Methods for computer-aided processing of spatially resolved mass spectrometry data

Abstract

Method for computer-aided processing of spatially resolved mass spectrometry data with a multitude of spectra assigned to respective measurement positions (x), wherein a spectrum (s x (m / z)) for several image channels (m / z) comprises respective intensities (I) which represent a physical quantity detected for the corresponding image channel (m / z), wherein the image channels (m / z) represent mass-to-charge ratios and the physical quantity detected for the corresponding image channel (m / z) represents the number of molecules detected for the corresponding mass-to-charge ratio, where: - the mass spectrometry data are decomposed using a non-negative matrix factorization, according to which a data matrix (X) is generated, which for each measurement position (x) represents the intensities (I) for the image channels (m / z) of the spectrum (s) assigned to the respective measurement position (x). x(m / z)) is represented as a matrix product of a component matrix (S) and a coefficient matrix (C), where the component matrix (S) contains, for a predetermined number of components (k), intensities of a spectrum (ψ) assigned to the respective component (k). k (m / z)) for the image channels (m / z) and wherein the coefficient matrix (C) for the predetermined number of components (k) includes coefficients for the measurement positions (x), wherein the non-negative matrix factorization is designed such that the decomposed mass spectrometry data have a smaller amount of data compared to the mass spectrometry data before decomposition; - based on the non-negative matrix factorization, an optimization of a cost function is carried out in the form of a maximization or minimization of the cost function depending on the component matrix (S) and the coefficient matrix (C) as variables, where the cost function comprises a functional (f(X, S, C)) that depends on the data matrix (X), the component matrix (S) and the coefficient matrix (C); - when optimizing the cost function, a first and a second constraint are applied, whereby according to the first constraint, the cost function is optimized towards the smallest possible number of non-zero entries in the component matrix (S), and according to the second constraint, the cost function is optimized towards the smallest possible number of non-zero entries in the coefficient matrix (C); - the entries of the component matrix (S) and the coefficient matrix (C) generated by the non-negative matrix factorization are stored.

Description

[0001] The invention relates to a method for computer-aided processing of mass spectrometry data, as well as a corresponding computer program product and a corresponding computer program.

[0002] The invention relates to the field of image processing of spatially resolved hyperspectral data, which are characterized by containing image information for more than one image channel. The application of the invention is spatially resolved mass spectrometry data, in which the respective image channels represent mass-to-charge ratios. In spatially resolved mass spectrometry (imaging mass spectrometry), the components contained in the sample are extracted in ionized form at a multitude of measurement positions and subsequently detected in a mass spectrometer as a function of their mass-to-charge ratio. A known method of spatially resolved mass spectrometry is MALDI mass spectrometry, in which a matrix is ​​applied to the sample and the molecules of the sample are detached by laser pulses (MALDI = Matrix-Assisted Laser Desorption / Ionization).To obtain meaningful information from mass spectrometry data, various analytical methods are known from the state of the art, such as peak picking, clustering, classification and the like (see document [1]).

[0003] The problem with processing spatially resolved hyperspectral data is that a large amount of data is generated for each measurement position and a multitude of image channels. Storing and processing this data is computationally expensive.

[0004] Publication US 2010 / 0299379 A1 discloses the decomposition of multivariate data using a non-negative matrix factorization based on the minimization of a cost function.

[0005] Document CN101487892A describes the decomposition of hyperspectral data using a factor analysis model to reduce the dimension of the hyperspectral data.

[0006] Documents US 2005 / 0047670 A1 and US 2011 / 0007819 A1 describe further methods for compressing hyperspectral data, where the hyperspectral data are spatially resolved data, for example, recorded by a satellite.

[0007] The object of the invention is to create a method for the computer-aided processing of spatially resolved mass spectrometry data, which enables the decomposition of the data into characteristic spectra and their spatial distribution with simultaneous data compression.

[0008] This problem is solved by the method according to claim 1 or the machine-readable carrier according to claim 13. Further developments of the invention are defined in the dependent claims.

