Why does the high frequency component of an image contain more noise? I am working with wavelet transforms. When we apply a discrete wavelet transform to an image, it decomposes into four components named the approximation component, thevertical component, the horizontal component, and the diagonal component. 

These components are indicated as LL, HL, LH, HH respectively. I understand how an image is decomposed by using a wavelet transform, but I don't know why generally in an image high frequency component contain more noise.
There are different types of noise sources in imaging process. 

Photoelectronic

photon noise: Poisson distribution, whole spectra;

thermal noise: Gaussian distribution, white noise, whole spectra;

Impulse

salt and pepper noise: mainly high frequency noise; (@user7358 made a very good point on the reason).

line drop: part or all of a line in the image lost, can be viewed as a deterministic high frequency noise;

Structured

periodic: low frequency noise;

aperiodic: JPEG noise, low frequency too;

detector striping: calibration differences among individual scanning detectors, mainly low frequency;

If you only observe the evident noise when you zoom in the high frequency band with wavelet, I assume it is mainly the shot noise (salt and pepper). When you are doing some simulations with noise added, try (1) salt and pepper,  (2) Gaussian, and (3) Gaussian with a high-pass band applied, and observe the difference after wavelet decomposition.