[Homer-users] Question on hmrMotionCorrectWavelet.

Mon Mar 23 12:07:34 EDT 2015

Hi Taka,

from my experience I can say that using IQR = 1.5 will put to 0 less
coefficients than when using Molavi's method with alpha = 0.1, and hence
IQR=1.5 is more conservative. Bear in mind that alpha and IQR have an
opposite relation, when alpha -> 0, no coefficients are set to 0, while
when IQR -> 0 more coefficients are set to 0.

Best,
Sabrina

2015-03-22 13:34 GMT+00:00 Takayuki Nozawa <nozawa at idac.tohoku.ac.jp>:

> 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
>
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-- 
Sabrina Brigadoi
sabrina.brigadoi at gmail.com
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