# What's the difference between parametric deconvolution (BedpostX) and non-parametric deconvolution (CSD)?

Hey all,
I’m new to diffusion imaging so maybe my question is a bit unclear. Sorry for that.

For my master-thesis I want to use your CSD approach and also the FSL BedpostX approach to analyse the direction information/voxel. I read all the paper about your method and the Fsl method. But I still do not understand the difference between parametric and non-parametric deconvolution.

1. In that case what exactly means parametric and non-parametric? I also read that bedpostX uses different models (ball-and-stick and a multi shell model)
I guess I do understand the SD approach (getting the ODF by deconvolute the signal with an response function) more than the parametric appraoch (bedpostX).

2. If somebody could tell me in in general the differences of this two appraoches it would be so helpful to me.

Thank you
Max

The main difference really boils down to how the fibre orientation information is represented. In SD, the fibre orientation density function (fODF) is a continuous function on the sphere, free to take on more or less arbitrary shapes. In MRtrix3, we use spherical harmonics to represent this function, but there’s no requirement that this be the case - others might chose spherical radial basis functions, spherical wavelets, etc.

In `bedpostX`, the fODF is represented as a discrete set of delta functions, each parameterised by its volume fraction, and (θ,φ) angles. So it’s can only represent a subset of the full range of possible fODFs, but the advantage is that is also offers a reduced representation of the information.

Personally, I find the words parametric and non-parametric confusing in this context. In non-parametric SD, we also have to represent the fODF using some set of coefficients, it’s a very subtle distinction between those and a set of parameters…

And yes, there is also the separate question of which model to use. In MRtrix3, we have always been of the opinion that it’s best to simply measure it from the data, if only to avoid making assumptions about what’s going on. Most other methods rely on some mathematical model, be it a simple tensor model, a more realistic model of diffusion in restricted geometries, or more elaborate functional forms that just happen to fit the data better. There’s nothing to stop you from using these models in MRtrix3, other than the logistics of converting the output of the model into a format MRtrix3 can use (basically the set of even l, m=0 spherical harmonic coefficients per shell). Not sure it’s so simple the other way around though, given how central to the problem formulation these models are likely to be in these other implementations. Note that in practice these different models probably don’t make an enormous amount of difference, at least for the case of single-shell spherical deconvolution - the biggest effect by far is an overall modulation of the amplitudes of the fODF, and maybe in the more extreme cases some blurring or spurious noisy peaks. The main thing is that the model should give you a fair approximation of the DW signal you’d expect for a single fibre voxel.

Hope that helps to clarify things?

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