In de-nosing of any signal or image the thresholding is applied on the high frequency or detail coefficient of discrete wavelet transformed (DWT) signal. However it is always assumed that the low frequency component (Approximation coefficient) is less affected by noise, why?
Hi! The corruption of a signal is mainly a big change of the amplitude of the signal compared with the original (the signal is supposed to be smooth). Thus, a signal of low frequency really do not represent a great change in the whole signal because it represent a small portion of the information if we take a fix period of analysis. If we increase the frequency of the signal, the change produced by noise represents a higher proportion of the whole signal and the corruption is higher compared with the low frequency signal.
A signal-to-noise (SNR) ratio is by definition signal-dependent. For audio signals (like speech, music, and other sounds we can hear) part of the answer is that low frequencies are typically much stronger than high frequency components for various physical reasons (the 10th harmonic of a violin tone is about 1/10 the amplitude of the fundamental component, for example). In addition, musical instruments that produce low frequencies are generally much larger than high-pitched instruments (consider the size differences between a tuba and a piccolo, for example). The reason for the size difference has little to do with the frequencies produced (a 1-inch string can vibrate at any frequency, theoretically, depending onn the tension and its mass per unit length, for example). Low-pitched instruments tend to be large because human hearing is much less ssensitive to low frequencies than higher ones (the threshold of hearing at 20 Hz is about 70 dB SPL greater than the threshod of hearing at 1000 Hx, which mean that in order to be barely heard at all, a 20 Hz tone would have to at least 107 times the power of a 1000 Hz tone.
No matter what the signal power, though, noise tends to have roughly the same power at all frequencies, so it is easy to see why the SNR for low frequencies would be much greater than that for higher frequencies, at least in the case of audio signals. In terms of human hearing, white noise (which has equal power at all relevant frequencies) with a level of 0 dB SPL would mean a barely audio tone at 20 Hz would have an SNR of about 70 dB, while a barely audio tone at 1000 Hz (with the same noise) would have an SNR of 0 dB.
Other signal types (such as video signals) may have different frequency distributions, but their SNR at any frequency still is the ratio of the signal at the frequency (which varies widely) to a noise "floor" which tends to be more-or-less constant at all frequencies.
Another way to put all this is simply that signals by definition concentrate their power at certain frequencies, while noise tends to spread its power evenly over all frequencies.
There are different types of noise. For many purposes, You will deal with white noise, then, by the averaging properties of the coarse parts of wavelet transforms, these will be affected only little by noise.
However, if you have to deal with 1/f-Noise, this does niö k k
Sorry for the typos, I sent the above message out of a travelling train, the connection was poor.
The last sentence should read: ... this does not necessarily apply.
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