wrong selection of the peak center when there is two DDY into the same DY min-max

[jobo322]

spectra_nmr_2025.03.19_65-85-0.10.0e3373b7.jdx.zip

it conducts to this result

In the peak at 7.53, there are two changes in the derivative, there is two local minima in the second derivative, but the one is selected is the ddy with the less value of DDY

DY -> first derivative
DDY -> second derivative

[jobo322]

@lpatiny, In this case, GSD could create candidates for each interval in the first derivative, then two possible approaches:

1. select the biggest and more centered (a score) minimum in the second derivative.
2. add peaks all the peaks more or less centered in the interval.

[jobo322]

Here is another example, the center of the peak is not in the top. It points it is really a bug in the package.

[targos]

So if I understand correctly, the "bug" is that we are returning the top of the deconvoluted peaks, but there are cases where we just want the "visible top" (what the user sees) ?

[jobo322]

Ok, I agree the last one is not the best example because the prominent peak is well catched, I think because of it is at right of the possible wrong peak.

But if you make focus on the first example, gsd catch the wrong peaks and ignore the prominent peaks because those are left to the wrong peak and the data.x is in ascending order.

peak result	derivative

reversing the data.y of it, I got it:

the peaks list resulting from it, catch now the prominent peaks, I mean the big local minimum in the second derivative per peak.

[
  {
    id: 'b64d09c1-50af-40e8-93d9-620c4bf02a88',
    x: 7.4897581032265155,
    y: 118899.4033342634,
    width: 2.811536901928946,
    shape: { fwhm: 3.3103317270032484, kind: 'gaussian' }
  },
  {
    id: '169af1a9-14f6-4f76-93a7-54e959eb349a',
    x: 7.509887750149345,
    y: 206666.46681187078,
    width: 2.9337776367952983,
    shape: { fwhm: 3.454259193394548, kind: 'gaussian' }
  },
  {
    id: '93998a82-a81b-4997-b420-8f82858f9a65',
    x: 7.52893711428191,
    y: 91232.53721304075,
    width: 2.6892961670625937,
    shape: { fwhm: 3.1664042606119485, kind: 'gaussian' }
  }
]

[targos]

Indeed this more complex example is wrong regardless.
It seems to me that the order of the data should not matter and we are using the wrong heuristic to select the peak?

[jobo322]

Checking the code, there is only one DDY point assigned to one interval in DY (min-max), the problem appear when the data there is more than one minimum in the DDY but the resolution is not enough to distinguish two intervals in DY. e.a

It is possible this deformation of the signal could be not the present of two peaks.
I think to prevent the possible selection of multiples peaks in one interval in DY due to the deformation of the signal, gsd should assign the DDY point with max absolute value if there is more than one in the same min max interval in DY.

if you are agree I could propose of refactor.

[targos]

That seems reasonable

[lpatiny]

@jobo322 Could you tell me if the minimum in green should really be there ? It does not corresponds to the top of the peak and it pretty much shifted to the left.

[lpatiny]

@jobo322 Please also try to find out why we don't use first derivative to identify the peaks and the second derivative for the width of the peaks. It seems in this example the first derivative at 0 match the top of the peak.

[jobo322]

The use of the second derivative increases the resolution of the analysis. one example is:

the shoulders first derivative never crossed zero, so the delta would be the center of the interval (min-max) in the first derivative.

[lpatiny]

Here is the original paper

TD_23_1.pdf

[lpatiny]

@jobo322

An interval is the zone between min and max first derivative (inflection points).

Add a new option: peakDetectionAlgorithm

• first: make the peak picking when the first derivative goes through 0.
• second: based on second derivative minima / maxima <- current algorithm but by taking the closest peak
• auto: if in the interval, the first derivative goes through 0, use this position. Otherwise use second derivative min (for positive peaks)

[lpatiny]

@jobo322 Also check the impact of the auto on the other multiplet and solutions on how to reduce possibly the number of peaks.

[jobo322]

the algorithm that use only the first derivative, has a result for it.

spectrum	result

So, if the first derivative of the shoulders reaches the zero we would catch the wrong x position for those shoulders. I mean:

const expectedPeaks = [
      { x: 0.1, y: 0.43, width: 0.05 },
      { x: -0.1, y: 0.43, width: 0.05 },
      { x: 0, y: 1, width: 0.1 },
    ]

spectrum	result