Image noise reduction method, electron energy loss spectroscopy analysis method, and analysis apparatus

Abstract

To provide an image noise reduction method, an electron energy loss spectroscopy method, and an analysis apparatus that reduce the effort required to remove noise from measurement images before deconvolving the instrument function. [Solution] This is an image noise reduction method in which a computer performs the following steps: a learning condition determination step, which determines the learning conditions for machine learning the noise reduction model based on a generated image from which noise has been removed using a noise reduction model trained with the Noise2Void algorithm and an analyzed image from which the generated image has been subjected to inverse convolution of the device function; a machine learning step, which performs machine learning of the measured image, which is the training data, using the Noise2Void algorithm according to the determined learning conditions; and a noise reduction step, which removes noise from the measured image, which is the analysis data, using the noise reduction model trained in the machine learning step, before performing inverse convolution of the device function from the measured image, which is the analysis data.

Description

Technical Field

[0001] The present invention relates to an image noise removal method for removing noise from a captured measurement image, an electron energy loss spectroscopy analysis method, and an analysis apparatus.

Background Art

[0002] When incident electrons pass through a substance to be observed (hereinafter referred to as a sample), they are scattered by Coulomb interaction with electrons and atomic nuclei in the sample and lose part of their energy. Electrons that have lost part of their energy (whose speed has decreased) are called inelastic scattered electrons. Electron energy loss spectroscopy (EELS) analysis is a measurement technique for spectroscopically analyzing the energy lost by inelastic scattered electrons to obtain a loss spectrum. The energy loss of inelastic scattered electrons varies depending on the elemental composition of the sample and also on the chemical state of each atom.

[0003] The EELS analysis method can measure the composition or valence of elements in a sample with high spatial resolution by being used in combination with a transmission electron microscope (TEM). In particular, the EELS analysis method can measure changes in the valence of a specific element and measure changes in the crystal structure of a minute region by being used in combination with a TEM. The change in valence can be analyzed from the change in the peak position of a specific spectrum of a specific element.

[0004] For accurate evaluation of the peak position, a data processing method called deconvolution is used. The EELS spectrum observed by the EELS spectroscopy method is convolved with an instrument function (the spread of the irradiated electron beam) with respect to the true spectrum. Therefore, the observed EELS spectrum becomes a spectrum with a broader spread compared to the true spectrum. Deconvolution is a technique for estimating the true spectrum using the observed EELS spectrum and the instrument function.

[0005] Applying the deconvolution process known as the Richardson-Lucy method to EELS spectra with high noise levels amplifies the noise, making accurate evaluation of peak positions difficult. Non-patent documents 1 and 2 disclose the Richardson-Lucy method. Therefore, when applying the deconvolution process known as the Richardson-Lucy method to EELS spectra with high noise levels, it is necessary to remove the noise from the EELS spectrum before applying the deconvolution process.

[0006] Furthermore, noise reduction can be achieved using methods such as Fourier transform, multivariate analysis, or neural networks. Non-patent document 3 discloses a method for noise reduction using a neural network. In addition, patent document 1 discloses a method for training a microscope noise reduction model by acquiring multiple training images with different image acquisition settings. [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] Japanese Patent Publication No. 2023-64737 [Non-patent literature]

[0008] [Non-Patent Document 1] William Hadley Richardson. Bayesian-based iterative method of image restoration. JoSA, Vol. 62, No. 1, pp. 55-59, 1972. [Non-Patent Document 2] Leon B Lucy. An iterative technique for the rectification of observed distributions. The astronomical journal, Vol. 79, p. 745, 1974. [Non-Patent Document 3] IEEE / CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019 [Overview of the project] [Problems that the invention aims to solve]

[0009] The noise reduction model in Patent Document 1 requires the preparation of multiple training images with different image acquisition settings for machine learning, which involves the time-consuming process of preparing training images with varying image acquisition conditions. Furthermore, the deconvolution method used in Non-Patent Documents 1 and 2 amplifies noise, making it impractical. The method disclosed in Non-Patent Document 3 did not provide sufficient noise reduction.

