Method and system for processing mass spectra

Abstract

A method for identifying pseudo-peaks in a mass spectrum generated by a time-varying transient signal detected in a mass spectrometer is provided. The method comprises the following steps: generating a first mass spectrum from the time-varying transient signal according to a first set of values ​​of the one or more adjustable parameters using a regularized inversion algorithm having one or more adjustable parameters; generating one or more perturbed mass spectra from the transient signal according to one or more corresponding perturbed versions of the first set of values ​​using the regularized inversion algorithm; and identifying one or more pseudo-peaks in the first mass spectrum by comparing the first mass spectrum with at least one of the perturbed mass spectra. Corresponding systems and computer-readable media are also provided.

Description

Technical Field

[0001] The present invention relates to systems and methods for identifying spurious peaks in mass spectra, particularly spurious peaks caused by applying a regularized inversion algorithm. Background Art

[0002] The goal of the family of analytical techniques commonly referred to as mass spectrometry is to characterize a sample by identifying the ion species produced when the sample is ionized and possibly fragmented, as well as the relative abundance of the ion species. A plot of the mass (or mass-to-charge ratio) of an ion species against the relative abundance of the ion species is a plot commonly referred to as a mass spectrum. However, the limited accuracy of mass spectrometry techniques may result in difficulty in distinguishing different ion species with similar mass-to-charge ratios present in an experiment. Specifically, the mass spectrum produced may contain peaks that appear to be individual peaks that are actually convolutions of two or more adjacent peaks, each of which corresponds to a different ion species. It should be appreciated that such convolutions may result in errors in sample characterization because important ion species may be overlooked and the abundance of other ion species may be overestimated or underestimated.

[0003] Therefore, many techniques have been developed to attempt to improve the resolving power of mass spectrometry by post-processing the mass spectrometry data. Specifically, a variety of techniques attempt to improve resolution by effectively deconvolving the peaks in the mass spectrum through post-processing. Such convolutions and attempts to mitigate such convolutions are perhaps best understood in the field of Fourier transform mass spectrometry (FTMS).

[0004] In FTMS, ion species and the relative abundance of their presence are identified in the form of coherent oscillating ion packets contained in a trapping field within a mass spectrometer. The oscillation frequency of the coherent ion packets is a function of the mass-to-charge ratio of the ion species and is referred to herein as the "characteristic frequency" of the ion species. The trapping field can be provided by a combination of an electrostatic field and a static magnetic field, such as in a Fourier transform ion cyclotron resonance (FTICR) mass analyzer, or by only the electrostatic field, such as in an orbital capture mass analyzer, such as the Orbitrap (TM) mass analyzer from Thermo Fisher Scientific (TM). FTMS using RF fields is also known.

[0005] Typically, ions are detected by an image current S(t) induced on a detection electrode of a mass analyzer when the oscillating ions pass nearby (also called a continuous transient image current and referred to herein as a "transient" or "time-varying transient signal"). Therefore, a transient comprises a superposition of one or more periodic signals. Each periodic signal corresponds to the oscillation of a corresponding coherent ion packet within the mass analyzer at a corresponding characteristic frequency. A transient is measured (or captured or recorded) only for a finite time T, which is called the "duration" of the transient.

[0006] Transient processing typically involves a discrete Fourier transform (DFT), which decomposes the transient into multiple periodic functions (also called Fourier basis functions). Each Fourier basis function is localized at a corresponding frequency (also called a Fourier transform bin). The frequencies corresponding to the Fourier basis functions form a frequency group (called a Fourier grid). The Fourier basis functions are equally spaced in the frequency domain, that is, the spacing between adjacent frequencies is constant. Specifically, the spacing between adjacent frequencies in a group of frequencies (referred to herein as the "spacing" of a group of frequencies) is determined by the inverse of the duration of the transient. Determine. The decomposition includes calculating a separate complex amplitude corresponding to each Fourier basis function based on the transient. Thereby forming a set of complex amplitudes. Therefore, the discrete Fourier transform (DFT) represents the transient in the frequency domain. Specifically, the transient is represented as a set of complex amplitudes. Each complex amplitude in the set of complex amplitudes corresponds to a corresponding frequency in a set of frequencies, i.e., the frequency localized by the corresponding Fourier basis function.

[0007] The periodic signals present in the transient state (as previously described) are related to the complex amplitude. Specifically, the periodic signal will contribute to the complex amplitude corresponding to multiple frequencies in a set of frequencies. Under given experimental conditions, the multiple frequencies will be substantially centered on the characteristic frequency of a particular ion species. Therefore, a plot of a set of complex amplitudes against a set of frequencies will show one or more peaks, each peak substantially centered on a corresponding characteristic frequency present in the transient state, i.e., the centroid of each peak will be substantially equal to the characteristic frequency.

[0008] As described above, the frequency of the periodic signal present in the transient is a function of the m / z ratio of the ion species. Therefore, the centroid of each peak can be converted (or transformed or interpreted) from the frequency to the corresponding m / z ratio, thereby identifying the corresponding ion species. In addition, the height of each peak can be converted (or transformed or interpreted) to the corresponding relative abundance of the corresponding ion species.

[0009] In this scheme, it is obvious that convolution of adjacent peaks may be caused. Specifically, due to the spacing of frequencies in the Fourier grid, if two (or more) different ion species have characteristic frequencies close enough to a common frequency point on the Fourier grid, the peak in the mass spectrum at the point will represent the convolution of the individual peaks of the two (or more) ion species. In fact, when the transient includes two or more close characteristic frequencies, the mass spectrum will include two or more overlapping peaks. If the spacing (or difference) between the two characteristic frequencies of the transient is less than the threshold, the two peaks will not be distinguishable. This error will result in errors in the converted m / z ratio (and therefore incorrect identification of ion species) and errors in the converted relative abundance. Although the error depends on the local spectral density, the actual threshold for reliable resolution is typically twice the spacing of the Fourier grid corresponding to the transient. It should also be understood that the reliable resolution of a given sample may also be affected by the phase relationship between the various components of the various ion species, which may cause constructive or destructive interference between adjacent components. This effect can be implicitly explained in the spectral density, where the explicit phase dependence is offset.

[0010] Figure 1a in the accompanying drawings shows an example of this problem. The figure shows a transient first signal 150, a transient second signal 160 and a transient spectrum 170. The first signal 150 has a characteristic frequency f1. The second signal 160 has a characteristic frequency f2. The difference between f1 and f2 is equal to the spacing of the Fourier grid. The spectrum 170 has two central peaks. The leftmost peak of the spectrum 170 corresponds to the second signal 160. The rightmost peak of the spectrum 170 corresponds to the first signal 150. There is also an error 174 between the center of mass of the peak and the associated characteristic frequency. There is an error 172 between the height (or intensity) of the peak and the height (or intensity) of the corresponding signal 150, 160. As the spectral density (i.e., the number of harmonic components in a given area of ​​the spectrum) increases and its spacing decreases, the error becomes more obvious. As described above with respect to reliable resolution, this error may also be affected by the phase relationship between the various components of the various ion species, which may cause constructive or destructive interference between adjacent components.

[0011] FIG. 1 b of the accompanying drawings illustrates the problem. The figure shows a first signal 150 of a transient, a second signal 160 of a transient, and a spectrum 170 to be regenerated from the transient. In this case, the difference between f1 and f2 is equal to half the interval of the Fourier grid. Spectrum 170 has a single peak, i.e., the characteristic frequencies corresponding to the two signals 150 and 160 are not resolved. There is an error in the centroid of the single peak of the spectrum compared with any one of the two characteristic frequencies. In addition, the height of the single peak is neither equal to the sum of the heights of the two signals 150 and 160, nor is it equal to any one of the heights of the two signals 150 and 160. Due to these errors, any one of the ion species corresponding to the signals 150 and 160 will be incorrectly identified. The relative abundance reported from the peak will also be incorrect. This may result in errors in the abundance ratios calculated using other peaks in the signal 170, which are accurate themselves.

[0012] To address these problems, deconvolution techniques have been developed that seek to deconvolute (or decompose) such convoluted peaks into separate component peaks and thereby produce an improved mass spectrum. Typically, such methods involve constructing a new mass spectrum on a finer Fourier grid (i.e., a grid with decreasing frequency spacing) and fitting the new mass spectrum on the finer grid to the original mass spectrum on the coarser grid. In effect, the original mass spectrum is deconvoluted onto the finer grid.

[0013] It will be appreciated that such deconvolution is inherently an ill-posed problem. Specifically, there may be more than one possible solution, in which case there may be more than one possible deconvolved mass spectrum. Likewise, it will be appreciated that such a problem is also inherently numerically ill-posed. To mitigate this problem, deconvolution techniques typically use regularized mathematical techniques to attempt to provide a stable solution. An example of such a deconvolution technique is the "Phase-constrained spectrum deconvolution method" (known as ΦSDM and referred to herein as PSDM for clarity) described in Grinfeld, D., Aizikov, K., Kreutzmann, A., Damoc, E., and Makarov, A., "Phase-constrained spectrum deconvolution for Fourier transform mass spectrometry," Anal. Chem., 89(2): 1202-1211 (2017), and European Patent Publication EP3086354(A1), the entire contents of which are incorporated herein by reference. This technique uses regularization in the form of phase constraints on the calculated complex amplitudes on a finer grid.