[0009] The method according to the invention serves for the computer-aided processing of spatially resolved mass spectrometry data, which comprise a plurality of spectra assigned to respective measurement positions, wherein a spectrum for several image channels comprises respective intensities that represent a physical quantity detected for the corresponding image channel. The image channels represent mass-to-charge ratios, and the physical quantity detected for the corresponding image channel represents the number of molecules detected for the corresponding mass-to-charge ratio. In a preferred embodiment, the mass spectrometry data are the MALDI mass spectrometry data already mentioned above. However, the spatially resolved mass spectrometry data can also be obtained using another method, e.g., DESI mass spectrometry (DESI = Desorption Electrospray Ionization) or SIMS (Secondary Ion Mass Spectrometry).

[0010] In the inventive method, the mass spectrometry data are decomposed using non-negative matrix factorization. For this purpose, a data matrix, which comprises the intensities for the image channels of the spectrum assigned to each measurement position, is represented as a matrix product of a component matrix and a coefficient matrix. In the data matrix, the respective measurement positions are represented, for example, by columns or, optionally, by rows. The parameters of the non-negative matrix factorization are selected such that the resulting data volume is smaller than that of the original mass spectrometry data.

[0011] The component matrix comprises, for a predetermined number of components, the intensities of a spectrum assigned to or characterizing each component, derived from intensities for the image channels. The individual components are represented by the columns of the component matrix and, optionally, also by its rows. The coefficient matrix comprises, for the predetermined number of components, coefficients for the multitude of measurement positions, with the components preferably being represented by the rows and, optionally, also by the columns of the matrix. The component matrix thus contains the characterizing spectra of the mass spectrometry data, and the coefficient matrix represents the spatial distribution of these spectra. Due to the non-negative matrix factorization, all entries in the component matrix and the coefficient matrix are greater than or equal to zero.

[0012] In the method according to the invention, an optimization of a cost function is performed based on non-negative matrix factorization, depending on the component matrix and the coefficient matrix as variables; that is, during the optimization, the entries of the component matrix and the coefficient matrix are varied. The optimization can be a minimization and, if necessary, also a maximization of the cost function.

[0013] The cost function comprises a functional that depends on the data matrix, the component matrix, and the coefficient matrix. Optimizing the cost function involves a first and a second constraint. The first constraint aims to optimize the cost function towards minimizing the number of non-zero entries in the component matrix (i.e., maximizing the number of zero entries). The second constraint aims to optimize the cost function towards minimizing the number of non-zero entries in the coefficient matrix (i.e., maximizing the number of zero entries). The component and coefficient matrix entries generated by the non-negative matrix factorization are then stored.

[0014] According to the invention, new constraints are introduced into the known methodology of non-negative matrix factorization, defining a sparse composition of the component matrix and the coefficient matrix. Non-negative matrix factorization allows, in particular, a high compression of the original mass spectrometry data to be achieved, while simultaneously preserving meaningful information in the mass spectrometry datasets, which can be represented, for example, based on the visualization of the spectra or coefficients assigned to the components as described below.

[0015] The optimization of the cost function within the framework of the non-negative matrix factorization used in the method according to the invention can be carried out using mathematical methods known per se, examples of which are given in the detailed description. Since these methods are part of the prior art and are familiar to those skilled in the art, they are not described in further detail.

[0016] In a variant of the inventive method, which is not defined in the claims, the non-negative matrix factorization is configured such that a predetermined accuracy of the reconstruction of the mass spectrometry data from the decomposed mass spectrometry data or a predetermined data size of the decomposed mass spectrometry data is achieved. Furthermore, the functional described above can optionally be extended by a random matrix so that the mass spectrometry data are reduced via a randomized linear combination.

[0017] In a particularly preferred embodiment, the functional contained in the cost function comprises the L2 norm of the difference between the data matrix and the matrix product of the component matrix and the coefficient matrix, wherein the cost function is optimized towards the smallest possible L2 norms.

[0018] In a further, particularly preferred embodiment, the first constraint is represented by a first function, which is part of the cost function and is added to the functional, such that the optimization of the cost function favors a component matrix with a small number of non-zero entries. Preferably, the first function comprises the L1 norm of the component matrix. Likewise, the first function can be a sum of norms of the component matrix, the sum preferably comprising the L1 norm and the L2 norm of the component matrix. The use of a sum of norms in a functional is known per se and is therefore not described in further detail.

