Dear Sahar,

Some approaches merging PCA/WT or ICA/WT for denoising exist:

Follow:

Starting with the first reference, it might be possible to extend to MRI denoising by substituting PCA by ICA. Indeed, ICA differs from PCA by decorrelating up to 4th (or higher) statistical order.

Regards

Article A New Approach to Denoising EEG Signals-Merger of Translatio...

PCA can help in obtaining a sparse representation in MRI transform domain. PCA can be adaptive to the image which may give more efficient representation of the image. Also PCA with other methods like rotational invariant NLM as a two stage process can be used for denoising. Following are some papers:

1. Multicomponent MR image denoising

https://dl.acm.org/citation.cfm?id=1807584

2. A MRI Denoising Method Based on 3D Nonlocal Means and Multidimensional PCA

https://www.hindawi.com/journals/cmmm/2015/232389/ref/

3. Complex denoising of MR data via wavelet analysis: Application for functional MRI

http://www.sciencedirect.com/science/article/pii/S0730725X99001009

etc...

That's a very delicate question. Could be more specific in your question? Are you working on fMRI or structural MRI? Is your work theoretical or are you working with real images? Have an idea of the origin of the noise? Good luck! 

I am trying to write a review paper about MRI denoising methods in Transform domain.I read that wavelet ,curvelet and contourlet are in this domain but I decided to add wave atom and Discrete cosine Transform and BM3D and ICA and PCA to this category. I want to know am I right by putting these methods in Transform domain category?My main concern is about PCA and ICA. Thanks

Hi, Sahar,

In my opinion, you should not put PCA and ICA methods in Transform Domain, once they are not related to a formal transform like Wavelets or even Fourier. Why do not you write a section on statistical approaches and put PCA and ICA there?

Best wishes.

Hi Wellington Pinheiro Dos Santos . Thanks for your reply. I read in a book about PCA. The book is 'Statistical Analysis of Noise in MRI Modeling, Filtering and Estimation by

Santiago Aja-Fernández Gonzalo Vegas-Sánchez-Ferrero'

I want to write a review paper just about MRI denoising methods in transform domain.I have searched a lot but did not get a fixed opinion about methods in transform domain.