Tensor data restoration device, tensor data restoration method, and program

Abstract

To provide a tensor data restoration device for restoring multidimensional tensor data including a missing value or noises, a restoration method, and a program.SOLUTION: A tensor data restoration device 1 includes: an input unit 10 for inputting multidimensional tensor data; a noise mitigation processing unit 22 for mitigating noises of the input tensor data; and an output unit 13 for outputting the tensor data in which noises are mitigated. The noise mitigation processing unit 22 performs: first noise mitigation processing 23 for performing noise mitigation processing on the tensor data by using image smoothness; second noise mitigation processing 24 for performing noise mitigation processing on the tensor data by using local similarity; and switch processing 25 for switching from the first noise mitigation processing 23 to the second noise mitigation processing 24.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a technique for restoring multidimensional tensor data that includes missing or noisy data. [Background technology]

[0002] A data structure with multidimensional indices is called a multidimensional tensor. Among multidimensional tensors, three-dimensional tensor structures are important in many practical applications. For example, video images can be considered a three-dimensional tensor, with two dimensions representing space and one dimension representing time. MRI (Magnetic Resonance Imaging) data can be considered a three-dimensional tensor, with one dimension representing the sweep direction and two dimensions representing the cross-sectional image perpendicular to that. Spectral images can be considered a three-dimensional tensor, with two dimensions representing space and one dimension representing wavelength (Non-Patent Document 1). To acquire spectral images, snapshot cameras use sensors with various patterns, such as Bayer filters and spectral filter arrays, and each pixel of the sensor observes an assigned quantity within each color or spectrum (Patent Document 1).

[0003] 3D tensor data can contain missing values. Here, a missing tensor means that some elements are not observed and are missing. Missing values ​​can have various origins, including unintended data acquisition errors, data acquisition errors caused by the purpose of reducing measurement time, and missing values ​​inherent to the sensing method. Furthermore, when 3D tensor data is a spectroscopic image, one pixel observes the incident light intensity of a certain wavelength or band, so it can be considered a 3D tensor with only some elements observed. Furthermore, the observed elements have a structural arrangement within the 3D tensor. This is the same as having a structural missing element in the observed 3D tensor.

[0004] Other instances of structural defects include when an entire scan line is missing during data acquisition that requires a line scan. Depending on the sensing method, defects may be considered random.

[0005] The data may also contain observation noise, which can be Gaussian noise, impulse noise, or sparse noise with high intensity. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Patent application 2020-195692 [Non-patent literature]

[0007] [Non-Patent Document 1] Calum Williams et al. “Grayscale-to-Color: Scalable Fabrication of Custom Multispectral Filter Arrays” ACS Photonics. 2019 Dec 18;6(12):3132-3141 Summary of the Invention [Problem to be solved by the invention]

[0008] When 3D tensor data contains structural missing values ​​and noise, data analysis becomes difficult. For example, when extracting time-series signals from video tensor data, missing values ​​and noise can introduce frequency components that do not actually exist. This can also lead to incorrect estimations in component analysis and segmentation using spectroscopic images.

[0009] In view of the above background, the present invention provides a technique for restoring multidimensional tensor data that includes missing values ​​and noise. [Means for solving the problem]

[0010] The tensor data restoration device of the present invention comprises an input unit that inputs multidimensional tensor data, a noise reduction processing unit that reduces loss and noise in the input tensor data, and an output unit that outputs tensor data with the loss and noise reduced, and the noise reduction processing unit performs a first noise reduction process that reduces noise in the tensor data by utilizing smoothness, a second noise reduction process that reduces noise in the tensor data by utilizing local similarity, and a switching process that switches from the first noise reduction process to the second noise reduction process.

[0011] By performing noise reduction processes with different properties on tensor data in this way, it is possible to appropriately reduce defects and noise and restore the tensor data. For example, in tensor data such as image information, time-series information, and energy spectra, there is a high correlation between neighboring elements. Noise reduction processes using smoothness are a method of smoothing and reducing noise by using information on neighboring elements. Noise reduction processes using local similarity are a method of reducing noise by using patch similarity in local areas (blocks) of tensor data.