[0019] In a further embodiment of the method according to the invention, the second constraint is represented by a second function, which is part of the cost function and is added to the functional, so that the optimization leads to a preference for a coefficient matrix with the fewest possible non-zero entries. In particular, the TV norm (TV = Total Variation) of the coefficient matrix and, optionally, also the L1 norm of the coefficient matrix can be used as the second function. The TV norm is known from the prior art and is defined, in particular, for two-dimensional images, as demonstrated by document [4]. The coefficient matrix can be considered as a corresponding image for which the TV norm is determined. The TV norm evaluates the jump height and edge length in an image.The use of this standard in the cost function thus ensures smooth edges in the corresponding image of the coefficient matrix.

[0020] In a further embodiment of the method according to the invention, the coefficient matrix is ​​represented as 2D wavelets, with a limited number of 2D wavelet coefficients being specified as a second constraint. The use of such a second constraint is known per se from the prior art and is described in particular in publication [5]. The corresponding wavelet representation with the constraints can be found in equation (4) of this document. According to the invention, the corresponding first constraint is additionally taken into account in the optimization. Optionally, the second constraint can also be designed such that the L1 norm of the 2D wavelet coefficients is as small as possible.

[0021] In a further, particularly preferred embodiment, the number of components of the non-negative matrix factorization is determined such that the total number of stored entries of the component matrix and the coefficient matrix corresponds to a predetermined percentage of the number of entries of the data matrix, wherein the predetermined percentage is particularly between 1% and 10% of the number of entries of the data matrix. By appropriately choosing the number of components, data reduction by a factor of 10 can also be achieved. 3 or more. For example, the number of components can range from 3 to 20 or from 5 to 10. The number of components depends on the data source and can also take other values.

[0022] In a further, particularly preferred embodiment, a visualization is generated on a display from the stored entries of the component matrix and the coefficient matrix, such that an image is created for at least some of the components, each consisting of pixels representing the measurement positions. Each pixel encodes, for example, the coefficient for the respective component of the coefficient matrix and the measurement position represented by that pixel, e.g., by color. The term "pixel" is to be understood broadly and can represent a single pixel or several adjacent pixels on the display. As can be seen from the detailed description, this embodiment of the method according to the invention yields meaningful images of the spatial distribution of different groups of substances in the sample analyzed by mass spectrometry.In other words, soft segmentation is achieved in which a tissue structure is not assigned to the individual tissue areas, but rather the relative proportion of the corresponding component is specified for the different tissue areas.

[0023] In a further embodiment of the method according to the invention, a visualization is generated on a display from the stored entries of the component matrix and the coefficient matrix such that a graphical representation is created for at least a portion of the spectra assigned to the components, showing the intensities of the spectrum assigned to the respective component as a function of the image channels, i.e., the mass-to-charge ratios. In this way, information is obtained on the proportion of certain compositions in the corresponding components. This forms, for example, the basis for subsequent biomarker identification.

[0024] In a further embodiment of the method according to the invention, the mass spectrometry data are reconstructed from the stored entries of the component matrix and the coefficient matrix by matrix multiplication of these matrices. The method according to the invention ensures a virtually lossless reconstruction of the original data. A tolerance δ can be specified, and depending on this, the parameters of the non-negative matrix factorization can be selected such that the deviation of the reconstruction from the original data is less than the tolerance δ.

[0025] The invention further relates to a machine-readable carrier with program code stored thereon for carrying out the method according to the invention or one or more preferred variants of the method according to the invention when the program code is executed on a computer.

[0026] In an embodiment not defined in the claims, the invention further relates to a computer program with program code for carrying out the method according to the invention or one or more preferred variants of the method according to the invention when the program code is executed on a computer.

[0027] Exemplary embodiments of the invention are described in detail below with reference to the accompanying figures.