[0014] However, even with regularization, deconvolution techniques often produce mass spectra with additional spurious peaks. These are artifacts of the pathological and ill-posed nature of the deconvolution and do not represent the actual ion species present in the mass spectrometer. However, the presence of these spurious peaks reduces the accuracy of the mass spectrum and may lead to errors when attempting to characterize the original sample using the mass spectrum. Summary of the invention

[0015] The present invention seeks to provide systems and methods for more accurately identifying pseudo peaks in a mass spectrum caused by a deconvolution process. Specifically, by varying the parameters used in the deconvolution process applied to an initial mass spectrum, a plurality of perturbed mass spectra can be generated. Pseudo peaks can then be identified as peaks that are substantially unchanged relative to changes in the parameters.

[0016] In a first aspect, a method for identifying pseudo-peaks in a mass spectrum generated by a time-varying transient signal detected in a mass spectrometer is provided. The method comprises generating (or calculating or otherwise forming) a first mass spectrum from the time-varying transient signal according to a first set of values ​​of the one or more adjustable parameters using a regularized inversion algorithm (such as a phase-constrained spectral deconvolution algorithm) with one or more adjustable parameters. In some embodiments, this generation step comprises applying the regularized inversion algorithm to an initial mass spectrum generated by the time-varying transient signal. The initial mass spectrum can be formed by applying a discrete Fourier transform to the time-varying transient signal. It should be understood that the initial mass spectrum can be generated as part of the method, or the initial mass spectrum can be generated or constructed and received separately.

[0017] The method proceeds with generating (or calculating or otherwise forming) one or more perturbed mass spectra from the transient signal based on one or more corresponding perturbed versions of the first set of values ​​using the regularized inversion algorithm. Likewise, in some embodiments, this generating step includes applying the regularized inversion algorithm to the initial mass spectrum generated from the time-varying transient signal. Each perturbed version of the first set of values ​​may be formed by applying at least one corresponding variation to at least one value in the first set of values.

[0018] In this aspect, one or more pseudo-peaks in the first mass spectrum are identified by comparing the first mass spectrum with at least one of the perturbed mass spectra. In some embodiments, at least one of the pseudo-peaks is identified based on the peak not being present in the intersection of the first mass spectrum and at least one of the perturbed mass spectra. Additionally or alternatively, at least one of the pseudo-peaks may be identified based on a mass-to-charge ratio (the mass-to-charge ratio may be expressed as a mass value or a frequency) of the peak between the first mass spectrum and at least one of the perturbed mass spectra exceeding a predetermined threshold.

[0019] In some embodiments, the regularized inversion algorithm includes applying a discrete Fourier transform to a version of the time-varying transient signal, the version of the time-varying signal including a number of zero blanking entries. In some cases, an adjustable parameter of the one or more adjustable parameters controls the number of zero blanking entries in the version of the time-varying transient.

[0020] In some embodiments, the regularized inversion algorithm is an iterative algorithm. One of the one or more adjustable parameters may control the number of iterations in the regularized inversion algorithm.

[0021] In some embodiments, the method further includes outputting a modified mass spectrum. This modified mass spectrum can take into account the identified pseudo-peaks. For example, the modified mass spectrum can have one or more (or all) pseudo-peaks of the identified one or more pseudo-peaks excluded. Additionally or alternatively, one or more (or all) pseudo-peaks of the pseudo-peaks can be present in the modified mass spectrum and marked (or identified or otherwise labeled) as (potentially) pseudo.

[0022] The present invention also provides apparatus corresponding to or including elements, modules or components arranged to implement the above methods, such as one or more various appropriately configured computing devices, such as those previously described.

[0023] Specifically, the present invention therefore provides a system (or device) for identifying pseudo-peaks in a mass spectrum generated by a time-varying transient signal detected in a mass spectrometer. The system includes a deconvolution module, which is configured to generate (or calculate or otherwise form) a first mass spectrum from the time-varying transient signal according to a first set of values ​​of the one or more adjustable parameters using a regularized inversion algorithm (such as a phase-constrained spectrum deconvolution algorithm) with one or more adjustable parameters. In some embodiments, the generation includes applying the regularized inversion algorithm to an initial mass spectrum generated by the time-varying transient signal. The initial mass spectrum can be formed by applying a discrete Fourier transform to the time-varying transient signal. It should be understood that the initial mass spectrum can be generated as part of the method, or the initial mass spectrum can be generated or constructed and received separately.

[0024] The deconvolution module is further configured to generate one or more perturbed mass spectra from the transient signal based on one or more corresponding perturbed versions of the first set of values ​​using the regularized inversion algorithm. Likewise, in some embodiments, such generation includes applying the regularized inversion algorithm to the initial mass spectrum generated from the time-varying transient signal.

[0025] The system further includes a comparison module configured to identify one or more pseudo-peaks in the first mass spectrum by comparing the first mass spectrum with at least one perturbed mass spectrum in the perturbed mass spectrum. In some embodiments, at least one of the pseudo-peaks is identified based on the peak not being present in the intersection of the first mass spectrum and at least one perturbed mass spectrum in the perturbed mass spectrum. Additionally or alternatively, at least one of the pseudo-peaks can be identified based on a mass-to-charge ratio (or mass or frequency) change of the peak between the first mass spectrum and at least one perturbed mass spectrum in the perturbed mass spectrum exceeding a predetermined threshold.

[0026] The present invention also provides one or more computer programs suitable for execution by one or more processors, such computer programs being arranged to implement the methods outlined above and described herein. The present invention also provides one or more computer readable media and / or data signals carried over a network, the one or more computer readable media and / or data signals comprising (or having stored thereon) such one or more computer programs. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The invention may be practiced in various ways and some of these will now be described by way of example only and with reference to the following drawings, in which:

[0028] FIG. 1 a shows an example of a known resolution problem.

[0029] FIG. 1 b shows another example of a known resolution problem.

[0030] Figure 2 A schematic arrangement of a typical mass spectrometer is shown.

[0031] Figure 3 An example of a computer system is schematically shown.

[0032] FIG4a shows an example graphical representation of a mass spectrum.

[0033] Figure 4B An example processing system for identifying pseudo-peaks is schematically illustrated.

[0034] Figure 4C A variant example processing system for identifying pseudo-peaks is schematically illustrated.

[0035] Figure 5A A schematic diagram is shown showing how Figure 4B and 4C Flowchart of a method for identifying pseudo peaks in a mass spectrum performed by any one of the example processing systems in the example processing systems.

[0036] Figure 5B A first mass spectrum corresponding to a converged set of values ​​for a set of parameters and a perturbed mass spectrum corresponding to a perturbed version of the set of values ​​for the parameter set are shown.

[0037] FIG. 6A shows a mass spectrum in the form of a frequency versus intensity plot, which is produced by applying a phase-constrained spectral deconvolution method to an artificially generated noise-free initial mass spectrum.

[0038] FIG. 6B shows a flow chart schematically illustrating a variant of the method previously described with respect to FIG. 5 , wherein the regularized inversion algorithm is a phase-constrained spectral deconvolution method.

[0039] Figure 6CA mass spectrum resulting from a method 600 such as that shown in FIG. 6B is shown where multiple spurious peaks have been identified.

[0040] Figure 7 Q Exactive treated with the method according to the invention is shown TM HF-X HybridQuadrupole- Orbitrap TM Mass spectrometer Three mass spectra generated from CalMix samples in a mass spectrometry experiment. DETAILED DESCRIPTION

[0041] In the following description and in the accompanying drawings, certain embodiments of the present invention are described. However, it should be understood that the present invention is not limited to the embodiments described, and some embodiments may not include all of the features described below. However, it is apparent that various modifications and variations may be made herein without departing from the broader spirit and scope of the present invention as set forth in the appended claims.

[0042] Figure 2 Shown is a schematic arrangement of a typical orbitrap-type mass spectrometer sold under the name Orbitrap(TM) by Thermo Fisher Scientific(TM). Figure 2 The arrangement of is described in detail in commonly assigned WO-A-02 / 078046, the entire contents of which are incorporated herein by reference, and will not be described in detail here. However, in order to better understand the use and purpose of the mass spectrometer, a description of Figure 2 A brief description of .

[0043] like Figure 2 As seen in Figure 1, the mass spectrometer 10 includes a continuous or pulsed ion source 20 that generates gas phase ions. These gas phase ions pass through an ion source block 30 into an RF transmission device 40 that cools the ions by colliding with a gas. The cooled ions then enter a mass filter 50 that extracts only those ions within a window of m / z ratios of interest. The ions within the mass range of interest then travel to a linear trap 60 (typically a C-shaped trap) that stores the ions in a trapping volume by applying an RF potential to a set of rods (typically quadrupoles, hexapole rods, or octopole rods).