[0012] The first noise mitigation process using smoothness can adequately fill missing values, but may not be able to sufficiently remove noise. On the other hand, the second noise mitigation process using local similarity is suitable for noise mitigation of tensors with periodic missing patterns, but if processing is performed using data corrupted by noise as initial values, structural artifacts may remain in the pattern itself. In the present invention, by switching between these two noise mitigation processes, appropriate noise mitigation can be performed for both missing structures and noise. Note that switching from the first noise mitigation process to the second noise mitigation process may be performed based on a user instruction.

[0013] In the tensor data restoration device of the present invention, the switching process may switch from the first noise mitigation process to the second noise mitigation process when a degree of noise mitigation by the first noise mitigation process becomes equal to or greater than a predetermined threshold.

[0014] In this way, by smoothing the tensor data to a predetermined threshold using the first noise mitigation process and then performing the second noise mitigation process using local similarity, the quality of the initial tensor data used in the second noise mitigation process is improved, allowing the second noise mitigation process to be performed appropriately.

[0015] The tensor data restoration device of the present invention may include a redundancy update unit that updates the tensor data so as to reduce the redundancy of the input tensor data, and the tensor data updated by the redundancy update unit may be input to the noise reduction processing unit.

[0016] Since tensor data often has redundancy, updating the tensor data to reduce the redundancy improves restoration accuracy and is also effective in mitigating noise. Furthermore, by inputting the tensor data updated by the redundancy update unit to the noise mitigation processing unit, noise that could not be completely removed by the redundancy update unit can be mitigated by the noise mitigation processing unit.

[0017] The tensor data restoration device of the present invention may input the tensor data that has been noise-reduced by the noise mitigation processing unit back into the redundancy update unit, and repeat the redundancy update processing by the redundancy update unit and the noise mitigation processing by the noise mitigation processing unit until a predetermined termination condition is met.

[0018] By performing a redundancy update process to reduce redundancy on the tensor data that has undergone noise mitigation in this manner and repeating the redundancy update and noise mitigation, it is possible to more appropriately mitigate missing values ​​and noise in the tensor data. Note that when repeatedly performing the redundancy update and noise mitigation, the redundancy update may be performed following the first noise mitigation process and the second noise mitigation process, or the redundancy update may be inserted between the first noise mitigation process and the second noise mitigation process, such as the first noise mitigation process, redundancy update, second noise mitigation process, and redundancy update.

[0019] The tensor data restoration device of the present invention may include a missing element designation unit that designates elements with missing data in the input tensor data. By providing a configuration for designating missing values ​​in this way, elements known to be missing in advance can be designated as missing values, preventing noise from being mixed in the missing value portion. This allows for appropriate redundancy updating and noise mitigation using local similarity.

[0020] The tensor data restoration method of the present invention is a method for mitigating loss and noise in multidimensional tensor data using a tensor data restoration device, and includes the steps of: inputting multidimensional tensor data to the tensor data restoration device; a first noise reduction processing step in which the tensor data restoration device performs noise reduction processing on the tensor data by utilizing smoothness; a step in which the tensor data restoration device determines whether to switch from the first noise reduction processing step to a second noise reduction processing step; a second noise reduction processing step in which the tensor data restoration device performs noise reduction processing on the tensor data by utilizing local similarity; and a step in which the tensor data restoration device outputs tensor data with loss and noise reduced.

[0021] The program of the present invention is a program for reducing loss and noise in multidimensional tensor data using a tensor data restoration device, and causes a computer to execute the following steps: inputting multidimensional tensor data; a first noise reduction processing step of performing noise reduction processing on the tensor data by utilizing smoothness; determining whether to switch from the first noise reduction processing step to a second noise reduction processing step; a second noise reduction processing step of performing noise reduction processing on the tensor data by utilizing local similarity; and outputting tensor data with loss and noise reduced. [Effects of the Invention]

[0022] According to the present invention, by switching between a first noise mitigation process that utilizes smoothness and a second noise mitigation process that utilizes local similarity, it is possible to perform appropriate noise mitigation for both defects and noise. [Brief explanation of the drawings]