[0010] One aspect of the present invention aims to provide an image noise reduction method, an electron energy loss spectroscopy method, and an analysis apparatus that reduce the effort required to remove noise from a measurement image before deconvolving the instrument function. [Means for solving the problem]

[0011] One aspect of the present invention is an image noise reduction method in which a computer performs the following steps: a learning condition determination step, which determines the learning conditions for machine learning the noise reduction model based on a generated image from which noise has been removed using a noise reduction model trained with the Noise2Void algorithm, and an analyzed image from which the generated image has been subjected to deconvolution of the device function; a machine learning step, which performs machine learning of the measured image, which is the training data, using the Noise2Void algorithm, in accordance with the determined learning conditions; and a noise reduction step, which removes noise from the measured image, which is the analysis data, using the noise reduction model trained in the machine learning step, before performing deconvolution of the device function from the measured image, which is the analysis data. [Effects of the Invention]

[0012] According to one aspect of the present invention, the effort required to remove noise from the measurement image before deconvolving the device function can be reduced.

Brief Description of Drawings

[0013] [Figure 1] It is a system configuration diagram of an example of the analysis device according to this embodiment. [Figure 2] It is a hardware configuration diagram of an example of the computer according to this embodiment. [Figure 3] It is a functional configuration diagram of an example of the analysis device according to this embodiment. [Figure 4] It is a configuration diagram showing an example of a TEM to which an EELS device is attached. [Figure 5] It is a flowchart of an example of the learning process of noise. [Figure 6] It is an explanatory diagram of an example of learning by changing pixel values only in the horizontal direction of the fork function spectrum image. [Figure 7] It is an explanatory diagram of an example of a noise removal model. [Figure 8] It is an example of the learning result in this embodiment. [Figure 9] It is an example of the learning result in this embodiment. [Figure 10] It is an example of the learning result in this embodiment. [Figure 11] It is a flowchart of an example of the process of EELS analysis. [Figure 12] It is an example of the result of detecting the peak of the Ni-L edge in four patterns for the sample (LiNiAlO).

Mode for Carrying Out the Invention

[0014] Hereinafter, with reference to the drawings, the mode for carrying out the present invention will be described.

[0015] The image noise reduction method of this embodiment uses, for example, an electron energy loss spectroscopy (EELS) spectrum image or a Voigt function spectrum image as a training image, and performs machine learning on the noise contained in the training image. Furthermore, the image noise reduction method of this embodiment estimates the noise contained in the measured EELS spectrum image (measured image) or Voigt function spectrum image from the results of the machine learning on the obtained noise, and generates a generated EELS spectrum image (generated image) or a generated Voigt function spectrum image (generated image) from which the noise has been removed.

[0016] Here, training images are the images used in machine learning. Measurement images are the images that were measured and captured. Generated images are the images generated after denoising. Analyzed images are the images that have undergone deconvolution after denoising.

[0017] Although this embodiment describes an example of an EELS spectral image, it can also be applied to astronomical images other than EELS spectral images or images of diseased areas in medicine.

[0018] [System Configuration] First, an example of the analysis system 1 according to this embodiment will be described. Figure 1 is a system configuration diagram of an example of the analysis device 10 according to this embodiment. Figure 1(A) is an example of the analysis system 1 in which a user operates the analysis device 10 to use the analysis device 10. Figure 1(B) is an example of the analysis system 1 in which a user operates a user terminal 12 to use the analysis device 10. The analysis device 10 and the user terminal 12 are connected to each other via a network 18 such as the Internet or a local area network (LAN) so as to be able to communicate.