[0028] They show: Fig. 1 a diagram illustrating data acquired by means of MALDI spectrometry and processed using the method according to the invention; Fig. 2 a diagram illustrating the essential steps of an embodiment of the method according to the invention; Fig. 3 and Fig. 4 Cross-sectional views of a rat brain, which were generated based on an embodiment of the method according to the invention; and Fig. 5 diagrams of characteristic spectra of a rat brain, which were generated using an embodiment of the method according to the invention.

[0029] The following describes an embodiment of the method according to the invention based on so-called MALDI mass spectrometry data. In this spectrometry, the molecules of the tissue sample to be analyzed are coated with a matrix solution, and a laser beam (e.g., a nitrogen laser) is directed at various measurement positions on the corresponding sample carrier. The laser pulses cause particle detachment from ionized molecules of the tissue, the mass-to-charge ratio of which is determined in a known manner using a mass spectrometer. For this purpose, for example, a TOF mass spectrometer (TOF = Time of Flight) or an FTICR mass spectrometer (FTICR = Fourier Transform Ion Cyclotron Resonance) can be used.The method of the invention is also applicable to other mass spectrometry data, provided that the data contain spatially resolved spectra at different measurement positions which, as a function of the mass-to-charge ratio, represent the number of ions detected by the mass spectrometer. Furthermore, the method of the invention can also be applied more generally to hyperspectral data (e.g., Raman spectroscopy, remote sensing), provided that the data contain spatially resolved intensity vectors at different measurement positions with entries for different image channels. An intensity can, for example, comprise the proportion of reflected light of a specific wavelength, with the wavelength representing the image channel.

[0030] In the embodiments described below, layers of a rat brain were examined using spatially resolved MALDI mass spectrometry. Fig. Figure 1 shows typical spectra acquired by MALDI spectrometry for a tissue section from a rat brain. The mass-to-charge ratio is indicated in Daltons along the m / z axis. The x axis encodes corresponding two-dimensional positions of the rat brain section. Spectra s1, s2, and s3 are shown as examples for three positions, each representing the number of detected ionized molecules as an intensity value I for the corresponding mass-to-charge ratios m / z. Depending on the resolution of the MALDI spectrometry, a specific interval of m / z values ​​is grouped around a given m / z value. The data acquired by MALDI spectrometry can then be visualized in a suitable manner, e.g.,Images of the rat brain can be generated for specific m / z values, with the intensity for the corresponding m / z value being color-coded in each image for the different measurement positions. Fig. Figure 1 shows two exemplary m / z values ​​at 4966 Da and 6717 Da, for which such images can be generated by coding the corresponding intensities for the different measurement positions.

[0031] In spatially resolved mass spectrometry, a disadvantage is the very large amount of data generated. In the example shown, a dataset for a section of a rat brain consists of 20,000 spectra, each with 8,000 spectral m / z values, i.e., a total of 160 million values. Spatially resolved mass spectrometry data typically generates significantly larger datasets, both through a much higher number of measured spectra (e.g., a factor of 100 to 1,000) and through better-resolved m / z values ​​(e.g., a factor of 2 to 2,000). One objective of the embodiment of the method according to the invention described below is to compress this dataset with minimal information loss.

[0032] The essential steps of the inventive method described here are set out in Fig. Figure 2 illustrates the procedure. It begins with step S1, in which the MALDI mass spectrometry data described above are arranged in the form of a matrix X. The matrix encodes the corresponding spectrum s for each measurement position x. x(m / z) of the intensity values ​​for the different mass-to-charge ratios m / z. The matrix X comprises N rows, indexed with i = 1, ..., N, where each row represents an m / z value. In contrast, the matrix XM contains columns, indexed with j = 1, ..., M, where each column represents a measurement position or image position. The image positions refer to two-dimensional positions x of a section through a rat brain, or, if applicable, to different sections of a rat brain, where in this case the position represents a three-dimensional value that indicates not only the position within a specific section but also which section it is.

[0033] In step S2 of the Fig. 2. The data matrix X of the mass spectrometry data is subjected to a non-negative matrix factorization. This non-negative matrix factorization is characterized by the inclusion of constraints according to which the matrices determined by the factorization are sparsely populated, i.e., have few non-zero entries, as will be explained in more detail below. Within the framework of the non-negative matrix factorization, the spectra s x (m / z) of the matrix X as follows by components or basis spectra ψ k (m / z), k = 1,...., K , approximated: sx(m / z)=∑k=1Kck(x)ψk(m / z).