[0023] [Figure 1] FIG. 1 illustrates a configuration of a tensor data restoration device according to first and second embodiments. [Figure 2] 4 is a flowchart showing the operation of the tensor data restoration device according to the first embodiment. [Figure 3] 10 is a flowchart showing the operation of the tensor data restoration device according to the second embodiment. [Figure 4] 10 is a flowchart showing the operation of the tensor data restoration device according to the third embodiment. [Figure 5] FIG. 10 is a diagram illustrating another configuration of the tensor data restoration device. DETAILED DESCRIPTION OF THE INVENTION

[0024] A tensor data restoration device according to an embodiment of the present invention will be described below with reference to the drawings. (First embodiment) FIG. 1 is a diagram showing the configuration of a tensor data restoration device 1 according to a first embodiment. The tensor data restoration device 1 of this embodiment handles spectroscopic images, which are a type of three-dimensional tensor data, as multidimensional tensor data. The tensor data restoration device 1 includes an input unit 10 that inputs tensor data, a calculation unit 11 that performs a process of restoring tensor data including missing values ​​and noise, and an output unit 12 that outputs the restored tensor data. The calculation unit 11 includes a missing element designation unit 20, a redundancy update unit 21, and a noise mitigation processing unit 22.

[0025] The missing element designation unit 20 designates missing values ​​for the input tensor data and assigns zeros to the designated elements. Missing values ​​are designated, for example, based on prior knowledge of the tensor data structure. Three-dimensional tensor data uses three-dimensional indices. For example, if it is determined that an element with index (i, j, k) will not be observed due to the observation method, that index is a missing value. For example, in a spectroscopic image, one pixel observes the incident light intensity of a certain wavelength or band. Therefore, when focusing on a certain wavelength, wavelengths other than the observed wavelength can be considered to have a structural defect in the three-dimensional tensor. Furthermore, if an error is found in the observation results of a certain index, it can be considered a missing value. The missing element designation unit 20 defines the set of indices with missing values ​​as Ω={(i, j, k)|i, j, k∈N} and assigns zeros to the values ​​designated by the index.

[0026] The redundancy update unit 21 performs calculations to reduce the redundancy of the tensor, and obtains an updated tensor with reduced redundancy. In the case of spectroscopic images handled in this embodiment, the same spectrum appears multiple times. In this way, three-dimensional tensors have redundancy, and it is often possible to assume that the tensor has a low rank. To cite another example, in the case of moving images, gradual changes are prevalent along the time axis, and redundancy also exists.

[0027] Here, we will explain redundancy updating using the recently proposed tensor average rank as an example. This low rank property is obtained by taking the average value of the matrix rank in each energy spectrum (we call it energy spectrum to avoid confusion with optical spectrum) of the transformed domain in a certain dimension of a 3D tensor. A convex relaxation of this is the tTNN (transformed tensor nuclear norm), which is defined for 3D tensors by the following equation. Note that in the following equation, the "3-axis" is the wavelength direction axis.

number

[0028] The redundancy update unit 21 may use any redundancy, such as a matrix expansion-based low-rank feature. The redundancy update unit 21 outputs the updated tensor to the noise reduction processing unit 22.

[0029] The noise reduction processing unit 22 performs two different types of reduction processing, namely, a first noise reduction processing unit 23 and a second noise reduction processing unit 24. Note that defects and noise are the same in the sense that they are not complete data, i.e., errors, and the processing for reducing these errors is collectively referred to as noise reduction. The noise reduction processing unit 22 not only reduces noise, but also reduces defects. In this embodiment, the tensor data handled by the tensor data restoration device 1 is a spectroscopic image, and the first noise reduction processing unit 23 is a noise reduction processing unit that utilizes image smoothness. The second noise reduction processing unit 24 is a noise reduction processing unit that utilizes local image patch similarity.

[0030] The first noise mitigation process 23 reduces the luminance difference between adjacent pixels, so that spatial luminance changes are not abrupt, creating a natural image, while preserving image structures such as edges and corners. Examples of the first noise mitigation process 23 include TV (Total Variation) smoothing (first derivative) and its higher-order generalization, TGV (Total Generalized Variation) smoothing (second derivative). TV is described, for example, in A. Beck et al., "Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems," IEEE Transactions on Image Processing (TIP), vol. 18, no. 11, pp. 2419-2434, 2009. TGV is described, for example, in K. Bredies et al., "Total generalized variation," SIAM Journal on Imaging Sciences, vol. 3, no. 3, pp. 492-526, 2010.