[0019] The analysis device 10 in Figure 1(A) is a device that performs machine learning on noise contained in training images, estimates noise contained in measurement images from the results of machine learning, generates a generated image from which noise has been removed from the measurement image, and performs deconvolution on the generated image to generate an analysis image. The analysis device 10 is, for example, a PC (personal computer) or a workstation. Alternatively, the analysis device 10 may be, for example, a tablet terminal, a smartphone, or a measuring instrument.

[0020] The analysis device 10 receives user input via a touch panel, controller, mouse, or keyboard. The analysis device 10 performs various processes as described below in accordance with the user input. The analysis device 10 also outputs the results of the processing performed according to the user input.

[0021] The user terminal 12 in Figure 1(B) is a device that receives user input via a touch panel, controller, mouse, or keyboard. The user terminal 12 can be, for example, a PC, tablet, or smartphone. The user terminal 12 communicates with the analysis device 10 via the network 18. The user terminal 12 requests processing from the analysis device 10 according to the input received from the user and outputs the processing results received from the analysis device 10. The output of the processing results may be a display output or a printed output.

[0022] The analysis device 10 in Figure 1(B) performs various processes as described later in accordance with requests received from the user terminal 12, and transmits the processing results to the user terminal 12. The analysis device 10 in Figure 1(B) may be implemented, for example, by a cloud computer. The number of analysis devices 10 is not limited to one. Two or more analysis devices 10 may be constructed and connected to each other via a network 18 so as to be able to communicate.

[0023] Note that a transmission electron microscope (TEM) and an EELS system are examples of devices that capture EELS spectrum images. Below, we will explain an example of an EELS system that captures images with noise removed.

[0024] The analysis device 10 may be connected to the TEM and EELS device in a communicative manner. The analysis device 10, which is connected to the TEM and EELS device in a communicative manner, can receive TEM images. The analysis device 10 may receive EELS spectrum images from a database that stores TEM images, or it may read EELS spectrum images from a storage medium such as a USB (Universal Serial Bus) memory that stores EELS spectrum images.

[0025] Note that the configuration of the analysis system 1 shown in Figure 1 is just one example and is not limited to the configuration shown in Figure 1. The analysis device 10 and user terminal 12 of the analysis system 1 according to this embodiment can be realized, for example, through the cooperation of hardware that constitutes a general computer and a program (software) executed on the computer.

[0026] The analysis device 10 and user terminal 12 according to this embodiment can be realized, for example, by the computer 20 in Figure 2 executing a program.

[0027] [Hardware configuration] Figure 2 is a hardware configuration diagram of an example of a computer according to this embodiment. The computer 20 shown in Figure 2 has a hardware configuration that includes, for example, a processor such as a CPU (Central Processing Unit) 21, memory such as a ROM (Read Only Memory) 22 and RAM (Random Access Memory) 23, an auxiliary storage device 24, an output device 25 such as a display device, an input device 27 such as an input device, an I / F device 26, and a bus connecting these parts. The auxiliary storage device 24, the output device 25, and the input device 27 may be provided outside the casing of the computer 20.

[0028] The program executed by computer 20 is provided by recording it on, for example, a magnetic disk, optical disk, semiconductor memory, or similar recording medium, and storing it in an auxiliary storage device 24 or the like. The recording medium on which the program is recorded may be any storage format as long as it is a recording medium that computer 20 can read. The program may also be pre-installed on computer 20. The program may also be stored in ROM 22. The program may also be distributed via network 18 and installed on computer 20 as appropriate.

[0029] The CPU 21 controls the overall operation of the computer 20. The CPU 21 reads programs stored in the ROM 22 and auxiliary storage device 24 into memory such as RAM 23 as needed and executes them, thereby realizing the various processing units described later.

[0030] ROM22 stores programs and data. RAM23 is used as the work area for CPU21. RAM23 may include non-volatile RAM. The auxiliary storage device 24 is a storage device such as an SSD (Solid State Drive) or HDD (Hard Disk Drive).