[0044] As explained in more detail in WO-A-02 / 078046, ions are held in a linear trap 60 in a potential well, the bottom of which may be positioned adjacent to an exit electrode of the potential well. By applying a DC pulse to the exit electrode of the linear trap 60, ions are ejected from the linear trap 60 into a lens arrangement 70. The ions pass through the lens arrangement 70 along a line that is curved to avoid blow-by and into an electrostatic trap 80 (also referred to as a mass analyser). Figure 2In the embodiment shown, the electrostatic trap 80 is of the so-called orbital trap type sold under the name Orbitrap(TM) by Thermo Fisher Scientific(TM), comprising segmented outer electrodes 84, 85 and an inner electrode 90.

[0045] In operation, a voltage pulse is applied to the exit electrode of the linear trap 60 to release the trapped ions. The ions arrive at the entrance of the electrostatic trap 80 as a series of short energetic packets, each comprising ions with similar m / z ratios.

[0046] The ions enter the electrostatic trap 80 as a coherent bunch and are squeezed towards the central electrode 90. The ions are then trapped in the electrostatic field so that they oscillate along the central electrode at a frequency that depends on the m / z ratio of the ions. The image current is detected by a first outer electrode 84 and a second outer electrode 85, providing a first harmonic transient signal 81 and a second harmonic transient signal 82, respectively. The two signals are then processed by a differential amplifier 100 and provide a transient image current signal 101 (referred to herein as transient).

[0047] Thus, transient state 101 comprises a superposition of one or more periodic signals (or harmonic spectral components). Each periodic signal corresponds to the oscillation of a respective coherent ion packet within the mass analyser at a respective characteristic frequency determined by the m / z ratio of the ions.

[0048] It should be understood that the mass spectrometer 10 outlined above serves merely as an example of how transient states 101 may be generated. The embodiments of the invention presented below may use any suitable transient states 101 produced by any mass spectrometer 10. In particular, although the mass spectrometer described above is an Orbitrap(TM) mass spectrometer, i.e., a specific example of a mass spectrometer using an orbital capture electrostatic trap, the embodiments of the invention described below are not limited to such a mass spectrometer.

[0049] As described above, the frequency of the periodic signal present in the transient state is a function of the m / z ratio of the ion species. Therefore, the center of mass of each peak can be converted (or transformed or interpreted) into the corresponding m / z ratio, thereby identifying the corresponding ion species. In addition, the height or intensity of each peak can be converted (or transformed or interpreted) into the corresponding relative abundance of the corresponding ion species. In this way, it should be understood that the mass in the mass spectrum can be expressed differently as an absolute mass value, a mass-to-charge ratio (m / z), a frequency value, etc. Similarly, the relative abundance mass spectrum in the mass spectrum can be expressed differently as an intensity value, a peak height, etc. In this specification, the term mass spectrum means an ion abundance spectrum in a mass (e.g., m / z) domain, wherein the mass (m / z) value can be expressed as a frequency value. Therefore, it should be understood that the reference to mass (m / z) herein includes a reference to frequency, and vice versa. Therefore, the terms mass spectrum and frequency spectrum are used interchangeably.

[0050] Figure 3 An example of a computer system 300 is schematically shown. The system 300 includes a computer 302. The computer 302 includes a storage medium 304, a memory 306, a processor 308, an interface 310, a user output interface 312, a user input interface 314, and a network interface 316, all of which are connected together via one or more communication buses 318.

[0051] The storage medium 304 may be any form of non-volatile data storage device, such as one or more of a hard drive, a magnetic disk, an optical disk, a ROM, etc. The storage medium 304 may store an operating system that is executed by the processor 308 to enable the computer 302 to operate. The storage medium 304 may also store one or more computer programs (or software or instructions or codes).

[0052] The memory 306 may be any random access memory (storage unit or volatile storage medium) suitable for storing data and / or computer programs (or software or instructions or code).

[0053] The processor 308 may be any data processing unit suitable for executing one or more computer programs (such as those stored on the storage medium 304 and / or in the memory 306), some of which may be computer programs according to embodiments of the present invention or such computer programs, which when executed by the processor 308, cause the processor 308 to implement a method according to embodiments of the present invention and configure the system 300 into a system according to embodiments of the present invention. The processor 308 may include a single data processing unit or multiple data processing units operating in parallel, individually or in cooperation with each other. The processor 308 may store data to the storage medium 304 and / or the memory 306 and / or read data therefrom when implementing data processing operations for performing embodiments of the present invention.

[0054] The interface 310 may be any unit for providing an interface to a device 322 that is external to the computer 302 or removable from the computer. The device 322 may be a data storage device, such as one or more of an optical disk, a magnetic disk, a solid-state storage device, etc. The device 322 may have processing capabilities—for example, the device may be a smart card. Thus, according to one or more commands received by the device 322 from the processor 308, the interface 310 may access data from the device, provide data to the device, or connect to the device.

[0055] The user input interface 314 is arranged to receive input from a user or operator of the system 300. The user may provide such input via one or more input devices of the system 300 connected to or in communication with the user input interface 314, such as a mouse (or other pointing device) 326 and / or a keyboard 324. However, it should be appreciated that the user may provide input to the computer 302 via one or more additional or alternative input devices, such as a touch screen. The computer 302 may store input received from the input devices via the user input interface 314 in the memory 306 for subsequent access and processing by the processor 308, or may transmit the input directly to the processor 308 so that the processor 308 may react accordingly to the user input.

[0056] The user output interface 312 is arranged to provide graphical / visual output to a user or operator of the system 300. As such, the processor 308 may be arranged to instruct the user output interface 312 to form an image / video signal representing the desired graphical output and to provide this signal to a monitor (or display screen or display unit) 320 of the system 300 connected to the user output interface 312.

[0057] Finally, network interface 316 provides functionality for computer 302 to download data from and / or upload data to one or more data communications networks.

[0058] It should be understood that Figure 3 The architecture of the system 300 described and described above is merely exemplary and may be used in embodiments of the present invention with different architectures (e.g., compared to Figure 3 , with fewer components, or compared to Figure 3 , with additional and / or alternative components). As an example, computer system 300 may include one or more of the following: a personal computer; a server computer; a laptop computer; etc.

[0059] FIG. 4 a shows an example graphical representation of a mass spectrum 390 .

[0060] The mass spectrum 390 includes one or more m / z values ​​(or mass-to-charge ratios) 394-n. Each m / z value corresponds to a corresponding ion species and is equal to the molecular mass of the corresponding ion species divided by the absolute elemental charge of the corresponding ion species. The mass spectrum 390 includes one or more intensity values ​​396-n, each intensity value 396-n is presented for a corresponding m / z value 394-n. Each intensity value 396-n is related to the relative abundance of the ion species corresponding to the corresponding m / z value 394-n. Each intensity value 396-n can be proportional to the relative abundance of the ion species corresponding to the corresponding m / z value.

[0061] Experimental mass spectra such as mass spectrum 390 can be plotted in the form of a continuous curve indicated by a dashed line and a centroid curve indicated by a vertical solid line. The width of the peak indicated by the dashed line represents the limit of mass resolving power, which is the ability to distinguish between two different ion species with close m / z ratios.

[0062] However, it is apparent that mass spectrum 390 need not be drawn in the form of a graph. In fact, mass spectrum 390 can be represented in any suitable form. For example, mass spectrum 390 can be represented as a list including one or more intensity values ​​396-n and one or more m / z values ​​394-n.

[0063] Figure 4B An example processing system 400 is schematically illustrated. The figure shows that the processing system 400 generates a plurality of mass spectra 390, 3901, 390 N , all mass spectra correspond to transient state 101 as described previously. Figure 4B The processing system 400 also shows the generated mass spectra 390, 3901, ..., 390 N The comparison is performed to identify one or more pseudo peaks in at least one of the following mass spectra: 390, 3901, ..., 390 N . Mass spectra 390, 3901, ..., 390 N can be as described above and Figure 4A As shown in . Figure 4B The mass spectra 390, 3901, ..., 390 N The first mass spectrum 390 and two perturbation mass spectra 3901, ..., 390 N However, it should be understood that this number of perturbed mass spectra is shown for ease of illustration, and the present invention is not limited to two perturbed mass spectra 3901, ..., 390 N The present invention can be operated with a single perturbation mass spectrum 3901 or more than two perturbation mass spectra 3901, ..., 390 N .

[0064] The processing system 400 includes a deconvolution module 420 and a comparison module 440. Figure 3 Processing system 400 is implemented on computer system 300 as depicted.

[0065] Processing system 400 may be communicatively coupled to mass spectrometer 10. For example, processing system 400 may be communicatively coupled to mass spectrometer 10 via network interface 316. Processing system 400 is arranged to receive transient 101. For example, processing system 400 may be arranged to receive transient 101 via any of: network interface 316; input interface 310; user input interface 314; etc. Processing system 400 may be arranged to have transient 101 stored thereon. For example, transient 101 may be stored on storage device 304.

[0066] The transient 101 can be represented by a time-varying function S(t). The transient is measured (or captured or recorded) only within a finite time T, which is referred to as the "duration" of the transient. For the purpose of discussion, the time-varying function S(t) representing the transient is shown as a continuous function of time t. However, it should be understood that the transient 101 can also or alternatively be sampled. Specifically, the transient can be measured by a set of times t0, t1, ..., t N A set of values To indicate that The transient can be sampled at regular time intervals. For example, t k =kΔt, where k is an integer and Δt is a regular time interval.