[0031] An example of the second noise mitigation process 24 is BM3D (Block-matching and 3D filtering). BM3D is a type of shrinkage-based noise mitigation process that utilizes local similarity in an image to perform noise mitigation. It creates blocks by collecting small patches in the depth direction within the image, statistically analyzes frequent patterns within the blocks, and uses the patterns as descriptors to represent the entire image. BM3D is described, for example, in V. Katkovnik et al., "Image denoising by sparse 3D transform-domain collaborative filtering," IEEE Transactions on Image Processing, vol. 16, no. 8, pp. 2080-2095, 2007. Note that the second noise mitigation process 24 may also use other shrinkage-based noise mitigation processes besides BM3D.

[0032] The first noise mitigation processing 23 and the second noise mitigation processing 24 are generally expressed by the following equations:

number

[0033] Here, the superscript (t) represents the number of times of processing. The noise reduction processor 22 performs the t-th processing, and the noise-reduced X (t+1) The parameter σ represents the degree of noise mitigation, and varies depending on the method used in the first noise mitigation process 23 and the second noise mitigation process 24.

[0034] The noise reduction processing unit 22 switches from the first noise reduction processing 23 to the second noise reduction processing 24 by the switching processing 25. As described above, the first noise reduction processing 23 and the second noise reduction processing 24 are different in method and have complementary characteristics. The switching processing 25 switches between the two noise reduction processing methods 23 and 24 in order to perform appropriate noise reduction.

[0035] In this embodiment, image smoothing is performed using a first noise mitigation process 23 up to a predetermined stage, and then a switching process 25 is performed to switch to a second noise mitigation process 24 at a stage where the image is less susceptible to the influence of the original defect pattern. The switching timing may be, for example, the timing when the degree of change in update due to image smoothing falls below a threshold. Specifically, the timing is the timing when the degree of change in update falls below a threshold between 0.01 and 0.0005, or 0.0001, in a state where the luminance has been normalized, that is, converted so that the pixel value falls between 0 and 1. The switching timing may also be set according to the magnitude of the defect and noise, rather than the degree of change in update.

[0036] The output unit 12 has a function of outputting tensor data restored from tensor data containing missing or noisy data. The output destination may be a display means such as a monitor, or a storage unit.

[0037] The configuration of the tensor data restoration device 1 of this embodiment has been described above, but an example of the hardware of the above-mentioned tensor data restoration device 1 is a computer equipped with a CPU, RAM, ROM, hard disk, display, keyboard, mouse, communication interface, etc. A program having modules that realize each of the above-mentioned functions is stored in RAM or ROM, and the above-mentioned tensor data restoration device 1 is realized by executing the program by the CPU. Such programs are also included in the scope of the present invention.

[0038] 2 is a flowchart showing the operation of the tensor data restoration device 1 of this embodiment. The tensor data restoration device 1 receives input of tensor data to be processed (S10), and then, if the input tensor data has structural missing values, designates missing elements and sets the missing elements to 0 (S11). Next, the tensor data restoration device 1 updates tensor redundancy based on the low rank of the tensor (S12).

[0039] Next, the tensor data restoration device 1 performs a correction process using TGV that utilizes the smoothness of the image as a first noise mitigation process (S13), and determines whether to switch to a second noise mitigation process based on the update rate of the image (S14). If it is determined not to switch to the second noise mitigation process (NO in S14), the tensor data restoration device 1 continues to perform the first noise mitigation process (S13). If it is determined to switch to the second noise mitigation process (YES in S14), the tensor data restoration device 1 performs a second noise mitigation process using BM3D (S15). After performing the second noise mitigation process, the tensor data restoration device 1 outputs noise-mitigated tensor data (S16).