[0031] For example, the auxiliary storage device 24 can store various programs, data, files, etc., necessary to realize the image noise reduction method, the electron energy loss spectroscopy analysis method, and the analysis apparatus 10 according to this embodiment. The output device 25 is an output device such as a monitor or display. The input device 27 is an input device such as a touch panel, controller, mouse, keyboard, or operation buttons. The I / F device 26 includes an interface for communication via the network 18 and an I / F for reading data from or writing data to a recording medium.

[0032] [Functional Configuration] Below, an example of the analysis system 1 according to this embodiment will be described as shown in Figure 1(A). In the case of the analysis system 1 shown in Figure 1(B), the analysis device 10 and the user terminal 12 work together to perform the processing described later.

[0033] The analysis system 1 according to this embodiment removes noise from a measured image using, for example, an image recognition AI (artificial intelligence) that has been trained on noise contained in training images, and generates a generated image. Furthermore, the analysis system 1 according to this embodiment performs deconvolution processing of the device function on the generated image.

[0034] This embodiment describes, as an example, the noise learning process and noise reduction process when using an EELS spectrum image or a Voigt function spectrum image as a training image.

[0035] Figure 3 is a functional configuration diagram of an example of the analysis device 10 according to this embodiment. The analysis device 10 shown in Figure 3 has an acquisition unit 50, an analysis unit 52, an output unit 54, a storage unit 56, and a learning unit 58. Note that the functional configuration in Figure 3 is just one example, and the functions for performing deep learning and denoising EELS spectral images (measured images) and deconvolving the generated images with the device function may be constructed in separate devices and communicated via the network 18. Also, in the functional configuration of Figure 3, functional components that are not necessary for the explanation of the analysis device 10 according to this embodiment are omitted from the illustration as appropriate.

[0036] The acquisition unit 50 captures training images or measurement images. The storage unit 56 stores the training images, measurement images, and the trained deep learning model described later that were captured by the acquisition unit 50. The learning unit 58 generates a deep learning model trained to handle noise by performing deep learning using the training images as described later. The learning unit 58 also uses the trained deep learning model to infer noise from the measurement images.

[0037] The noise reduction unit 60 of the analysis unit 52 generates a generated image by removing the noise inferred by the learning unit 58 from the measured image. The deconvolution unit 62 of the analysis unit 52 performs deconvolution processing of the device function on the generated image generated by the noise reduction unit 60 to generate an analysis image. The output unit 54 outputs the analysis image generated by the analysis unit 52.

[0038] Figure 4 is a configuration diagram showing an example of a TEM with an EELS device attached. The TEM in Figure 4 includes an electron gun 101, a condenser lens 102, a sample stage 103, an objective lens 104, an intermediate lens 105, a projection lens 106, a projection chamber 107, an analyzer 108, a CCD camera 110, a control device 111, an image processing device 112, and a memory 113.

[0039] The electron gun 101 generates an electron beam. The condenser lens 102 focuses the electron beam generated from the electron gun 101. The sample stage 103 is a sample holder located downstream of the condenser lens 102.

[0040] The objective lens 104 focuses the electron beam that has passed through the sample placed on the sample stage 103. The intermediate lens 105 focuses the electron beam that has passed through the objective lens 104. The analyzer 108 is an energy filter located downstream of the intermediate lens 105. The projection lens 106 magnifies the electron beam image that has passed through the analyzer 108. The projection chamber 107 observes the electron beam image. The CCD camera 110 is a detector that converts the electron beam image into an electrical signal.

[0041] The image processing device 112 receives the output from the CCD camera 110 and processes the measurement image 112a. The control device 111 controls the analyzer 108. The control device 111 also controls the image processing device 112. The control device 111 is, for example, a computer. The memory 113 can store, for example, the measurement image 112a.

[0042] [Noise learning process and noise reduction process] In this embodiment, a deep learning model (denoising model) is generated using the Noise2Void algorithm. The Noise2Void algorithm is a method for training a convolutional neural network (CNN) that removes noise.