[0067] The deconvolution module 420 includes a transient processing module 410. The transient processing module 410 is arranged to generate (or calculate or otherwise produce) an initial mass spectrum 390 from the transient 101. Init It should be understood that the mass spectrum used to generate this initial mass spectrum 390 Init The technique will depend on the mass spectrometer 10 used to generate the transient state 101. For example, if the mass spectrometer 10 is of the FTMS type (e.g., an Orbitrap (TM) mass analyzer or an FT-ICR mass analyzer), generating a mass spectrum from the transient state will typically involve performing a discrete Fourier transform on the transient state 101. It will be appreciated that generating a mass spectrum from a transient state produced by a mass spectrometer will be a routine task for those skilled in the art and will therefore not be described in further detail herein.

[0068] Consistent with the above discussion, it should be understood that the initial mass spectrum 390 Init The mass spectra 390, 3901, 3902, 3903 may contain multiple convolution peaks, and in order to improve the accuracy of the mass spectrum, it is desirable to deconvolve (or decompose) the multiple convolution peaks. The deconvolution module 420 is arranged to generate (or calculate or otherwise produce) mass spectra 390, 3901, . . . , 390 N , the mass spectrum corresponds to the time-varying transient signal 101. Specifically, the deconvolution module 420 is arranged to generate mass spectra 390, 3901, ..., 390 using a regularized inversion (or deconvolution) algorithm. NThe regularized deconvolution algorithm will be briefly discussed below, however, it should be understood that this regularized deconvolution algorithm seeks to convert the initial mass spectrum, such as the initial mass spectrum 390 Init deconvolutes one or more peaks in the mass spectrum, which typically generates another mass spectrum 390, 3901, ..., 390 N As output, some or all of the peaks in the peaks have been deconvolved. The algorithm is affected by one or more adjustable parameters, which can usually be varied to ensure that the algorithm converges to a solution. Examples of such regularized deconvolution algorithms include PSDM and regularized deblurring. In regularized deblurring, under appropriately selected penalty constraints, the deblurring kernel (such as Gaussian) is approximately compensated by subsequent deconvolution and regularization. Examples of regularized deblurring are described in the following literature: Mueller, JL, Siltanen, S., "Linear and Nonlinear Inverse Problems with Practical Applications" (2012), Cambridge University Press. ISBN 978-1-61197-233-7, which is incorporated herein by reference in its entirety.

[0069] The nature of the adjustable parameters typically varies between different regularized inversion algorithms. However, many regularized inversion algorithms are iterative. In other words, the regularized inversion algorithm may include an iterative procedure, such as an optimization procedure. In such cases, an adjustable parameter that governs the number of iterations may be used. For example, the adjustable parameter may be a maximum number of iterations; a convergence threshold that terminates the iterative procedure if met; a time limit (such as wall clock time or number of processing cycles) that terminates the iterative procedure if exceeded; and so on. It should also be understood that many regularized inversion algorithms blank multiple entries of the time-varying transient before processing. Typically, entries at the beginning or end of the time-varying transient are blanked, for example to eliminate or reduce boundary effects where the signal is substantially non-periodic (such as due to voltage accumulation). In such cases, an adjustable parameter that governs blanking may be used. For example, the adjustable parameter may be the number of blanked entries of the time-varying transient; a signal threshold that blanks the portion of the time-varying transient if the time-varying transient does not exceed; and so on.

[0070] The value of the adjustable parameter of the regularized inversion algorithm is used when generating a mass spectrum from a set of values ​​of the adjustable parameter, the set of values ​​corresponding to the generated mass spectra 390, 3901, ..., 390 N The deconvolution module 420 is arranged to generate two or more mass spectra 390, 3901, ..., 390 using different sets of values ​​of the adjustable parameters.N Specifically, a first mass spectrum 390 is generated using a first set of values ​​of an adjustable parameter, and at least one perturbed version of the first set of values ​​of the adjustable parameter is used to generate at least one perturbed mass spectrum 3901, ..., 390 N A perturbed version of a first set of values ​​is a set of values ​​in which at least one of the values ​​is different from a corresponding value in the first set of values. The difference(s) between a value in the first set of values ​​and a value in the perturbed version of the first set of values ​​is typically small relative to the magnitude of the value in question. However, it will be appreciated that in some cases the difference may be larger.

[0071] The first set of values ​​is typically selected based on the convergence criteria of the regularized inversion algorithm. Specifically, the first set of values ​​may be selected as in order to provide a first mass spectrum of appropriate convergence. In this way, the first set of values ​​may be automatically selected as by the deconvolution module 420. Additionally or alternatively, the first set of values ​​may be at least partially selected by a user or by a user input to an automatic selection process. It should be appreciated that the selection of the first set of values ​​depends on the regularized inversion algorithm. Similarly, the generation of a perturbed version of the first set of values ​​may be automatic. Additionally or alternatively, the selection of the generation of a perturbed version of the first set of values ​​may be at least partially performed by a user or based on a user input to an automatic generation process.

[0072] The comparison module 440 may be arranged to identify one or more pseudo-peaks in the first mass spectrum 390 by comparing the first mass spectrum 390 and the perturbed mass spectra 3901, ..., 390 N Specifically, the comparison module 440 can compare the at least one perturbed mass spectrum present in the first mass spectrum 390 and not present in the perturbed mass spectrum 3901, ..., 390 N In one or more perturbed mass spectra of the first mass spectrum 390, a peak is identified as a pseudo peak. Additionally or alternatively, if a peak in the first mass spectrum 390 is in the perturbed mass spectra 3901, ..., 390 N If a peak appears in at least one perturbed mass spectrum in the first mass spectrum at a frequency (or m / z value) that exceeds a predetermined threshold relative to the position of the peak in the first mass spectrum, the peak can be identified as a pseudo peak. It should be understood that multiple relevant criteria can be used in combination or alone to determine pseudo peaks. If a peak is unstable across one or more mass spectra, the peak can be determined to be pseudo. Specifically, unstable peaks can be in mass spectra 390, 3901, ..., 390 N For example, when the frequency position of a peak does not change by more than a predetermined threshold between one or more mass spectra in mass spectra 390, 3901, ..., 390 NIn some embodiments, the peak is considered to be stable when the intensity of a peak does not change by more than a threshold amount. When the distance between the peaks in the mass spectra is greater than half the bin width of the frequency grid in the mass spectra, the peak can be considered to be stable. In addition or alternatively, the measure of the distance on the intensity axis can be used as a criterion for stability. For example, when the intensity of a peak does not change by more than a threshold amount, the peak can be considered to be stable. A combination of these criteria can be used. Therefore, if the distance between the difference in intensity and / or frequency (m / z) of a peak between mass spectra is greater than a predetermined threshold, the peak can be considered to be pseudo. In general, it should be understood that any suitable measure of the distance between the peaks in the two mass spectra can be used to determine whether the peak is pseudo.

[0073] It should also be appreciated that in some instances, the comparison module 440 can identify pseudo peaks in the first mass spectrum by identifying non-pseudo (or valid) peaks in the first mass spectrum and determining that the remaining peaks are pseudo. It should be appreciated that the criteria for identifying pseudo peaks can be used in reverse to identify peaks as valid. For example, if a peak is present in the intersection of each mass spectrum in the first mass spectrum and the perturbed mass spectrum, the peak can be considered valid. Typically, if there is a peak in each mass spectrum whose frequency change does not exceed the above-mentioned stability threshold, a peak will be considered to be present in two or more mass spectra. More generally, if the distance of a peak between mass spectra based on the difference in intensity and / or frequency (m / z) is greater than a predetermined threshold, the peak can be considered to be pseudo. An example of measuring distance is (where dM is the frequency (m / z) difference and dI is the intensity difference)

[0074] (a)|dM|+|dI|

[0075] (b)√((dM) 2 +(dI) 2 )

[0076] In addition, peaks can be classified as suspicious (e.g., neither obviously valid nor invalid). For example, if a peak is not present in at least one but not all of the perturbed spectra, the peak can be defined as "suspicious". The processing system 400 is typically arranged to output one or more identified pseudo peaks. The system can be arranged to output the pseudo peaks directly as data representing a set of pseudo peaks 145. In addition or alternatively, the processing system 400 can be arranged to output one or more pseudo peaks as part of a modified mass spectrum 151. The modified mass spectrum can correspond to a first mass spectrum in which one or more pseudo peaks are removed. Alternatively, the modified mass spectrum can correspond to a first mass spectrum in which one or more pseudo peaks are marked (or otherwise identified) as pseudo.

[0077] References in the above Figure 4BIn the processing system 400 described, the processing system receives the transient state 101 as input. However, it should be understood that variations of the processing system 400 may directly receive the initial mass spectrum 390 Init As input. Specifically, Figure 4C As shown in FIG. , the processing system 400 receives the initial mass spectrum 390 Init as input. Figure 4C The processing system 400 shown in FIG. 4 also omits the mass transient processing module 410. In such cases, it may be assumed that the processing performed by the mass transient processing module is performed elsewhere, such as on the mass spectrometer 10 itself.