[0040] The configuration and operation of the tensor data restoration device 1 according to the first embodiment have been described above. Different noise mitigation methods have their strengths and weaknesses. The second noise mitigation method 24, which utilizes local similarity, may be affected by the loss pattern in the case of a tensor with periodic losses. On the other hand, the first noise mitigation method 23, which utilizes image smoothing, tends to have inferior noise mitigation capabilities compared to the second noise mitigation method 24. In terms of computational cost, the first noise mitigation method 23 is less expensive than the second noise mitigation method 24.

[0041] The tensor data restoration device 1 of this embodiment can appropriately mitigate noise and missing values ​​in tensor data while reducing calculation costs by switching between noise mitigation processes with complementary characteristics at an appropriate stage.

[0042] In this embodiment, the first noise mitigation process 23 utilizing image smoothness is performed first, followed by the second noise mitigation process 24 utilizing local similarity, thereby enhancing the effectiveness of the second noise mitigation process 24. Experiments conducted by the inventors have confirmed that a higher noise mitigation effect is achieved when relaying from the first noise mitigation process 23 to the second noise mitigation process 24, compared to when only the second noise mitigation process 24 is performed.

[0043] (Second embodiment) Next, a tensor data restoration device according to a second embodiment of the present invention will be described. The basic configuration of the tensor data restoration device 2 according to the second embodiment is the same as that of the tensor data restoration device 1 according to the first embodiment (see FIG. 1). The tensor data restoration device 2 according to the second embodiment differs from the first embodiment in that it repeatedly updates redundancy and reduces noise in tensor data.

[0044] 3 is a flowchart showing the operation of the tensor data restoration device 2 according to the second embodiment. The tensor data restoration device 2 according to the second embodiment receives input of tensor data to be processed (S20), and then, if the input tensor data has structural missing values, designates missing elements and sets the missing elements to 0 (S21). Next, the tensor data restoration device 2 updates tensor redundancy based on the low rank of the tensor (S22).

[0045] Next, the tensor data restoration device 2 performs a correction process using TGV that utilizes the smoothness of the image as a first noise mitigation process (S23), and determines whether to switch to a second noise mitigation process based on the update rate of the image (S24). If it is determined not to switch to the second noise mitigation process (NO in S24), the tensor data restoration device 2 continues to perform the first noise mitigation process (S23). If it is determined to switch to the second noise mitigation process (YES in S24), the tensor data restoration device 2 performs a second noise mitigation process using BM3D (S25).

[0046] After performing the second noise mitigation process, the tensor data restoration device 2 determines whether or not to terminate the process (S26). The termination determination can be made, for example, when the change in input / output between the first noise mitigation process and the second noise mitigation process (such as the square root of the sum of squares of the differences between the elements of the tensor) falls below a predetermined threshold. Here, as an example, the threshold is 10 in the case of data normalized to [0-1]. -4 Ya10 -5 can be used.

[0047] If this termination determination determines not to terminate the processing (NO in S26), the tensor data restoration device 2 passes the tensor data after the second noise mitigation processing to the redundancy update unit 21 and performs redundancy update (S22). Then, the tensor data restoration device 2 performs noise mitigation processing on the tensor data after the redundancy update in the same manner as described above (S23 to S25). However, in the second and subsequent noise mitigation processing, the threshold used in determining (S24) whether to switch from the first noise mitigation processing (S23) to the second noise mitigation processing (S25) may be different from the threshold used previously. Specifically, the threshold may be gradually decreased. This allows the degree of noise mitigation to be increased each time the noise mitigation processing is repeated.

[0048] In determining whether to terminate the processing after performing the second noise mitigation processing (S25), if it is determined that the processing is to be terminated (YES in S26), the tensor data restoration device 2 outputs the noise-mitigated tensor data (S27).

[0049] The above has described the tensor data restoration device 2 of the second embodiment. Similar to the tensor data restoration device 1 of the first embodiment, the tensor data restoration device 2 of the second embodiment has the effect of being able to appropriately mitigate noise and missing values ​​in tensor data while suppressing calculation costs.

[0050] The processing by the redundancy update unit 21 has the effect of mitigating noise in addition to improving the restoration accuracy of tensor data, and noise that could not be completely removed by the redundancy update unit 21 can be mitigated by the noise mitigation processing unit 22. The tensor data restoration device 2 of the second embodiment can perform more accurate noise mitigation by repeatedly performing redundancy update and noise mitigation.