[0043] Specifically, the Noise2Void algorithm, for example, if a training image of 1000 pixels × 1000 pixels is given, divides the training image into regions of 10 pixels × 10 pixels. Then, two pixels are randomly selected within each divided region of the training image. The value of one pixel is then substituted for the value of the other pixel. This operation is performed for each divided region of the training image. Because a part of the original image is randomly modified through this operation, training data is generated. The Noise2Void algorithm uses the training data (training image) generated by the above operation and the target data (measured image) to learn the parameters of a noise reduction model that appropriately removes noise, and generates a noise reduction model.

[0044] Generally, any image contains noise caused by the equipment. The Noise2Void algorithm does not require a noise-free training image; instead, it learns the parameters of a noise reduction model that appropriately removes noise from training images generated by randomly changing a portion of a single measurement image that contains noise. The Noise2Void algorithm then estimates a true noise-free image and generates a generated image by bringing the values ​​of the modified parts of the training data closer to the values ​​of the training data regarding the noise in the image. It also derives the optimal training conditions (number of epochs) for generating a noise-free generated image.

[0045] Figure 5 shows a flowchart of an example of a noise learning process. In the noise learning process shown in Figure 5, in steps S10 to S18, the optimal learning conditions are first determined using the Voigt function. The Voigt function is a distribution function found in the width of a spectroscopic spectrum.

[0046] In step S10, the operator operates the analysis device 10 to construct a deep learning model for noise reduction. The deep learning model for noise reduction is stored in the memory unit 56.

[0047] In step S12, the operator operates the analysis device 10 to cause the learning unit 58 to generate training data. The learning unit 58 adds Gaussian noise, which is noise commonly added by measuring instruments, to the Voigt function spectrum image, and then generates the training data.

[0048] In step S14, the operator operates the analysis device 10 to train the denoising model using the training data generated in step S12. The learning unit 58 learns the parameters of the denoising model through the training data generated in step S12.

[0049] In step S16, the operator operates the analysis device 10 to perform a deconvolution process in which the device function is deconvolved from the generated image from which noise has been removed using the denoising model learned in step S14. The analysis unit 52 obtains an analysis image by deconvolving the device function from the generated image from which noise has been removed using the denoising model learned in step S14 using the Richardson-Lucy method (RL method). The RL method is a technique that estimates a truly clear image through iterative processing using Bayesian estimation.

[0050] In step S18, the analysis unit 52 determines the optimal number of epochs for learning conditions in the process of obtaining the analysis image by deconvolution, and constructs a noise reduction model.

[0051] In step S20, the operator operates the analysis device 10 to cause the learning unit 58 to generate training data from the EELS spectrum image. The learning unit 58 generates training data from the EELS spectrum image.

[0052] In step S22, the operator operates the analysis device 10 and uses the training data generated in step S20 to train the denoising model under the optimal training conditions determined in step S18. The learning unit 58 learns the parameters of the denoising model through the training data generated in step S20.

[0053] In step S22, the operator operates the analysis device 10 to perform a deconvolution process in which the device function is deconvolved from the generated image from which noise has been removed using the trained noise reduction model. The analysis unit 52 deconvolves the device function from the generated image from which noise has been removed using the trained noise reduction model using the Richardson-Lucy method (RL method) to obtain an analysis image. The analysis unit 52 generates the training results.

[0054] Here, we will explain how to generate training images.

[0055] For example, in EELS spectral images, measurements are taken from the inside of the particle to the particle surface. When applying the Noise2Void algorithm to such EELS spectral images, if the image is divided into squares as in a typical image and the pixel values ​​are swapped, the consistency between the generated image and the original data (measured image) is greatly disrupted. Therefore, as shown in the Voigt function spectrum image in Figure 6, it is desirable to change the pixel values ​​only in the horizontal direction, such as 1pix × 10pix, for training. Figure 6 is an explanatory diagram of an example of how to change the pixel values ​​only in the horizontal direction of a Voigt function spectrum image for training. In other words, in the image noise reduction method of this embodiment, it is preferable to perform noise reduction by making the number of pixels different in the horizontal and vertical directions.