[0078] The processing system 400 may be communicatively coupled to the mass spectrometer 10. For example, the processing system 400 may be communicatively coupled to the mass spectrometer via the network interface 316. The processing system 400 is arranged to receive the initial mass spectrum 390 Init For example, processing system 400 may be arranged to receive initial mass spectrum 390 by any of the following: Init : network interface 316 ; input interface 310 ; user input interface 314 ; etc. Transient processing system 400 may be arranged to have transient 101 stored thereon. For example, transient 101 may be stored on storage device 304 .

[0079] In addition to the changes outlined above, it should be understood that Figure 4C The variation of the processing system 400 shown in FIG. 4 is as described above. Figure 4B The processing system 400 shown in FIG. 4 operates.

[0080] As discussed herein, regularized inversion can be understood as a reasonable choice of constrained inversion scheme for recovering a signal that is robust to variations in noise, see, for example, the already cited Mueller, JL, Siltanen, S., "Linear and Nonlinear Inverse Problems with Practical Applications" for a discussion of this. Regularization can be understood as a way of reducing the degrees of freedom of the inversion method, with the goal of producing a version of the inversion problem with a unique (or substantially unique) solution. Typically, regularization is used to introduce a priori knowledge of the expected solution into the inversion procedure. For example, in PSDM, the expected phase of each of the calculated complex amplitudes is introduced via a phase constraint.

[0081] Therefore, the regularized inversion algorithm generally includes an inversion algorithm with one or more constraints (or is affected by the one or more constraints). The algorithm converges to a solution and is generally governed (or affected) by one or more parameters. Such parameters can directly control regularization. For example, in PSDM, an example parameter can be uncertainty (or relaxation) around the expected phase. In addition or alternatively, such parameters can be parameters of the inversion algorithm. For example, in PSDM, such parameters can include any one of the following: the weighting of the cutoff (maximum) number of iterations in the optimization, the number of blanking entries in the time-varying transient, or the optional penalty term (such as L1-penalty, L2-penalty) in the optimization problem (see, for example, Mueller, JL, Siltanen, S., "Linear and nonlinear inverse problems in practical applications" already cited).

[0082] Figure 5A FIG. 5 is a flow chart schematically illustrating a method 500 for identifying pseudo peaks in a mass spectrum. The method 500 may be performed by a processing system as described above with respect to Figure 4B and 4C The method 500 may be performed by any of the example processing systems 400 discussed above. The mass spectrum is a mass spectrum generated by the time-varying transient signal 101 detected in the mass spectrometer 10. The steps of the method 500 are set forth below.

[0083] At step 510, a first mass spectrum is generated using a regularized inversion algorithm. Step 510 may be performed by deconvolution module 420. The regularized inversion algorithm has one or more adjustable parameters as discussed briefly below. The first mass spectrum is generated based on (or by) the time-varying transient signal 101.

[0084] It should be understood that step 510 may include applying (or performing) a regularized inversion algorithm to the time-varying transient signal 101. In other words, the first mass spectrum may be generated directly by the time-varying transient signal 101. Alternatively, step 510 may include applying a regularized inversion algorithm to an initial mass spectrum. In this case, the initial mass spectrum is a mass spectrum calculated (or determined or otherwise generated) by the time-varying transient signal 101. The initial mass spectrum may be or correspond to a mass spectrum generated at a standard resolution of the time-varying transient signal. For example, for a time-varying transient signal generated using an FTMS mass spectrometer 10, the initial mass spectrum may correspond to a mass spectrum generated using a Fourier grid spaced 1 / T.

[0085] The value of one or more adjustable parameters for generating the first mass spectrum in step 510 comes from a first set of values. For ease of discussion, discussion herein will relate to a set of values ​​including the corresponding value of each adjustable parameter in the adjustable parameters. However, it should be appreciated that in an embodiment where a single adjustable parameter is present, a set of values ​​will be formed by a single value. The first set of values ​​can generally be a set of values ​​that produce a first mass spectrum that converges about one or more accuracy metrics. The accuracy metric and its convergence threshold are generally specified by the user. This selection can be based on the convergence of a suitable difference metric and / or be subject to the limitation of real-time processing constraints. For example, the variation between iterations, like the disappearance difference variation of one of the spectrum or auxiliary spectrum in the PSDM output during iteration can be used as a metric. It should be appreciated that it is a conventional procedure for a technician to adjust a parameter to determine a suitable set of values ​​for producing a mass spectrum that is appropriately converged and therefore no longer discussed further herein.

[0086] At step 520, a perturbed mass spectrum is generated using a regularized inversion algorithm. Step 520 may be performed by the deconvolution module 420. The perturbed mass spectrum is generated based on (or by) the time-varying transient signal 101. As with step 510, it should be appreciated that step 520 may include applying (or executing) the regularized inversion algorithm directly to the time-varying transient signal 101.

[0087] The values ​​of the one or more adjustable parameters used to generate the perturbed mass spectrum in step 520 form a perturbed version of the first set of values. The perturbed version of the first set of values ​​is a set of values ​​in which at least one of the values ​​is different from the corresponding value in the first set of values. The difference (one or more) between the values ​​in the first set of values ​​and the perturbed version of the first set of values ​​is typically small relative to the magnitude of the value in question. However, it should be appreciated that in some cases the difference may be larger.

[0088] Step 520 may be repeated to form a plurality of perturbed mass spectra. Each perturbed mass spectrum in the plurality of perturbed mass spectra is generated using a corresponding perturbed version of the first set of values. It should be understood that the various perturbed versions of the first set of values ​​will differ by one or more values.

[0089] At step 530, one or more pseudo peaks in the first mass spectrum are identified by comparing the first mass spectrum to at least one of the perturbed mass spectra. Although the comparison of mass spectra can be performed in the mass (m / z) domain, it is generally more efficient to perform the comparison in the frequency domain. Step 530 can be performed by comparison module 440. As described above, if a peak is unstable, the peak can be marked as pseudo. An unstable peak can be defined as a peak whose frequency varies by more than a threshold amount between two or more mass spectra. Figure 5BAn example of this is shown in , which shows two mass spectra, a first mass spectrum corresponding to a set of converged values ​​for a set of parameters and a perturbed mass spectrum corresponding to a perturbed version of a set of values ​​for the parameter set. The frequency difference Δf of the two peaks 5921 and 5922 of the first mass spectrum and the perturbed mass spectrum, respectively, is less than a predetermined threshold δ (or within the predetermined threshold), and is therefore determined to be stable. The frequency difference Δf of the two peaks 5941 and 5942 of the first mass spectrum and the perturbed mass spectrum, respectively, is greater than a predetermined threshold δ (or outside the predetermined threshold), and is therefore determined to be unstable.

[0090] Additionally or alternatively, if a peak is not present in both the first mass spectrum and all perturbed mass spectra, the peak may be identified as being spurious. If a peak appears in less than a predetermined number of perturbed mass spectra, the peak may also be identified as being spurious. It should be appreciated that such pseudo-peaks may be further classified based on which criteria such pseudo-peaks have or have not met. For example, a peak that appears in less than a predetermined number of perturbed mass spectra may be so identified (e.g., using the label "suspicious"), while a peak that appears only in the first mass spectrum and does not appear in any perturbed mass spectra may be defined as "invalid".

[0091] It will be appreciated that step 530 may further include outputting the identification in a suitable form. The pseudo peaks may be directly output as data representing a set of pseudo peaks 145. Additionally or alternatively, a modified mass spectrum 151 may be output. The modified mass spectrum may correspond to a first mass spectrum 390 in which one or more pseudo peaks are removed. Alternatively, the modified mass spectrum may correspond to a first mass spectrum 390 in which one or more pseudo peaks are marked (or otherwise identified) as pseudo. Likewise, it will be appreciated that where the pseudo peaks have been further classified, such further classification may form part of the output in a similar manner.

[0092] In the above discussion, it should be understood that since pseudo-peaks, which are artifacts of the regularized inversion, are more sensitive to changes in the values ​​of the parameters used for the regularized inversion than true (or effective) peaks, the identification of pseudo-peaks is improved. This is described in detail in Appendix A. Therefore, by comparing the perturbed mass spectrum with the first mass spectrum, pseudo-peaks can be identified. It should be understood that such identification can be performed in many ways based on this difference in sensitivity between true peaks and pseudo-peaks. Therefore, the specific criteria for identification described above are merely exemplary.

[0093] In order to better understand the present invention, various specific examples are now discussed with reference to specific regularized deconvolution algorithms. However, it should be understood that the present invention is not limited to the use of these specific deconvolution algorithms.

[0094] FIG. 6A shows a mass spectrum 600 in the form of a frequency versus intensity plot, which is produced by applying the PSDM to an artificially generated noise-free initial mass spectrum.

[0095] In this example, the transient is generated by the following steps:

[0096] Obtain a list of random masses and constant corresponding abundances of the known components of the calibration mixture;

[0097] Convert mass lists and abundance lists to the frequency domain;

[0098] Generate transients in the time domain by linear superposition of harmonic components;

[0099] • Transient intensity noise has been ignored to indicate that artifacts still occur at vanishing noise levels.

[0100] This minimal example has ignored transient decay.

[0101] The transients were digitized according to the sampling rate (4996kHz), A / D discretization (+ / -32768 integer steps), and acquisition length (65536 samples) to mimic a common experimental setup.

