How the noise in time series can be reduced? I have asked the question in the following link: Are time series data always contain noise?
I wonder if we could use variational methods to denoise the time series data just as in computer vision? 
Thanks in advance...
Yes indeed, there is a huge body of works on the topic of variational methods for signal restoration (more general than denoising), one example being total variation denoising, or proximal methods.

If you can be more specific, you could get more accurate and precise answers.