[0051] (Third embodiment) Next, a tensor data restoration device 3 according to a third embodiment of the present invention will be described. The basic configuration of the tensor data restoration device 3 according to the third embodiment is the same as that of the tensor data restoration device 1 according to the first embodiment (see FIG. 1). The tensor data restoration device 3 according to the third embodiment differs from the first embodiment in that it interposes a tensor data redundancy update process between the first noise mitigation process and the second noise mitigation process, and repeatedly performs redundancy update and noise mitigation.

[0052] 4 is a flowchart showing the operation of the tensor data restoration device 3 according to the third embodiment. The tensor data restoration device 3 according to the third embodiment receives input of tensor data to be processed (S30), and then, if the input tensor data has structural missing values, specifies missing elements and sets the missing elements to 0 (S31). Next, the tensor data restoration device 3 updates tensor redundancy based on the low rank of the tensor (S32).

[0053] Next, the tensor data restoration device 3 performs noise reduction processing, and at this time, determines whether or not this is the first noise reduction processing (S33). If this is the first noise reduction processing (YES in S33), the tensor data restoration device 3 performs correction processing by TGV utilizing image smoothness as the first noise reduction processing (S35). Thereafter, the tensor data restoration device 3 determines whether or not to end the processing (S37). If it is determined not to end the processing (NO in S37), the tensor data restoration device 3 passes the tensor data after the first noise reduction processing to the redundancy update unit 21, and performs processing to update the tensor redundancy (S32).

[0054] If the noise mitigation process is not the first noise mitigation process (NO in S33), the tensor data restoration device 3 determines whether to switch to the second noise mitigation process (S34). If it is determined not to switch to the second noise mitigation process (NO in S34), the tensor data restoration device 3 performs the first noise mitigation process (S35). If it is determined to switch to the second noise mitigation process (YES in S34), the tensor data restoration device 3 performs the second noise mitigation process using BM3D (S36).

[0055] After performing the second noise mitigation process, the tensor data restoration device 3 determines whether or not to terminate the process (S37). The termination determination is performed as described in the above-described embodiment. If this termination determination determines that the process should not be terminated (NO in S37), the tensor data restoration device 3 passes the tensor data after the second noise mitigation process to the redundancy update unit 21 and performs redundancy updating (S32). Then, the tensor data restoration device 3 performs noise mitigation processing on the tensor data for which the redundancy has been updated in the same manner as described above (S34 to S37).

[0056] In determining whether to terminate the processing after performing the second noise mitigation processing (S36), if it is determined that the processing is to be terminated (YES in S37), the tensor data restoration device 3 outputs the noise-mitigated tensor data (S38).

[0057] The above has described the tensor data restoration device 3 of the third embodiment. Similar to the tensor data restoration device 1 of the first embodiment, the tensor data restoration device 3 of the third embodiment has the effect of being able to appropriately mitigate noise and missing values ​​in tensor data while suppressing calculation costs.

[0058] The processing by the redundancy update unit 21 has the effect of mitigating noise in addition to improving the restoration accuracy of tensor data, and noise that could not be completely removed by the redundancy update unit 21 can be mitigated by the noise mitigation processing unit 22. The tensor data restoration device 3 of the third embodiment can perform more accurate noise mitigation by repeatedly performing redundancy update and noise mitigation.

[0059] Here, we will show a calculation example and a comparative example using the tensor data restoration device 3 of the third embodiment. The data used for the calculation is the CAVE dataset (https: / / www.cs.columbia.edu / CAVE / databases / multispectral / ) provided by Columbia University in 2008. Accuracy was evaluated using input that assumed that a 250 x 250 pixel image cut out of sponge in the CAVE dataset was added with noise and captured with the same filter as the snapshot spectroscopic image. The following table shows the results of evaluating the discrepancy between the true value and the calculation result using three indices: RSE (Relative Squared Error), PSNR (Peak Signal to Noise Ratio) [dB], and SSIM (Structural SIMilarity). [Table 1]

[0060] As can be seen from these experimental results, when the first noise mitigation process and the second noise mitigation process are relayed as in this embodiment, the accuracy of restoration is good in all three indices.In addition, the calculation time was 2 minutes when using only TGV and 17 minutes when using only BM3D, while it was 5 minutes with the method of this embodiment, a reduction of about three times.