[0102] A plurality of peaks 610 are shown in the mass spectrum 600. However, as shown in a magnified portion 650 of the mass spectrum 600, a plurality of spurious peaks 620 are present in the mass spectrum 600. These spurious peaks are due to the inherent ill-posed and ill-posed nature of the deconvolution problem.

[0103] As previously discussed, the PSDM method uses a phase constraint in the form of a feasibility cone in the complex solution plane to regularize the calculated complex amplitude. However, in the artificially generated birth mass spectrum discussed above, the expected phase of the complex amplitude is exactly known (by construction). However, even if all input parameters (including the initial phase) are exactly known without any uncertainty, the potential discrete deconvolution problem is still pathological, resulting in pseudo peaks 620 in the generated PSDM mass spectrum 600, as can be seen from Figure 6A. As described in Appendix A, this is inherent to any regularized inversion algorithm and is not only applicable to the PSDM technique.

[0104] FIG. 6B schematically shows the previously described Figure 5AFlow chart of variant 660 of method 500 described for identifying pseudo peaks in mass spectrum. Variant method 660 is an example of method 500, wherein the regularized inversion algorithm is a phase-constrained spectral deconvolution method. The phase-constrained spectral deconvolution method is discussed in more detail in Appendix B, however, it should be understood that the phase-constrained spectral deconvolution method is well known to the technician. Except for the differences described below, variant method 660 is the same as method 500 described above. In this case, the time-varying transient signal 101 is generated using a FTMS type mass spectrometer 10.

[0105] At steps 510 and 520, the regularized inversion algorithm includes a phase-constrained spectral deconvolution method. A set of parameters may include any combination of the following: the number of zero blanking entries of the transient; the number of cutoff iterations in the iterative optimization of the PSDM; or the weight of an optional penalty term (L1-penalty, L2-penalty) in the optimization problem. It has been found that it is particularly advantageous to use one or both of the number of zero blanking entries of the transient and the number of cutoff iterations in the iterative optimization of the PSDM as parameters whose values ​​vary in a perturbed version of the values ​​of a set of parameters. The change in the number of zero blanking entries of the transient results in significantly different frequency distributions of spectral artifacts, while the change in the number of cutoff iterations presents another degree of freedom that is less sensitive to small perturbations. Typically, the computation time is directly proportional to the number of cutoff iterations, while the effect of the number of zero blanking entries on the computation time is often negligible. The accuracy of the identification can be achieved by changing a reasonable compromise between the computational workload.

[0106] Thus, at step 510, a PSDM calculation with a standard (convergent) value of the number of zero blanking entries and the number of cutoff iterations for the transient can be performed. For example, when the initial portion of the transient representing the ramp of the voltage in the ion trap is completely blanked, the PSDM calculation converges with respect to the number of zero blanking entries for the transient. It should be appreciated that the voltage ramp can usually be clearly identified by inspection as a large non-periodic signal at the beginning of the transient. This produces a first mass spectrum 390.

[0107] At step 520, a perturbed mass spectrum 3901 is calculated using a set of values ​​of the PSDM and a set of perturbations of a set of parameters. The set of values ​​of the perturbations may include corrections for both the number of zero blanking entries of the transient and the number of cutoff iterations in the iterative optimization of the PSDM. Alternatively, a correction for only one of the number of zero blanking entries of the transient and the number of cutoff iterations in the iterative optimization of the PSDM may be included. For reasons of computational efficiency, the number of iterations in the set of values ​​of the perturbations may be reduced and / or the number of blanking portions may be increased. However, it should be appreciated that the present invention is not limited to such perturbations.

[0108] As previously described, step 520 may be repeated to generate a plurality of perturbed mass spectra 3901, ..., 390 N .

[0109] In step 530, pseudo-peaks may be identified by comparing two or more of the mass spectra as previously described.

[0110] Figure 6C The mass spectrum produced by the method 600 shown in FIG. 6B is shown in which multiple pseudo peaks have been identified. The mass spectrum shown in FIG. 6C is a computer simulated spectrum from an artificially generated calibration mixture ("CalMix") transient containing artificially generated noise. The time-varying transient is based on the Figure 6C The peak 690 indicated as "ground truth" in FIG. 1 is generated. The total length of the transient is 262144 entries (which corresponds to 64 milliseconds at a sampling rate of 4096 kHz). In this example, the transient is generated by the following steps:

[0111] Obtain a list of masses and relative abundances of the known components of the calibration mixture;

[0112] Convert mass lists and relative abundance lists to the frequency domain;

[0113] Generate transients in the time domain by linear superposition of harmonic components and quadratic phase crossover frequency functions;

[0114] Added generation of phase noise and transient intensity noise using a pseudo-random number generator. The probability distribution and distribution parameters (e.g., variance, correlation time, etc.) were chosen based on values ​​measured in previous experiments;

[0115] The decay constant of the signal was simulated to be 2.25 1 / s based on the decay constant measured in previous experiments.

[0116] • Digitize transients with sampling rate, A / D discretization, and dynamic range consistent with the example measurement instrument.

[0117] The transients were digitized with sampling rate (4996kHz), A / D discretization (+ / -32768 integer steps), and acquisition length (262144 samples) to mimic common experimental setups.

[0118] For the first mass spectrum, the number of cutoff iterations n used iter is 50, and the number of blanking entries in the transient state is N zb is 1876. Two perturbed mass spectra were generated, one with n iter =3 and N zb =1876+400, another perturbation spectrum has n iter =20 and N zb,2=1876+200. When identifying pseudo peaks, a peak is considered stable if the frequency change does not exceed half the bin width under parameter changes. With respect to the above stability criteria, a peak marked as valid with a circle meets the criterion that the peak is in the intersection of all three mass spectra. A peak marked as suspicious with a triangle meets the criterion that the peak is in the intersection of the first mass spectrum 390 and only one of the perturbed mass spectra. In addition, a noise band is shown, which shows an intensity threshold below which the peak is considered noise.

[0119] exist Figure 7 , three mass spectra 710, 720, 730 are shown, which are obtained using Q Exactive TM HF-X Hybrid Quadrupole-Orbitrap TM The mass spectrometry experiments were performed using a commercially available CalMix sample generated as described above. Figure 6C The transients were processed in the same manner as described in . The transient settings sampling rate and acquisition length are the same as those in the computer simulation examples mentioned above. The PSDM phase parameters are obtained by a calibration procedure that uses exactly the same CalMix reagent to fit the frequency-phase dispersion relationship to a quadratic function. Mass spectrum 710 corresponds to the first mass spectrum and shows a central caffeine peak surrounded by peaks suspected of being false positive peaks. Mass spectrum 720 shows the first mass spectrum in which some false positive peaks in the false positive peaks are removed by the method of the present invention. This mass spectrum 720 contains peaks marked as valid and peaks marked as suspicious. Mass spectrum 730 shows the first mass spectrum in which only the central caffeine peak is marked as valid. This confirms that the false positive peaks are successfully removed using the method of the present invention.

[0120] Revise

[0121] It should be understood that the described methods have been shown as individual steps performed in a particular order. However, the skilled person will appreciate that these steps can be combined or performed in a different order while still achieving the desired result.

[0122] Although the above discussion generally relates to Fourier transforms, it should be appreciated that the methods and systems herein are generally applicable to any form of suitable transform. A skilled person will understand a suitable transform as one that is suitable for a particular mass spectrometry experiment, in particular a particular type of mass analyzer, used to generate the transient signal.

[0123] It should be understood that a variety of different information processing systems can be used to implement embodiments of the present invention. Specifically, although the figures and their discussion provide exemplary computing systems and methods, these are only presented to provide useful references when discussing aspects of the present invention. Embodiments of the present invention can be performed on any suitable data processing device, such as a personal computer, a laptop computer, a personal digital assistant, a mobile phone, a server computer, etc. Of course, for the purpose of discussion, the description of the system and method has been simplified, and they are only one of many different types of systems and methods that can be used for embodiments of the present invention. It should be understood that the boundaries between the logic blocks are only illustrative and alternative embodiments can merge logic blocks or elements, or alternative decompositions of functions can be applied to various logic blocks or elements.

[0124] It should be understood that the above functionality can be implemented as hardware and / or software as one or more corresponding modules. For example, the above functions can be implemented as one or more software components executed by a processor of the system. Alternatively, the above functionality can be implemented as hardware such as on one or more field programmable gate arrays (FPGAs), and / or one or more application specific integrated circuits (ASICs) and / or one or more digital signal processors (DSPs) and / or other hardware arrangements. The method steps implemented according to the flowcharts contained herein or as described above can each be implemented by a corresponding corresponding module; multiple method steps implemented according to the flowcharts contained herein or as described above can be implemented together by a single module.