[0056] Next, we will discuss machine learning for noise reduction models.

[0057] Figure 7 is an explanatory diagram of an example of a noise reduction model. The noise reduction model in Figure 7 learns by feeding training images from left to right. The learning unit 58 takes training images from the left of the noise reduction learning model in Figure 7 and evaluates the generated image output from the right by comparing it with the training image (measured image). The difference between the generated image and the training image is expressed as an evaluation value. Therefore, a lower evaluation value is considered better. However, if this evaluation value is "0" and there is no difference between the generated image and the training image, it means that the noisy data, i.e., the training image, has been perfectly reproduced. Therefore, it is necessary to proceed with learning so as not to perfectly reproduce the training image.

[0058] Furthermore, in machine learning for denoising models, determining the training conditions is a challenge. Therefore, in this embodiment, a Voigt function spectrum image was used as the training image. The optimal training conditions were explored during the denoising and deconvolution process on the Voigt function spectrum image shown in Figure 6.

[0059] One example of this embodiment aims to accurately evaluate the peak position of the EELS spectrum by appropriately removing noise from the EELS spectral image (measured image) and performing deconvolution processing.

[0060] In steps S10 to S18 of Figure 5, the results are evaluated using a Voigt function spectrum image with Gaussian noise added to determine the learning conditions for machine learning denoising using the Noise2Void algorithm. The evaluation items for denoising using the Noise2Void algorithm are: how well the denoised Voigt function spectrum image reproduces the unnoised Voigt function spectrum image; whether the peak positions of the denoised Voigt function spectrum can be accurately evaluated; and whether the peak positions of the Voigt function spectrum can be accurately evaluated when deconvolution is performed after denoising. The optimal learning conditions can be determined based on these three items.

[0061] Furthermore, in steps S20-S22 of Figure 5, machine learning is performed on a denoising model that denoises EELS spectrum images using the Noise2Void algorithm, according to the optimal learning conditions determined by the processing in steps S10-S18.

[0062] Examples of learning results in this embodiment are shown in Figures 8, 9, and 10. "EPOCH1" to "EPOCH300" in Figures 8 to 10 show examples of the number of epochs. The number of epochs indicates how many times the entire training data is repeated for learning. The peak position to be accurately evaluated is "0". From the learning results in Figure 8, it was found that the accuracy of the noise-free Voigt function is good for epochs of "10 to 100". From the learning results in Figure 9, it was found that there is no significant difference depending on the number of epochs, as the evaluation of the peak position after noise reduction is generally poor. From the learning results in Figure 10, it was found that for the evaluation of the peak position after deconvolution following noise reduction, epochs of "10 to 100" accurately evaluate the peak position at any noise level. By processing steps S10 to S18 in Figure 5, an appropriate number of epochs for the learning conditions can be determined, and the optimal learning conditions are constructed. Furthermore, if the number of epochs exceeds "100," overfitting may occur, potentially preventing proper noise removal.

[0063] According to the flowchart in Figure 5, the optimal training conditions for the denoising model can be determined using the Voigt function spectrum image. Furthermore, according to the flowchart in Figure 5, the optimal training conditions determined using the Voigt function spectrum can be used in the machine learning of the denoising model that performs denoising on the EELS spectrum image.

[0064] Next, we will explain the deconvolution process.

[0065] In the deconvolution process of this embodiment, it is preferable to deconvolve the instrument function of the generated image, which has been denoised using the Noise2Void algorithm, using the Richardson-Lucy method.

[0066] In the EELS spectrum image, which is an example of this embodiment, even if noise is removed using only the conventionally known Richardson-Lucy method, the change points shown in Figure 12 cannot be identified due to the influence of noise in the measured image. On the other hand, when noise is removed using the Noise2Void algorithm, the change points become clear as shown in Figure 12, and when the generated image after noise removal with the Noise2Void algorithm is deconvolved using the Richardson-Lucy method, the change points become even clearer as shown in Figure 12.

