Hi,
This week I was looking at a Siemens csi acquisition protocol. True acquisition was 15x15 but reconstructed to a 16x16 grid. I also see that the processing of the spectrum itself often has zero filling as part of the steps.
What is the role of zero filling? Does it help in any way in the quantification or retrieving useful information?
Paul
Hi @Paul,
Robin de Graaf describes zero-filling nicely in chapter 1, section 1.10.4 of his textbook, but to summarize: As the MR signal we work with is the digitization of the analog signal detected by the MR scanner, there are only so many discrete points that are sampled by the analog-to-digital converter. So, visually, we don’t see all the spectral features after Fourier transformation. Zero-filling (or zero-padding) is commonly understood to help with this by enhancing the visualization of spectral features of the MR signal. This is done by adding zeroes to the end of the FID signal. Importantly, no new information is being added to the data (as all the added data points are 0), so the the intrinsic spectral resolution is not actually being enhanced. However, adding zeros artificially increases the acquisition time, which improves the digital resolution after (discrete) Fourier transformation.
I would also recommend reading this commentary that shows that zero-filling actually is not simply a cosmetic enhancement, but improves signal modeling accuracy by a factor of ~sqrt(2) when 2x zero-filling is applied (further zero-filling steps do not appear to be of benefit in this respect).
Mark
Hi Mark,
Thanks for your response! I hadn’t come across that before in the context of spectroscopy - very cool. It’s actually the first example I’ve seen where zero-filling provides a real, quantifiable benefit, rather than just cosmetic interpolation.
Do you know whether there’s a general consensus in imaging that zero-filling doesn’t improve diagnostic value or any quantifiable outcome? That’s always been my understanding, though I’ve seen articles like this one suggest otherwise:
https://onlinelibrary.wiley.com/doi/10.1002/cmr.a.21256
Paul
I’m afraid I’m not aware of a consensus within the imaging community, but the Fourier transform is also used there, so I imagine there could be arguments that zero-filling is more than cosmetic for images.
Fwiw, I’ve always thought there must be a benefit when it comes to statistical modeling (i.e., more data points = a better solution). Now, one may have to add an asterix to the data underlying the solution, but it’s a solution nonetheless.
We need to be careful with comparison to imaging here - the key difference is that in MRS, we need to model the zero-filled data.
Zero-filling exactly once (i.e. 2x the number of acquired points) and then modeling only the real part of the spectrum is statistically equivalent to not zero-filling at all and then simultaneously modeling the real and the imaginary parts of the spectrum. Another way to think of this: zero-filling effectively mixes the information from the real and imaginary parts.
As the paper posted by Mark above shows, there is no benefit from zero-filling more than once. Another recent paper studies this in greater detail and claims some further accuracy/precision gains by doing complex modeling (owed to some improvement to baseline estimation but I can’t quite figure out how that would work), but these effects appear to be rather marginal.
In fact, zero-filling more than once in fact destroys the independence of the samples. This, however, is an important assumption of the least-squares modeling: the least-squares solution is only identical to the maximum-likelihood solution if the points are independent (more precisely, if the random errors are independent and identically distributed). The LCModel manual states very clearly that zero-filling and linebroadening destroy this assumption. No one has really looked how far off the estimates end up being, but what we can say with certainty is that the CRLB estimates become invalid. (LCModel zero-fills exactly once and then models only the real part)
TLDR: For cosmetic purposes, zero-fill your data to your heart’s content, but be careful what you do before you feed them into a least-squares model.