[0125] It should be understood that, in the scope of the embodiment of the present invention being implemented by a computer program, the storage medium and transmission medium carrying the computer program form aspects of the present invention. The computer program may have one or more program instructions or program codes, which execute embodiments of the present invention when executed by a computer. As used herein, the term "program" may be an instruction sequence designed to be executed on a computer system, and may include subroutines, functions, programs, modules, target methods, target implementation schemes, executable applications, applets, server applets, source code, object code, shared libraries, dynamic link libraries, and / or other instruction sequences designed to be executed on a computer system. The storage medium may be a disk (such as a hard disk drive or a floppy disk), an optical disk (such as a CD-ROM, DVD-ROM or BluRay disk) or a memory (such as a ROM, RAM, EEPROM, EPROM, flash memory or a portable / removable memory device), etc. The transmission medium may be a communication signal, a data broadcast, a communication linked between two or more computers, etc.

[0126] Appendix A

[0127] The invention proposed herein exploits the inherent instability of the underlying deconvolution procedure to the space of input parameters. Specifically, the greater sensitivity of the frequency positions of false positive solutions (which correspond to pseudo-peaks in the resulting mass spectrum) to small changes in the convolution kernel is used to classify peaks as valid or invalid. The mathematical operations that demonstrate that this is the case will now be discussed below. The discretized transients discussed above It can be expressed as:

[0128]

[0129] where w k is a window function, and x k Corresponding to time t k The original time-varying transient signal in this example will be acquired from t0 to t N-1 , and the discretized transient will consist of N samples. In the simplest case, the window function will project an acquisition time window where wk=1 for 0≤k≤N-1, and wk=0 for other values ​​of k. Such a windowing function is often known as a Boxcar window. In this simple case, the discretized transient will be reduced to

[0130] It will be appreciated that the windowing function may be more complex in order to take into account additional effects such as attenuation or dephasing. For example, attenuation may be manifested as a (multi) exponential decay of the transient envelope. Additionally or alternatively, the windowing function may contain an additional single processing window function (e.g. as is commonly used for sidelobe suppression). Applying a discrete Fourier transform (DFT) to the discretized transient yields a set of complex amplitudes c n , each complex amplitude is located at the corresponding frequency f on the Fourier grid defined by the discrete Fourier transform n Each frequency corresponds to a specific m / z ratio, and the complex amplitude (and therefore the m / z value) of a given frequency is proportional to the relative abundance of the ion species with that m / z ratio. Therefore, the complex amplitude c n and its corresponding frequency f n To form (or represent) a mass spectrum.

[0131] For the typical case of using the boxcar window mentioned above, the spacing between adjacent frequencies in a set of frequencies is given by the inverse of the duration of the transient. It should be understood that such complex amplitude c n is the real complex amplitude a n and the convolution kernel. Then c n Written as:

[0132]

[0133] Here, ψ k =DFT(w t ) (which follows directly from the discrete form of the convolution theorem in Fourier analysis) is a convolution kernel defined on a base K, … ... denotes a commutative circular convolution operation, and [kn] N : = (kn) mod N reflects the N-periodic nature of the discrete Fourier transform. In order not to lose the generality of the existing conclusions, the above formula assumes that ψ and a are sampled on an equidistant point grid and a symmetrical point grid, respectively. The first assumption is relaxed in PSDM to achieve a super-DFT solution, but the condition {k} = {n} is then reproduced at each iteration step by zero-filling interpolation in the upper domain.

[0134] Therefore, in order to obtain the true complex amplitude (and therefore the true mass spectrum), a deconvolution kernel ψ is used. k and the true complex amplitude a k This deconvolution problem can be reformulated as a matrix-vector multiplication

[0135] (3) c = Ψa

[0136] The matrix is ​​a square

[0137]

[0138] This matrix is ​​a so-called circulant matrix, i.e., all rows are circulant permutations of the first row. It should be noted that in the simplest continuous boxcar window case 0≤t≤T with a continuous limit Δt→0 and an acquisition time T, ψ k It can be identified by the function Ψ(n,k), as described in paragraph 88 of patent application EP3086354, which discusses PSDM. From matrix algebra it is known that any matrix (and therefore Ψ) can be decomposed into

[0139]

[0140] The unitary matrices are U, V, and the conjugate transpose is indicates, and the semi-positive definite diagonal matrix is ​​D = diag (d k ). k constitute the singular values ​​of Ψ.

[0141] The condition number of an invertible matrix is ​​defined as the ratio of the largest singular value to the smallest singular value of the matrix Ψ:

[0142]

[0143] and constitutes a measure of the accuracy lost when solving a linear system with a mapping. This definition of the condition number is well known, see for example Cheney, EW and Kincaid, DR, "Numerical Mathematics and Computing", 6th edition, Brooks / Cole Publishing Co (2007).

[0144] It should be understood that for non-rectangular matrices and / or non-invertible matrices (both of which arise in super-resolution Fourier deconvolution), the inverse kernel Ψ -1 Moore-Penrose pseudo-inverse + For alternatives, see, for example, Moore, EH, "On the reciprocal of the general algebraic matrix." Bulletin of the American Mathematical Society. 26(9):394-95 (1920). For readability, Ψ will be maintained from now on. -1 , however, those skilled in the art will appreciate that it can be replaced by the Moore-Penrose pseudo-inverse Ψ under appropriate circumstances + It has been shown in the backward stabilization algorithm that the logarithm in b of cond(Ψ) estimates how many base-b digits may be lost each time Ψ is used.

[0145] It should be understood that the condition number and its meaning do not arise simply because of the particular algorithm used to solve equation (3). Rather, the condition number is an inherent property of the mathematical mapping itself. This can be seen from the inversion of the linear deconvolution problem in equation (3) when augmented by a component ∈. Such a component ∈ can be used to take into account any one or more of the following: instrument noise, rounding errors, and other uncertainties. Equation (3) and its solution here become:

[0146]

[0147] It will be appreciated that due to the submultiplicative nature of any derived norm ||…||, the error of the inverse mapping may then be bounded by:

[0148] (8)||Ψ -1 ∈||≤||Ψ -1 ||||∈||.

[0149] Therefore, if ||Ψ -1|| is large enough, then even if the noise level ||∈|| is arbitrarily small, the error ||Ψ -1 ∈|| may also be large. In addition, it is found from the singular value decomposition that

[0150]

[0151] where d k Yes -1 Therefore, any complete solution Ψ -1 c may contain the maximum noise amplification in terms of the component ∈, which has been related to Ψ -1 The derivative of the smallest singular value of It should be appreciated that any numerical inversion will be hampered by large condition numbers. This is because D -1 Then there are floating point numbers at many scales, which will amplify any truncation errors.

[0152] By construction, a circulant matrix such as Ψ will be diagonalized by the discrete Fourier transform. Therefore, the eigenvalues ​​λ of Ψ are j Given as follows:

[0153]

[0154] Therefore, the eigenvalues ​​can be obtained by the discrete Fourier transform of the first column of Ψ, since this equation is the descaled forward transform λ k =DFT(ψ k ) standard definition.

[0155] By definition, the singular values ​​d i yes The non-negative square root of the eigenvalue of (the unitarity of these matrices) shows that:

[0156]

[0157] If the window function w t is real-valued, then Ψ is also symmetric, because the discrete Fourier spectrum is Hermitian, that is, ψ k =[ψ (-k) ] * It should be appreciated that, according to standard linear algebra, if Ψ is reversible, then diag(|d k |)=diag(λ k ). In summary, in view of the above, it will be appreciated that the condition number for deconvolution is then given by:

[0158]

[0159] It should be appreciated that this result is independent of the specific deconvolution algorithm used.

[0160] Therefore, to increase the resolution from N data points to K data points, simply resize the boxcar-shaped acquisition time window w t It is not feasible to invert the N×K, (K>N) convolution matrix obtained by (in the range of {1,0}). t The zero-valued entries in will make Ψ non-invertible and cause the condition number to diverge. This cannot be avoided by replacing the zeros with very small approximate "floating point zeros", because then we still have min(w t )<<max(w t ) and therefore has cond(Ψ)>>1 which makes the inversion unstable due to pathology.

[0161] Although this result has been shown based on a boxcar-like acquisition time window, it should be appreciated that the results apply generally to any simple inversion of an N×K, (K>N) convolution matrix, and therefore to any simple attempt to deconvolve a mass spectrum on an N-point grid into a mass spectrum on a K-point grid. This is because any such deconvolution operation can be mapped to the above inversion (see again Mueller, JL, Siltanen, S., "Linear and Nonlinear Inverse Problems for Practical Applications" (2012), Cambridge University Press. ISBN 978-1-61197-233-7).

[0162] If regularization techniques are used correctly in deconvolution (or inversion), the noise content of the regularized solution can still be expected to be proportional to the window function w t is sensitive to any modification of the zero-valued entries in . In particular, the additional zero blanking of the transient entries corresponds to a larger portion of zero-valued singular values. Similarly, it should be appreciated that this will be the case regardless of the regularization of the inversion algorithm used or any FT-related inversion scheme that aims to deconvolute the spectrum to recover the effect of the window function as defined in equation (1).

[0163] Appendix B - Phase Constrained Spectral Deconvolution Method

[0164] Examples of phase-constrained spectrum deconvolution methods are described in detail in Grinfeld, D., Aizikov, K., Kreutzmann, A., Damoc, E., and Makarov, A., "Phase-constrained spectrum deconvolution for Fourier transform mass spectrometry," Analytical Chemistry, 89(2): 1202-1211 (2017) and European Patent Application EP 3086354. Such methods are well known to the skilled person and are not discussed in detail herein.