[0061] Although the tensor data restoration device of the present invention has been described in detail above by way of an embodiment, the present invention is not limited to the above embodiment. 5 is a diagram showing the configuration of a tensor data restoration device 4 according to a modified example. The tensor data restoration device 4 according to the modified example has a threshold setting unit 13 for setting a threshold for determining whether to switch from the first noise mitigation processing 23 to the second noise mitigation processing 24. This configuration allows the user to set an appropriate threshold depending on the tensor data to be processed.

[0062] The user may also decide to switch from the first noise mitigation process 23 to the second noise mitigation process 24. Specifically, tensor data may be displayed during the processing of the first noise mitigation process 23, and the user may input the timing of switching by looking at the displayed tensor data.

[0063] In the above embodiment, a configuration including a missing element designation unit 20 that designates missing values ​​has been described, but the missing element designation unit 20 is optional and may not be required depending on the tensor data to be processed. Furthermore, the redundancy update unit 21 is also optional and may not be required depending on the tensor data to be processed. In the second embodiment, if the redundancy update unit 21 is not provided, when it is determined not to terminate the processing in the determination of whether or not the processing has terminated (NO in S26), the process returns to the first noise mitigation processing (S23). [Explanation of symbols]

[0064] 1~4 Tensor data recovery device 10 Input section 11 Arithmetic section 12 Output section 13 Threshold setting section 20 Missing element specification section 21 Redundancy update section 22 Noise reduction processing section 23 First noise reduction process 24 Second noise reduction process 25 Switching process

Claims

1. an input unit for inputting multidimensional tensor data; a redundancy update unit that updates the input tensor data so as to reduce redundancy of the tensor data; a noise mitigation processing unit that mitigates loss and noise in the tensor data updated by the redundancy update unit; an output unit that outputs tensor data in which loss and noise have been alleviated; Equipped with The noise reduction processing unit a first noise mitigation process for performing noise mitigation on the tensor data using smoothness; a second noise reduction process for reducing noise in the tensor data using local similarity; a switching process for switching from the first noise mitigation process to the second noise mitigation process; A tensor data restoration device comprising:

2. The tensor data restoration device according to claim 1 , wherein the switching process switches from the first noise mitigation process to the second noise mitigation process when a degree of noise mitigation by the first noise mitigation process becomes equal to or greater than a predetermined threshold.

3. The tensor data restoration device according to claim 1, wherein the tensor data noise-reduced by the noise mitigation processing unit is input again to the redundancy update unit, and the redundancy update processing by the redundancy update unit and the noise mitigation processing by the noise mitigation processing unit are repeated until a predetermined termination condition is satisfied.

4. The tensor data restoration device according to claim 1 , further comprising a missing element designation unit that designates an element having missing data in input tensor data.

5. A method for mitigating loss and noise in multi-dimensional tensor data by a tensor data restoration device, comprising: inputting multidimensional tensor data into the tensor data reconstruction device; a step of updating the tensor data by the tensor data restoration device so that redundancy of the input tensor data is reduced; a first noise reduction processing step in which the tensor data restoration device performs noise reduction processing on the tensor data updated in the tensor data updating step by utilizing smoothness; a step of determining whether to switch from the first noise mitigation processing step to a second noise mitigation processing step by the tensor data restoration device; a second noise reduction step in which the tensor data restoration device performs noise reduction processing on the tensor data by utilizing local similarity; a step in which the tensor data restoration device outputs tensor data in which loss and noise have been alleviated; A tensor data restoration method comprising:

6. 1. A program for mitigating loss and noise in multidimensional tensor data, comprising: inputting multi-dimensional tensor data; updating the tensor data so that redundancy of the input tensor data is reduced; a first noise mitigation processing step of performing noise mitigation processing on the tensor data updated in the tensor data updating step by utilizing smoothness; determining whether to switch from the first noise mitigation processing step to the second noise mitigation processing step; a second noise reduction step of reducing noise in the tensor data using local similarity; outputting the tensor data with the defects and noise mitigated; A program that executes the following.

Images