Relative noise is a single scalar value that is used to predict the maximum value of the expected noise at any point and is calculated from the measured signal and a mathematical noise model. The mathematical noise model is selected or estimated from an observation that includes statistical and/or numerical modeling based on a population of measurement points. An absolute noise for a plurality of points of the measured signal is estimated. An array of values is calculated by dividing each of a plurality of points of the absolute noise by a corresponding expected noise value calculated from the mathematical noise model. The relative noise is calculated by taking a standard deviation of a plurality of points of the array. The relative noise can be used to calculate scaled background signal noise, filter regions, denoise data, detect false positives from features, calculate S/N, and determine a stop condition for acquiring data.
1. A method for calculating a relative noise of a measured signal, comprising:
selecting a mathematical noise model;
estimating an absolute noise for a plurality of points of the measured signal;
calculating a plurality of expected noise values from the mathematical noise model for each of the plurality of points;
calculating an array of values by dividing each of a plurality of points of the absolute noise by a corresponding expected noise value from the plurality of expected noise values; and
calculating the relative noise by taking a standard deviation of a plurality of points of the array.
2. The method of claim 1 , wherein the mathematical noise model is selected based on knowledge about a data acquisition process of the measured signal.
3. The method of claim 1 , wherein the mathematical noise model is selected based on an observation made from the measured signal.
4. The method of claim 1 , further comprising estimating an underlying signal from the measured signal.
5. The method of claim 4 , wherein the absolute noise is estimated by subtracting the underlying signal from the measured signal.
6. The method of claim 4 , wherein the underlying signal is obtained by smoothing the measured signal.
7. The method of claim 4 , wherein the underlying signal is obtained by applying a noise filter to the measured signal.
8. The method of claim 1 , wherein the absolute noise is estimated by applying a filter to the measured signal.
9. The method of claim 8 , wherein an underlying signal is estimated by subtracting the absolute noise from the measured signal.
10. The method of claim 1 , further comprising:
predicting an expected noise using the mathematical noise model and a signal; and
calculating a scaled noise by multiplying the expected noise by the relative noise.
11. The method of claim 10 , wherein the signal comprises an underlying signal.
12. The method of claim 10 , wherein the signal comprises a signal of interest.
13. The method of claim 10 , wherein the signal comprises the measured signal.
14. The method of claim 1 , further comprising:
estimating a background signal;
predicting an expected background signal noise using the mathematical noise model and the background signal; and
calculating a scaled background signal noise by multiplying the expected background signal noise by the relative noise.
15. The method of claim 14 , further comprising determining if a region of a signal includes a signal of interest by:
comparing a sum of a background signal value of the background signal in the region and a scaled background signal noise value of the scaled background signal noise in the region with a signal value of the signal in the region; and
if the signal value is greater than the sum, determining that the region comprises the signal of interest.
16. The method of claim 15 , wherein the signal comprises the measured signal.
17. The method of claim 15 , wherein the signal comprises an underlying signal.
18. The method of claim 14 , further comprising determining if a first feature of a signal and an adjacent second feature of the signal are analyzed together by:
selecting a point of the signal that is between the first feature and the second feature;
comparing a sum of a background signal value of the background signal at the point and a scaled background signal noise value of the scaled background signal noise at the point with a signal value of the signal at the point; and
if the signal value is greater than the sum, analyzing the first feature and the second feature together.
19. The method of claim 18 , wherein the first feature comprises a first group of neighboring data points in the signal and the second feature comprises a second group of neighboring data points in the signal.
20. The method of claim 18 , wherein the signal comprises liquid chromatography mass spectrometry data.
21. The method of claim 18 , wherein the signal comprises image data.
22. The method of claim 18 , wherein the signal comprises a mass spectrum.
23. The method of claim 18 , wherein the signal comprises a chromatogram.
24. The method of claim 18 , wherein the signal comprises the measured signal.
25. The method of claim 18 , wherein the signal comprises an underlying signal.
26. The method of claim 14 , further comprising determining if a second feature of a signal is a separate feature and not part of an adjacent first feature of the signal by:
estimating a first feature signal using the first feature, the signal, and a mathematical model for a feature;
predicting an expected first feature noise using the mathematical noise model, the first feature signal, and the background signal;
calculating a scaled first feature noise by multiplying the expected first feature noise by the relative noise;
comparing a sum of a background signal value of the background signal at the second feature, a first feature signal value of the first feature signal at the second feature, and a scaled first feature noise value of the scaled first feature noise at the second feature with a signal value of the signal at the second feature; and
if the signal value is greater than the sum, determining that the second feature comprises the separate feature.
27. The method of claim 26 , wherein the signal comprises the measured signal.
28. The method of claim 26 , wherein the signal comprises an underlying signal.
29. The method of claim 14 , further comprising denoising a point of a signal by:
comparing a scaled background signal noise value of the scaled background signal noise at the point with a difference between a signal value of the signal at the point and a background signal value of the background signal at the point;
if the difference is smaller than the scaled background signal noise value, assigning a value of zero to the point;
if the difference exceeds the scaled background signal noise value by a value greater than zero but less than a threshold, assigning a product of the difference and a multiplier to the point; and
if the difference exceeds the scaled background signal noise value by a value greater than or equal to the threshold, assigning the difference to the point.
30. The method of claim 29 , wherein the signal comprises the measured signal.
31. The method of claim 29 , wherein the signal comprises an underlying signal.
32. The method of claim 14 , further comprising calculating a signal-to-noise ratio at a point of a signal by:
dividing a difference between a signal value of the signal at the point and a background signal value of the background signal at the point by a product of the relative noise and a noise value at the point.
33. The method of claim 32 , wherein the noise value comprises an underlying signal noise value.
34. The method of claim 32 , wherein the noise value comprises a background signal noise value.
35. The method of claim 32 , further comprising:
if the signal-to-noise ratio is greater than or equal to a threshold signal-to-noise ratio, stopping acquisition of the measured signal.
36. The method of claim 32 , further comprising:
if the relative noise is less than or equal to a threshold signal-to-noise ratio, stopping acquisition of the measured signal.
37. A non-transitory computer-readable medium containing computer instructions stored therein, for calculating a relative noise of a measured signal, causing a computer processor to perform:
selecting a mathematical noise model;
estimating an absolute noise for a plurality of points of the measured signal;
calculating a plurality of expected noise values from the mathematical noise model for each of the plurality of points;
calculating an array of values by dividing each of a plurality of points of the absolute noise by a corresponding expected noise value from the plurality of expected noise values; and
calculating the relative noise by taking a standard deviation of a plurality of points of the array.
38. A computing system for calculating a relative noise of a measured signal, comprising:
a computer processor programmed to calculate the relative noise of the measured signal that, when executed by the computer processor:
selects a mathematical noise model,
estimates an absolute noise for a plurality of points of the measured signal,
calculates a plurality of expected noise values from the mathematical noise model for each of the plurality of points,
calculates an array of values by dividing each of a plurality of points of the absolute noise by a corresponding expected noise value from the plurality of expected noise values, and
calculates the relative noise by taking a standard deviation of a plurality of points of the array.