[Camino-users] How to derive the noise variance

[Philip A Cook]

Hi Michael,

Sorry for the delay in getting back to you. In answer to your questions,

1.

Yes, this formula is valid if the noise is Rician distributed, however as Dietrich et al [JMRI 26:376-385 (2007)] showed, this is often not the case. You have to be careful doing it this way, the background can often become structured in various ways.


2, and 3:

The noise standard deviation should be used, I have updated the tutorial to remove the reference to the variance. Sorry about that.

Many people have found that a larger estimate of \sigma (compared to what estimatesnr says) improves results. RESTORE classifies outliers as anything with a residual more than 3 * \sigma. The constant 3 can't be modified at run time but the estimate of \sigma can be increased to give the same effect. This won't affect the regression algorithm that computes the DT, because that uses constant weights as a first pass, and the Geman–McClure M-estimator (derived purely from the residuals) after that.   

Another problem is that the noise can be spatially varying. I usually run estimatesnr with a few ROIs in major white matter structures around the brain, and take the average.


On Nov 3, 2011, at 4:11 AM, Ed Gronenschild wrote:

> Hi,
> 
> I'm sorry that I did not correctly formulated my question.
> There are a few things I want to clarify in relation to
> using RESTORE:
> 
> 1.
> The man page on estimatesnr tells that the noise standard
> deviation can be estimated as
> 
> sigma = sqrt( 2.0 / ( 4.0 - pi ) ) * stddev( bgnd signal).
> 
> In my case: stddev( bgnd signal) = 1.10, so that would
> result in sigma = 1.68
> 
> Is this the value I should pass to RESTORE?
> 
> 2.
> I've downloaded the DIG ActiveAX data set as illustrated
> in the DTI tutorial. I've derived the sttdev of the
> bgnd signal and found a value of 107. According to
> the formula above this would result in a sigma of 162.
> However, in the tutorial you are using sigma = 200.
> 
> 3.
> In addition, it's confusing that the man pages on RESTORE
> are telling that one should supply <noise std> as argument
> whereas the tutorial on DTI says that it is the noise
> VARIANCE (see chapter 9.3).
> 
> My first experience with RESTORE is that the results are
> dependent on the supplied value of the noise. So I would
> appreciate if you could advice me on a valid method
> to derive a reliable estimate of the noise.
> 
> Cheers,
> Ed
> 
> 
> On 2 Nov 2011, at 23:04, Philip A Cook wrote:
> 
>> Hi,
>> 
>> I believe you pass the noise sigma directly. You can use the Camino command estimatesnr to assist in this computation
>> 
>> On Oct 31, 2011, at 11:28 AM, Ed Gronenschild wrote:
>> 
>>> Hi,
>>> 
>>> It;s not entirely clear to me how to derive the noise variance
>>> in the DTI data, the value I have to supply with the RESTORE
>>> command.
>>> Suppose I define contours in the background of the B0 volume
>>> and I derive a standard deviation of 1.68. What should I
>>> specify in that case?
>>> 
>>> Cheers,
>>> Ed
>>> 
>>> _______________________________________________
>>> Camino-users mailing list
>>> Camino-users at www.nitrc.org
>>> http://www.nitrc.org/mailman/listinfo/camino-users
>> 
> 
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