[0067] [EELS analysis processing] Figure 11 is a flowchart of an example of the EELS analysis process.

[0068] In step S30, the acquisition unit 50 acquires an EELS spectral image.

[0069] In step S32, the noise reduction unit 60 of the analysis unit 52 performs noise reduction on the EELS spectral image based on the Noise2Void algorithm using a previously learned noise reduction model.

[0070] In step S34, the deconvolution unit 62 of the analysis unit 52 generates an analysis image by deconvolving the device function. The Richardson-Lucy method may be used for deconvolution.

[0071] In step S36, the analysis unit 52 can accurately analyze the chemical state at the atomic level by determining the peak top energy of the sample from the generated analysis image. The output unit 54 outputs the analysis image or analysis result generated by the analysis unit 52.

[0072] According to the image noise reduction method of this embodiment, noise contained in the measured image can be removed without preparing noise-free training data. As a result, the effort required to remove noise from the measured image before deconvolving the device function can be further reduced.

[0073] [Examples] (1) Determining the learning conditions Deep learning was performed in advance according to the flowchart shown in Figure 5.

[0074] In this example, we are verifying EELS spectrum images, which are measured from the inside of a particle to the particle surface. Therefore, if we divide the image into squares and swap the pixel values ​​as with typical images, the consistency between the generated image and the original data (measured image) will be greatly disrupted. For this reason, as shown in the Voigt function spectrum image in Figure 6, we changed the pixel values ​​horizontally, such as 1pix × 10pix, and created a noise reduction model trained using the Noise2Void algorithm.

[0075] The learning process proceeded according to the denoising model shown in Figure 7. In this example, the objective is to appropriately remove noise from the EELS spectral image (measured image) and accurately evaluate the peak position of the EELS spectrum. To determine the learning conditions for machine learning of denoising using the Noise2Void algorithm, the results were evaluated using a Voigt function spectrum image with noise added, assuming Gaussian noise. The evaluation items for denoising using the Noise2Void algorithm were the extent to which the denoised Voigt function spectrum image reproduces the noise-free Voigt function spectrum image, whether the peak position of the Voigt function spectrum after denoising can be accurately evaluated, and whether the peak position of the Voigt function spectrum can be accurately evaluated when deconvolution is performed after denoising. The optimal learning conditions were determined based on these three items. The results in this example are shown in Figures 8, 9, and 10. Note that the peak position to be accurately evaluated is "0". From the learning results in Figure 8, it was found that the reproduction of the noise-free Voigt function is good for a number of epochs of "10 to 100". From the training results in Figure 9, it was found that the evaluation of peak positions after denoising was generally poor, indicating that there was no significant difference depending on the number of epochs. From the training results in Figure 10, it was found that the evaluation of peak positions after deconvolution following denoising was accurate at all noise levels when the number of epochs was between 10 and 100. However, the Voigt function is a simple simulation model compared to actual EELS spectrum images. Therefore, the number of epochs for training the EELS spectrum images was set to 30, slightly more than that for the Voigt function. Under these conditions, training for denoising EELS spectrum images was performed.

[0076] (2) Detection of peak positions in EELS spectrum images Figure 12 shows the results of peak detection of the Ni-L edge on the sample (LiNiAlO) using four patterns: Original (solid line, unprocessed), RL (dotted line, deconvolution using the RL method), Noise2Void (dashed line, noise reduction using Noise2Void), and Nose2Void+RL (dash-dotted line, noise reduction using Noise2Void followed by deconvolution using the RL method). In the Original and RL patterns, the influence of noise is significant, and the peak position detection is not accurate. In the Noise2Void and Noise2Void+RL patterns, the peak position detection is performed without being affected by noise. In the case of Noise2Void+RL, the change point is more pronounced compared to the other data.

