Cross-Correlation for noise reduction

Dear All,

I have two signals one is highly noisy (x1) and the other has less noise (x2) where the original signal x is the same. I want to denoise the signal (x2), and the fisrt method comes to my mind is using cross-correlation method, provided that I dont know the original function form and only have these two noisy sequences. However I am not sure how to do this. Accosring to my understanding, the cross correlation returns peaks where these signals are correlated as a fuction of lag and not return a denoised time domain signal. Can I use cross-correlation method to get third time-domain (which should be near or the same of x) signal let say x3 with less noise than x1 and x2?

Your omments are highly appreciated.

t=0:0.001:10;
x=sin(t);
x1=x+0.5*rand(size(x));
x2=x+0.1*rand(size(x));

[Gabriel H Gosselin]

Hi, I am facing a similar problem to the one you described in this post where noise is introduced in "Sensor A" by a process measured by "Sensor B". My first thoughts were along the lines of using cross correlation and I found your post.

The ICA method suggested above could be uesd by iteratively comparing its independent components to the "Sensor B" time series, but I think it should be possible tio directly use that time series to denoise the "Sensor A" time series.

May I ask what kind of method you ended up using?

Several aspects of signal processing are still rather new to me. Any pointers would be greatly appreciated!

Answer 1

[Image Analyst]

Have you considered using a wiener filter (very simple with toolbox function) or BSS (blind source separation) or ICA (Independent Components Analysis) (both more complicated) to tease out your true signal?

ICA

ICA2

ICA3

Or consider using a lock-in amplifier to capture your signal without noise to begin with?

[Alin Brad]

Thank you for answer. I am investigating specifically using cross-corrrelation since most of these methods already employed. any suggestions for cross correlation? can I obtain time domain signal?

[Image Analyst]

Then why don't you use one of those methods already employed?

[Alin Brad]

Because want to introduce a new approach for noise reduction using cross-correlation

[Image Analyst]

Sorry, that's not what I want to do. Besides if I invented the new approach, it wouldn't be you introducing it, it would be me. If you want to introduce/invent a new approach, like for your MS or PhD, please go ahead. We won't be inventing algorithm for you but would be happy to answer any questions about MATLAB syntax or error messages that you have. Attach your code in that case.

[Alin Brad]

My main concern was if the cross correlation could reduce the noise and obtain the correspnding time signal. Of course I will develope the algorithm. General speaking, I am asking about the concept. Thank you

[Image Analyst]

I believe it can, and I think that is at the heart of the concepts of BSS and ICA. Have you studied up on those? Or even heard of them? Sorry but they're not my strength so I can't help much with them, but at least I let you know about them, and you have to know about existing algorithms before you can come up with your own new and improved algorithm. There may be other techniques I'm not familiar with. But anyway, good luck with your research.