[0034] In other words, according to the non-negative matrix factorization, matrix X is represented by a product of matrices S and C, which may only contain positive entries. Matrix S has the dimension N×K, where the rows represent the m / z values ​​and the columns the components k, and each entry represents an intensity value of the corresponding basic spectrum ψ. k (m / z) represents. In contrast, matrix C is a coefficient matrix with dimension K×M. The rows of this matrix represent the components k = 1, ..., K, and the columns represent the measurement positions. The values ​​c k (x) represent the entries and thus the coefficients of this matrix.

[0035] According to the embodiment described here, a non-negative matrix factorization is used, which is based on minimizing a cost function of three functions f, f1, and f2. That is, the non-negative matrix factorization minimizes the following expression: minf(X,S,C)+f1(S)+f2(C).

[0036] The functional f(X, S, C) used is the Euclidean or L2-norm of the difference between the data matrix X and the matrix product SC, i.e., the following holds: f(X,S,C)=‖X−SC‖2.

[0037] The functions f1 and f2 represent penalty terms that favor solutions with sparsely populated matrices S and C, respectively. That is, the term f1 is defined such that, when minimizing the cost function, matrices S with a small number of non-zero entries, and thus a large number of zero entries, are favored. Similarly, the function f2 is defined such that, when minimizing the cost function, matrices C with a small number of non-zero entries, and thus a large number of zero entries, are favored. These penalty terms ensure that the compressed dataset represented by matrices S and C contains important information from the original mass spectrometry data, as will be explained below using the visualizations generated from the compressed dataset.

[0038] In the embodiment described here, the L1 norm is used as the penalty term f1, i.e., the following applies: f1(S)=‖S‖l1.

[0039] In contrast, the penalty term f2(C) describes the so-called TV norm (TV = Total Variation), i.e., the following applies: f2(C)=|C|TV.

[0040] The TV standard is known from the state of the art, as is demonstrated by the publication mentioned above [4].

[0041] The minimization problem described above according to equation (2) can be solved using known methods, such as blind-source separation with L1 constraints, an orthogonal matching pursuit (OMP) method, or similar dictionary learning methods. In particular, the iterative hard thresholding (IHT) method (see publication [2]) or a multiplicative algorithm as described in publication [3] can be used.

[0042] The constraints described above, according to which solutions with sparsely populated matrices S and C are preferred, can also be realized in other ways or with other functions f1 and f2. For example, the constraint regarding the sparse population of matrix C can also be achieved by representing matrix C in a wavelet basis with corresponding sparsity conditions, as described in publication [5] (see especially equation (4) therein).

[0043] As a result of the matrix factorization according to step S2 of the Fig. In step 2, the two matrices S and C are finally obtained, which are stored in a corresponding memory in step S3. By appropriately choosing the number K of components k, a considerable data reduction can be achieved compared to the original data matrix X. In an embodiment of the method where K = 6 components are used, the example described above of 20,000 spectra with 8,000 m / z values ​​yields 8,000 × 6 values ​​for matrix S and 20,000 × 6 values ​​for matrix C, i.e., a total of 168,000 values, compared to 160 million values ​​in the original data matrix X. Thus, a data compression factor of approximately 950 can be achieved. However, the essential information from the spectra in matrices S and X is retained, which is ensured by the penalty terms described above.

[0044] In one variant of the inventive method, the original mass spectrometry data can be reconstructed with minimal loss by multiplying matrices S and C, if required. In a further, particularly preferred embodiment, respective rows of the coefficient matrix C, and thus corresponding components k, are visualized. The tissue is represented on a display by a multitude of pixels, each pixel corresponding to a measurement position x and encoding the value of the coefficient of component k from matrix C. This is demonstrated by Fig. 3 and Fig. 4 is indicated for MALDI mass spectrometry data of a section through a rat brain.