[0077] [Examples of application] The Noise2Void and Richardson-Lucy algorithms described above are applicable to images as well as spectra. The conditions for application are the analysis data to be analyzed (spectrum or image, etc.) and the instrument function. If the instrument function is unknown or cannot be estimated, the Richardson-Lucy method cannot be applied because it becomes computationally impossible. The Blind-Richardson-Lucy method allows for the estimation of the instrument function. However, the Blind-Richardson-Lucy method is less accurate compared to cases where the instrument function can be actually measured or estimated with high accuracy.

[0078] While several embodiments of the present invention have been described, these embodiments are presented as examples only and are not intended to limit the scope of the invention. These novel embodiments can be carried out in a variety of other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their variations are included in the scope and spirit of the invention, as well as in the claims and their equivalents. [Explanation of Symbols]

[0079] 1. Analysis System 10 Analysis device 12 User terminals 18 Network 50 Collection Department 52 Analysis Department 54 Output section 56 Memory section 58 Learning Department 60 Noise reduction section 62 Reverse convolution section

Claims

1. A procedure for determining learning conditions for the machine learning of the noise reduction model, based on a generated image from which noise has been removed using a noise reduction model trained with the Noise2Void algorithm, and an analyzed image obtained by performing an inverse convolution of the device function on the generated image, A machine learning procedure is performed using the Noise2Void algorithm to perform machine learning on the measurement images, which are the training data, in accordance with the learning conditions determined above. Before performing the deconvolution of the instrument function on the measurement image, which is the analysis data, a noise reduction procedure is performed to remove noise from the measurement image, which is the analysis data, using a noise reduction model that has been trained using the aforementioned machine learning procedure. A computer-based method for removing image noise.

2. The aforementioned procedure for determining learning conditions is: We use a machine learning-based denoising model on training data generated from Voigt function spectrum images with added Gaussian noise. The image noise reduction method according to claim 1.

3. In the Noise2Void algorithm described above, the regions of the training image to be divided have different numbers of pixels in the vertical and horizontal directions. The image noise reduction method according to claim 1.

4. The Richardson-Lucy method is used to deconvolve the aforementioned device function and obtain the analyzed image. The image noise reduction method according to any one of claims 1 to 3.

5. A procedure for determining learning conditions for the machine learning of the noise reduction model, based on a generated image from which noise has been removed using a noise reduction model trained with the Noise2Void algorithm, and an analyzed image obtained by performing an inverse convolution of the device function on the generated image, A machine learning procedure is performed using the Noise2Void algorithm to perform machine learning on generated electron energy loss spectral images, which are the training data, according to the learning conditions determined above. Before performing the deconvolution of the instrument function from the generated electron energy loss spectral image, which is the analysis data, a noise reduction procedure is performed to remove noise from the generated electron energy loss spectral image, which is the analysis data, using a noise reduction model that has been trained using the machine learning procedure described above. A computer-based method for analyzing electron energy loss using spectroscopy.

6. The analysis procedure involves performing deconvolution of the instrument function using the Richardson-Lucy method, and then determining the peak top energy from the analysis image obtained by removing noise from the generated electron energy loss spectral image. The electron energy loss spectroscopy method according to claim 5, wherein the computer further performs the above.

7. An analysis unit determines the learning conditions for the machine learning of the noise reduction model based on a generated image from which noise has been removed using a noise reduction model trained with the Noise2Void algorithm, and an analyzed image obtained by performing an inverse convolution process of the device function on the generated image. A learning unit that performs machine learning on measurement images, which are training data, using the Noise2Void algorithm, according to the learning conditions determined above, Before performing the deconvolution of the device function on the measurement image, which is the analysis data, a noise reduction unit removes noise from the measurement image, which is the analysis data, using a noise reduction model that has been machine-learned in the learning unit. An analytical device having the following features.

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