[FieldTrip] interpolate missing grad positions

[Schoffelen, J.M. (Jan Mathijs)]

Hi Fan,

Perhaps I need to rephrase my previous reply. If your recorded data has 269 sensors worth of data, rather than 275, a call to ft_channelrepair might give you 275 sensors (indeed if you use a template to specify the positions of the missing gradiometers), but you don’t improve the quality of your measurement.
At least, your source reconstruction will not get better after the interpolation, because you don’t have more information in the data, since the missing sensors are ‘created’ by linearly combining the data from the other sensors. You write in your e-mail that the forward solution will be ‘better’ with more sensors. I don’t think that this is true. With more sensors, your forward solution just has more sensors, nothing more, nothing less. 
The point of rank deficiency, this cannot be solved with filtering after interpolation. 

Best wishes,
Jan-Mathijs


> On 5 Oct 2021, at 13:14, go puluto via fieldtrip <fieldtrip at science.ru.nl> wrote:
> 
> Hi All, 
> 
> Thanks for the reply. The reason I wanted to interpolate the missing grad is that I thought more sensors would give a better forward solution. For the forward modelling, we calculate how the unit activation in the souces transformed to the sensors. Is it correct that If there are missing channels, after the forward calculation, the gap between sensors need to be interpolated in the sensor space? I thought this is the reason for a better forward solution using a higher number of sensors. 
> I am sorry that I don't get the point of rank deficiency, first of all, after interpolation, could we solve the dependent (rank deficient) problem by filtering? Secondly, how the rank deficiency affects the activity transformation from a higher-dimension (source) to a lower dimension (sensors), we could transform dependent 2d vectors to a 3d space, right? 
> The interpolation function, ft_chanrepair, solves the interpolation when the grad position is given, i.e., we can interpolate the missing channels using the ctf275 template. However, for the source reconstruction, we need the online recorded grad positions, in which some sensors were initially missed at the data collection stage. So, I was wondering could I reconstruct the missing grad positions. 
> Thanks for all the answers, I am very happy to learn in the community. 
> 
> best,
> Fan
> 
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