[Homer-users] Question on hmrMotionCorrectWavelet.

[Takayuki Nozawa]

Dear Sabrina,

Thank you very much for the detailed reply, and also thank you for the
useful functions.

Yes, I understand that for the thresholding of coefficients,
the method in Molavi2012 is based on the assumption of Gaussian distribution
and the estimation of its SD,
while your method is more directly based on the quantiles of
coefficient distribution.
In my earlier message, by "basically" I meant "if the assumption of
Gaussian distribution holds".

> I am not sure about the relation between Molavi's alpha and iqr used in
> Homer2, but looking at the maths it seems that the interquartile range of a
> normal distribution is defined as: 2 Φ−1(0.75)σ  where  Φ−1 is the quantile
> function and in Homer2 therefore, I think that the threshold can be defined
> as Φ−1(0.75) + IQR*2 Φ−1(0.75)σ where IQR is the user set variable for the
> upper threshold and Φ−1(0.25) - IQR*2 Φ−1(0.75)σ  for the lower threshold.

Thank you for clarifying this out!
Following your explanation, I rechecked the WaveletAnalysis.m (lines 52-55)
and found my mistake.
>From the help comment, I was initially assuming that the below-threshold range
would be "iqr times the interquartile range", or equivalently in terms
of the code
the lower and upper thresholds would be set as
"prob2= quants(1)*iqr" and "prob1=quants(3)*iqr",
respectively.
(And sorry, even so the correspondence between params should have been
2 * (1 - pnorm(qnorm(0.75)*iqr)) = alpha,
where qnorm = Φ^−1 = pnorm^-1. )

Now having the correct definition of thresholding with iqr, I deduce
the correspondence would be
2 * (1 - pnorm(qnorm(0.75)*(1+2*iqr))) = alpha.
If this is correct, then alpha=0.1 corresponds to iqr ~ 0.7.
Does this agree with your experience?
is this what you meant by
> Using IQR = 1.5 is usually more conservative than using
> the alpha=0.1 by Molavi.

Thanks again for your kind help!

Best,
Taka


2015-03-21 7:55 GMT+09:00 Sabrina Brigadoi <sabrina.brigadoi at gmail.com>:
> Dear Taka,
>
> the wavelet motion correction algorithm implemented in Homer2 is not exactly
> the method explained in Molavi and Dumont's paper. It is inspired by that
> work and most of the code is very similar, though using a different wavelet
> toolbox. The main difference is the threshold used. Molavi uses alpha, a
> probability threshold for the coefficient distribution. The IQR metric used
> in Homer2 is instead related to the interquartile range of the wavelet
> coefficients distribution. All coefficients above Q3 + IQR times the
> interquartile range (iqr) or below Q1 - IQR times the interquartile range
> (iqr) are set to 0 and considered outliers of the distribution. Usually, for
> outlier detection, IQR = 1.5. But for the nirs data, IQR can be a tuning
> parameter, and can be set by the user depending on the amount of noise
> present in the data. Using IQR = 1.5 is usually more conservative than using
> the alpha=0.1 by Molavi. Reducing IQR, more coefficients are set to 0 and
> more noise is removed. IQR should be set by the user depending on the data,
> it cannot be fixed.
>
> I am not sure about the relation between Molavi's alpha and iqr used in
> Homer2, but looking at the maths it seems that the interquartile range of a
> normal distribution is defined as: 2 Φ−1(0.75)σ  where  Φ−1 is the quantile
> function and in Homer2 therefore, I think that the threshold can be defined
> as Φ−1(0.75) + IQR*2 Φ−1(0.75)σ where IQR is the user set variable for the
> upper threshold and Φ−1(0.25) - IQR*2 Φ−1(0.75)σ  for the lower threshold.
>
> I hope this is useful and makes sense.
>
> Sabrina
>
> --
> Sabrina Brigadoi, PhD
> Research Associate
> Biomedical Optics Research Laboratory
> Malet Place Engineering Building, Rm 3.18
> University College London
> Gower Street
> London WC1E 6BT
>
>
> 2015-03-20 10:39 GMT+00:00 Takayuki Nozawa <nozawa at idac.tohoku.ac.jp>:
>>
>> Dear Homer2 experts,
>>
>> Thank you for sharing the great toolbox.
>> I have a question about the Wavelet motion correction function,
>> hmrMotionCorrectWavelet.m and WaveletAnalysis.m.
>>
>> Comparing the code with the original paper
>> Molavi et al.,Physiol Meas, 33, 259-270 (2012),
>> I deduced that the interquartile multi factor iqr would basically
>> correspond to the outlier threshold alpha in Molavi2012 by
>> 2 * (1 - pnorm(0.75*iqr)) = alpha,
>> with pnorm(q) being the normal cumulative distribution function.
>> Am i correct on this?
>>
>> Confirmation or correction would be much appreciated!
>>
>> Best,
>> Taka
>>
>> --
>> Takayuki Nozawa
>> Assistant Professor, Smart Ageing International Research Center
>> Institute of Development, Aging and Cancer (IDAC), Tohoku University
>> nozawa at idac.tohoku.ac.jp
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-- 
Takayuki Nozawa
Assistant Professor, Smart Ageing International Research Center
Institute of Development, Aging and Cancer (IDAC), Tohoku University
nozawa at idac.tohoku.ac.jp