the light dots as a focusing reference. A reflection on a shiny object can do too. What I do is focus back and forth while looking at a bright dot. When it gets out of focus it looks like a disc, so I move the focus trying to get the disc as small as possible.
For completely dark scenes, I Use manual focus, try to focus and then intentionally defocus a little on certain direction. Then take several shots, but making very little adjustments to the focus ring in the opposite direction between shots. Repeat until you know that you are definitely out of focus again. Then select in post the shot that has the right focus. (This is some sort of focus bracketing).
A third option is to use focus scales. This are focusing markings that where mostly found in old manual lenses, so that if you knew the distance from subject to camera, you could focus by setting the lens to the corresponding marking on the focusing ring. However it is very unlikely that you have one of these lenses. I don't have one, so I make it.
I simply adhere a couple of stickers to my lens. One on a fixed part of the barrel an the other on the focusing ring. If I can access the scene during the day, then I go in that time, focus, and make the necessary markings. If not, I can calibrate the focusing on various distances by intentionally placing objects at measured distances from the lens.
However, this only works for lenses that have a solid linkage between the focusing ring and the corresponding elements inside the lens, and specially with prime lenses. On most zoom lenses, it works only for the focal distance used when the markings are made.
Bear in mind that some lenses may be sensible to temperature changes, so they can be out of focus even if set on the correct marking, so, combining this method with focus bracketing is advisable.
I have a better description of these tricks on this answer: How does one get manual focus right with a fast-aperture lens?. The question itself is relevant and other answers there may help you.
This is entirely normal and expected. The image is read from the sensor as this is Live-View. Since it is dark, ISO has to be increased in order to give you a decent refresh rate. Otherwise, you would only have one update every several seconds or minutes which would be very hard to compose with. Incidentally, a number of Panasonic cameras have such modes and I consider them useless because framing is just too difficult like that.
There is one thing you can do: Get a brighter lens. This would let more light reach the sensor and less gain would be required. Compare a typical 18=55mm F/3.5-5.6 lens with a 1.4 or even 1.2 and you will have much more light passing through and so the preview would appear less grainy.
As you write the noise level is bound to the refresh rate. If you have difficulties to focus, use the digital viewfinder.