[0165] In summary, the phase-constrained spectral deconvolution method generally involves generating a mass spectrum represented by a set of complex amplitudes on a Fourier grid whose spacing is less than the inverse of the length of the time-varying transient signal. The generation of the mass spectrum is performed by optimizing the complex amplitudes of the mass spectrum to minimize the measure of the difference between the complex amplitudes and the corresponding complex amplitudes of the initial mass spectrum generated by the discrete Fourier transform of the time-varying transient signal. The optimization is performed under the constraint of the phase of the complex amplitudes of the mass spectrum.

[0166] In this manner, it should be understood that the phase constrained spectral deconvolution method generally includes the following steps.

[0167] Generating an initial mass spectrum forms a time-varying transient signal. This is typically accomplished by performing a Fourier transform on the transient signal to produce a first set of complex amplitudes, wherein each of the complex amplitudes corresponds to a corresponding frequency in the first set of frequencies. The first set of complex amplitudes corresponds to {c n The first set of frequencies may be equally spaced in frequency. A second set of complex amplitudes is generated, wherein each of the complex amplitudes corresponds to a corresponding frequency in the second set of frequencies. The second set of complex amplitudes corresponds to {a k}. The second set of frequencies may be equally spaced in frequency. The spacing of the second set of frequencies may be less than the spacing of the first set of frequencies (or the spacing of the second set of frequencies is minimal). The spacing of the second set of frequencies may be less than the inverse of the duration of the transient signal (or the spacing of the second set of frequencies is minimal). The second set of complex amplitudes may cover (or span or correspond to) the same frequency range as the frequency range of the first set of complex amplitudes, and thus the second set may contain more complex amplitudes than the first set. Thus, the second set of complex amplitudes may provide greater resolution.

[0168] The second set of complex amplitudes is optimized to produce an improved second set of complex amplitudes. At least some of the complex amplitudes from the improved second set of complex amplitudes are used to generate and display a mass spectrum. The improved second set of complex amplitudes provides a mass spectrum of better quality.

[0169] Optimizing the second set of complex amplitudes comprises changing at least one of the second set of complex amplitudes based on (or in dependence on) the objective function. For example, in order to obtain a substantial extremum of the objective function, at least one of the complex amplitudes may be changed. Optionally, all of the complex amplitudes from the second set may be changed as part of the optimization step, or a subset may be optimized as part of the optimization step.

[0170] The optimization is performed under constraints. That is, for at least some of the second set of complex amplitudes, constraints are imposed on the phase of each of the at least some of the complex amplitudes relative to one or more expected phases. The expected phase may be frequency dependent. The objective function depends on one or more of the first set of complex amplitudes and one or more of the second set of complex amplitudes. For each frequency in the first set of frequencies, the objective function may relate the one or more complex amplitudes of the second set to the corresponding complex amplitudes from the first set (such as by making the objective function a function of the one or more complex amplitudes of the second set and the corresponding complex amplitudes from the first set). The constraints may be applied to all of the complex amplitudes of the second set that are varied as part of the optimization step, or to a subset of those complex amplitudes.

[0171] It can be seen that by generating and optimizing the second set of complex amplitudes, the transient can be considered to be decomposed into a finer frequency grid. Since the second set of complex amplitudes is not combined with the first set of complex amplitudes as a linear combination of these amplitudes, unlike the interpolation method previously described, the resolution increases as the grid spacing of the second set of frequencies decreases. This greatly improves the accuracy of the mass spectrum produced. In other words, the method can be considered to operate with two sets of frequencies. The first set of frequencies can include frequencies with a minimum spacing of 1 / T, where T is the duration of the transient signal. The second set of frequencies can include frequencies with a minimum spacing of less than 1 / T. The second set of frequencies can contain the first group as a subset. Since the minimum spacing of the second set of frequencies is less than the minimum spacing of the first set of frequencies, the second set of complex amplitudes can provide greater resolution.

[0172] According to the form of Appendix A above, the objective function to be minimized can be expressed as:

[0173]

[0174] The norm ‖…‖ can be any convex norm. Specifically, the norm can be L m norm, i.e., any of the following: L1 norm; L2 norm; L3 norm; etc. As mentioned earlier, in the simplest continuous boxcar window case 0≤t≤T with continuous limit Δt→0 and acquisition time T, ψ in Appendix A kIt can be identified by the function Ψ(n,k). The function Ψ(n,k) usually follows the following relationship:

[0175]

[0176] The function can also be expressed as:

[0177]

[0178] where F k is the complex amplitude a k The frequency, and f n is the complex amplitude c n frequency.

[0179] The optimization is subject to one or more constraints based on the expected phase data. Specifically, for at least some of the second set of complex amplitudes, the optimization may be subject to a constraint on the phase of each complex amplitude relative to the corresponding expected phase. The constraint may require an exact or substantially exact phase:

[0180] arg a k =φ k

[0181] Alternatively, the constraint may require (or impose or set or otherwise force) that the phase of the corresponding complex amplitudes in the second set of complex amplitudes be within a predefined range around (or substantially centered on, within or otherwise based on) the corresponding expected phase. For example, such a constraint may be expressed as:

[0182] φ k -Δφ≤arg a k ≤φ k +Δφ

[0183] The range may be any of the following: set by a user; based on the mass spectrometer 10; dependent on the frequency corresponding to the expected phase; based on the expected phase jitter of the mass spectrometer 10; etc.

[0184] The optimization step is typically performed using the alternating direction method of multipliers (ADMM), however, any suitable numerical optimization technique, many examples of which are known in the art, such as Newton's method; Quasi-Newton method; conjugate gradient method; steepest descent method; proximal minimization, etc.

[0185] The optimization is iterative, and when the value of the objective function obtained is appropriately close to (or estimated to be appropriately close to) the extreme value of the objective function (or the estimated or predicted extreme value), the optimization may be completed (or succeeded or may be terminated). The optimization described above may be completed if any of the following conditions are met:

[0186] (a) Exceed or meet the predefined number of iterations;

[0187] (b) the change in the value of the objective function relative to the previous iteration is below a predefined threshold;

[0188] (c) a change in the value (or values) of one or more complex amplitudes of the improved second set of complex amplitudes relative to a previous iteration is below a predefined threshold;

[0189] (d) a change in the value (or values) of one or more functions, each dependent on one or more complex amplitudes of the improved second set of complex amplitudes, relative to a previous iteration is below a predefined threshold;

[0190] (e) a predefined amount of time has elapsed;

[0191] (f) a predefined number of processor cycles have elapsed; etc.

[0192] It should be appreciated that any one of these conditions may represent a parameter of the PSDM, and that the set of adjustable parameters described herein may include any combination of these parameters.

Claims

1. A method for identifying pseudo-peaks in a mass spectrum generated by a time-varying transient signal detected in a mass spectrometer, the method comprising: generating a first mass spectrum from the time-varying transient signal using a regularized inversion algorithm having one or more adjustable parameters according to a first set of values ​​of the one or more adjustable parameters; generating one or more perturbed mass spectra from the transient signal based on one or more corresponding perturbed versions of the first set of values ​​using the regularized inversion algorithm; One or more spurious peaks in the first mass spectrum are identified by comparing the first mass spectrum to at least one of the perturbed mass spectra.

2. The method of claim 1, wherein each generating step comprises applying the regularized inversion algorithm to an initial mass spectrum generated from the time-varying transient signal.

3. The method of claim 2, wherein the method further comprises forming the initial mass spectrum by applying a discrete Fourier transform to the time-varying transient signal.

4. The method of any one of claims 1-3, wherein the regularized inversion algorithm comprises applying a discrete Fourier transform to a version of the time-varying transient signal, the version of the time-varying signal comprising a certain number of zero-blanking entries. 5 . The method of claim 4 , wherein an adjustable parameter of the one or more adjustable parameters controls the number of zero blanking entries in the version of the time-varying transient.

6. The method according to any one of claims 1-3, wherein the regularized inversion algorithm is an iterative algorithm.

7. The method of claim 6, wherein one of the one or more adjustable parameters controls the number of iterations in the regularized inversion algorithm.

8. The method according to any one of claims 1-3, wherein the regularized inversion algorithm comprises a phase constrained spectral deconvolution algorithm.

9. The method according to any one of claims 1-3, wherein at least one of the pseudo-peaks is identified based on a mass-to-charge ratio change of the peak between the first mass spectrum and at least one of the perturbed mass spectra exceeding a predetermined threshold.

10. The method of claim 9, wherein the mass-to-charge ratio is expressed as a frequency.

11. The method of any one of claims 1-3, wherein at least one of the pseudo-peaks is identified based on the peak not being present in an intersection of the first mass spectrum and at least one of the perturbed mass spectra.

12. The method of any one of claims 1-3, further comprising outputting a modified mass spectrum in which the identified one or more spurious peaks are excluded.

13. The method of any one of claims 1-3, wherein each perturbed version of the first set of values ​​is formed by applying at least one corresponding change to at least one value in the first set of values.

14. A system arranged to perform the method according to any one of claims 1-13.

15. A computer readable medium having stored thereon instructions which, when executed by a computer, cause the computer to perform the method according to any one of claims 1 to 13.

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