[0045] Fig. Figure 3 shows a section of a rat brain for component k = 1 and Fig. 4. Rat brain section for component k = 2. Non-negative matrix factorization for six components (K = 6) was applied to MALDI mass spectrometry data of the corresponding rat brain section. Fig. 3 and Fig. In this case, higher coefficient values ​​are coded using darker colors. How to... Fig. 3 recognizes that the component k = 1 describes the CO area of ​​the rat brain cortex or the H1 and H2 areas of the hippocampus. In contrast, in Fig. 4. The component k = 2 describes tissue regions T1 and T2, which correspond to the thalamus of the rat brain. From Fig. 3 and Fig. As shown in Figure 4, it becomes clear that the representation of corresponding rows in the coefficient matrix C represents biologically meaningful regions of the analyzed tissue. This achieves a soft segmentation of the tissue by encoding the relevance of the corresponding basic spectra or components at the different measurement positions through the representation of the coefficients. This follows from the fact that the coefficients indicate how strongly a corresponding component k relates to the spectrum s measured at position x. x (m / z) contributes to the original mass spectrometry data. Thus, the coefficients are represented by pixels according to Fig. 3 and Fig. 4 the characteristic metabolic structure of regions is shown which have a molecular composition corresponding to component k = 1 or k = 2.

[0046] In a further embodiment of the method according to the invention, the values ​​of the corresponding column of the matrix S are represented graphically for at least some of the components k. This is shown in Fig. 5 for component k = 1 and k = 2. This yields a single characteristic spectrum for a component k, which represents the corresponding intensities I for the different m / z values. In this way, information is presented about which molecular compositions are dominant in the different components. This information can be used, for example, in the identification of proteins or biomarkers. In particular, the metabolic structures with the greatest dominance in the data can be determined. How to from Fig.5. Characteristic spectra are obtained for the components k = 1 and k = 2, which show peaks for certain m / z values, from which conclusions can be drawn about the molecular composition of the corresponding components.

[0047] The embodiments of the method according to the invention described above offer a number of advantages. In particular, a high compression of mass spectrometry data is achieved by non-negative matrix factorization with appropriate penalty terms, while retaining important information from the mass spectrometry data. This information can be displayed in a visualization. Bibliography: [1] Dennis Trede, Jan Hendrik Kobarg, Janina Oetjen, Herbert Thiele, Peter Maass, and Theodore Alexandrov. On the importance of mathematical methods for analysis of MALDI-Imaging mass spectrometry data. Journal of Integrative Bioinformatics, 9(1):189, 2012. [2] T. Blumensath, M.E. Davies (2008): Iterative Thresholding for Sparse Approximations. Journal of Fourier Analysis and Applications, Volume 14, Issue 5-6, pp 629-654 [3] D.D. Lee, H.S. Seung (1999): Learning the parts of objects by non-negative matrix factorization. Nature, Volume 401, pp 788-791 [4] L.I. Rudin, S. Osher, E. Fatemi (1992): Nonlinear total variation based noise removal algorithms. Physica D, Volume 60, pp 259-268 [5] M. Golbabaee, S. Arberet, P. Vandergheynst (2010): Distributed compressed sensing of hyperspectral images via blind source separation. The Asilomar Conference on Signals, Systems, and Computers, November 2010

Claims

[1] Method for the computer-aided processing of spatially resolved mass spectrometry data with a plurality of spectra assigned to respective measurement positions (x), wherein a spectrum (s x (m / z)) for several image channels (m / z) comprises respective intensities (I) representing a physical quantity detected for the corresponding image channel (m / z), wherein the image channels (m / z) represent mass-to-charge ratios and the physical quantity detected for the corresponding image channel (m / z) represents the number of molecules detected for the corresponding mass-to-charge ratio, in which: - the mass spectrometry data are decomposed by means of a non-negative matrix factorization, according to which a data matrix (X) which contains, for respective measuring positions (x), the intensities (I) for the image channels (m / z) of the spectrum (s) assigned to the respective measuring position (x) x(m / z)) is represented as a matrix product of a component matrix (S) and a coefficient matrix (C), wherein the component matrix (S) for a predetermined number of components (k) contains intensities of a spectrum (ψ k (m / z)) for the image channels (m / z) and wherein the coefficient matrix (C) for the predetermined number of components (k) each comprises coefficients for the measurement positions (x), wherein the non-negative matrix factorization is designed such that the decomposed mass spectrometry data has a smaller amount of data compared to the mass spectrometry data before the decomposition; - based on the non-negative matrix factorization, an optimization of a cost function is carried out in the form of a maximization or minimization of the cost function depending on the component matrix (S) and the coefficient matrix (C) as variables, wherein the cost function comprises a functional (f(X, S, C)) which depends on the data matrix (X), the component matrix (S) and the coefficient matrix (C); - a first and a second constraint are taken into account in the optimization of the cost function, wherein according to the first constraint the cost function is optimized towards the smallest possible number of entries in the component matrix (S) that are not equal to zero, and according to the second constraint the cost function is optimized towards the smallest possible number of entries in the coefficient matrix (C) that are not equal to zero; - the entries of the component matrix (S) and the coefficient matrix (C) generated by the non-negative matrix factorization are stored. [2] Method according to claim 1, characterized by that the mass spectrometry data are MALDI mass spectrometry data (MALDI = Matrix-Assisted Laser Desorption / Ionization) or DESI mass spectrometry data (DESI = Desorption Electrospray Ionization) or SIMS mass spectrometry data (SIMS = Secondary Ion Mass Spectrometry). [3] Method according to claim 1 or 2, characterized by that the functional (f(X, S, C)) comprises the L2 norm of the difference between the data matrix (X) and the matrix product of the component matrix (S) and the coefficient matrix (C), whereby the optimization of the cost function is carried out towards the smallest possible L2 norms. [4] Method according to one of the preceding claims, characterized bythat the first constraint is represented by a first function (f1(S)), which is part of the cost function and is added to the functional (f(X, S, C)), so that the optimization of the cost function leads to the preference of a component matrix (S) with the smallest possible number of non-zero entries. [5] Method according to claim 4, characterized by that the first function (f1(S)) comprises the L1 norm of the component matrix (S) or a sum of norms of the component matrix (S), wherein the sum preferably comprises the L1 norm and the L2 norm of the component matrix (S). [6] Method according to one of the preceding claims, characterized bythat the second constraint is represented by a second function (f2(C)), which is part of the cost function and is added to the functional (f(X, S, C)), so that the optimization of the cost function leads to a preference for a coefficient matrix (C) with the smallest possible number of non-zero entries. [7] Method according to claim 6, characterized by that the second function (f2(C)) includes the TV norm of the coefficient matrix (C). [8] Method according to one of the preceding claims, characterized by that the coefficient matrix (C) is represented as 2D wavelets, whereby as a second constraint a limited number of 2D wavelet coefficients is specified or according to the second constraint the L1 norm of the 2D wavelet coefficients is as small as possible. [9] Method according to one of the preceding claims, characterized bythat the predetermined number of components (k) is set such that the number of stored entries of the component matrix (S) and the coefficient matrix (C) corresponds to a predetermined percentage of the number of entries of the data matrix (X), wherein the predetermined percentage is in particular between 1% and 10% of the number of entries of the data matrix. [10] Method according to one of the preceding claims, characterized by that a visualization is generated on a display from the stored entries of the component matrix (S) and the coefficient matrix (C) in such a way that for at least some of the components (k) an image is generated from pixels representing the measuring positions (x), wherein a respective pixel represents the coefficient (c k (x)) for the respective component (k) of the coefficient matrix (C) and the measurement position (x) represented by the respective pixel (BP). [11] Method according to one of the preceding claims, characterized by that from the stored entries of the component matrix (S) and the coefficient matrix (C) a visualization is generated on a display such that for at least some of the spectra (ψ k (m / z)) a graphical representation is generated which shows the intensities of the spectrum (ψ k (m / z)) depending on the image channels (m / z). [12] Method according to one of the preceding claims, characterized by that the mass spectrometry data are reconstructed from the stored entries of the component matrix (S) and the coefficient matrix (C) by matrix multiplication of these matrices. [13] Machine-readable carrier having program code stored thereon for carrying out a method according to one of the preceding claims when the program code is executed on a computer.

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