Information processing apparatus, method, and program

Abstract

To prevent a reduction in signal intensity at a peak to remove noise included in observation data.SOLUTION: An information processing apparatus resolves an optimization problem for optimizing an objective function including a loss function and a regularization item to estimate signal data that is spatial data or time-series data of a signal included in observation data. The information processing apparatus includes an operation unit that updates an estimated value of the signal included in the observation data so as to optimize the objective function, and a convergence determination unit that causes the operation unit to repeat the update until a predetermined convergence determination condition is satisfied. In the update in the operation unit, the regularization item is determined to correct the estimated value of the signal after the update according to the size of the signal data that is the spatial data or the time-series data of the signal and whether the value of a normalized signal is close to 1.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to an information processing device, method, and program. [Background technology]

[0002] Conventionally, adding an L1 regularization term to an optimization problem has yielded a solution in which many variables are 0. For example, a technique for clearly estimating signals in noise removal is known (Patent Document 1). In Patent Document 1, the positions and activities of cells in observed data are determined by solving an optimization problem of an objective function that includes an L1 regularization term. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent Publication No. 2017-192313 Summary of the Invention [Problem to be solved by the invention]

[0004] In situations where a time series containing noise is observed, removing noise from the observed data and extracting the signal is an important technique in various fields. For example, using LASSO with an L1 regularization term added to error minimization assumes a signal that occurs infrequently (a sparse signal), enabling more effective noise removal than simple error minimization. However, the signal estimated by the regularization term is underestimated compared to the original signal. Furthermore, it requires the appropriate coefficient to be set according to the signal-to-noise ratio, making it difficult to simultaneously process signals with different signal-to-noise ratios. This is because L1 regularization has a structure in which a penalty is imposed in proportion to the signal strength.

[0005] The present invention has been made in consideration of the above circumstances, and aims to provide an information processing device, method, and program that can suppress a decrease in signal strength at peaks and remove noise contained in observation data. [Means for solving the problem]

[0006] In order to achieve the above object, an information processing device according to the present invention is an information processing device that estimates signal data, which is spatial data or time-series data of a signal included in observation data, by solving an optimization problem that optimizes an objective function including a loss function and a regularization term, and includes: a calculation unit that updates an estimate of the signal included in the observation data so as to optimize the objective function; and a convergence determination unit that causes the calculation unit to repeat updating until a predetermined convergence determination condition is satisfied, wherein the regularization term is determined so that, in the updating by the calculation unit, the updated estimate of the signal is corrected depending on the magnitude of the signal data, which is spatial data or time-series data of the signal, and whether the value of the normalized signal is close to 1.

[0007] An information processing method according to the present invention is an information processing method for estimating signal data, which is spatial data or time-series data of signals included in observation data, by solving an optimization problem that optimizes an objective function including a loss function and a regularization term, the method including causing a computer to update estimates of signals included in the observation data so as to optimize the objective function, and repeatedly updating the estimates of signals included in the observation data until a predetermined convergence determination condition is satisfied, wherein the regularization term is defined so that, in updating the estimates of signals included in the observation data, the updated estimates of signals are corrected depending on the magnitude of the signal data, which is spatial data or time-series data of the signals, and whether the value of the normalized signal is close to 1.

[0008] A program according to the present invention is a program for estimating signal data, which is spatial data or time-series data of signals included in observation data, by solving an optimization problem that optimizes an objective function including a loss function and a regularization term. The program causes a computer to update estimates of the signals included in the observation data so as to optimize the objective function, and to repeatedly update the estimates of the signals included in the observation data until a predetermined convergence determination condition is satisfied. In updating the estimates of the signals included in the observation data, the regularization term is defined so that the updated estimates of the signals are corrected depending on the magnitude of the signal data, which is spatial data or time-series data of the signals, and whether the value of the normalized signal is close to 1. [Effects of the Invention]

[0009] As described above, the information processing device, method, and program of the present invention have the effect of suppressing a decrease in signal intensity at peaks and removing noise contained in observation data. [Brief explanation of the drawings]

[0010] [Figure 1] 1 is a block diagram illustrating an information processing device according to an embodiment of the present invention. [Figure 2] 1 is a functional block diagram illustrating an information processing device according to an embodiment of the present invention. [Figure 3] 4 is a flowchart showing the contents of an estimation processing routine of the information processing device according to the embodiment of the present invention. [Figure 4] 10 is a graph showing experimental results. [Figure 5](A) Graph showing the observation and estimated signal with noise added to the original signal when the objective function does not include a regularization term. (B) Graph showing the observation and estimated signal with noise added to the original signal when LASSO is used. (C) Graph showing the observation and estimated signal with noise added to the original signal when group LASSO is used. (D) Graph showing the observation and estimated signal with noise added to the original signal when the objective function includes the regularization term L1 ∞. (E) Graph showing the observation and estimated signal with noise added to the original signal when the objective function includes the regularization term L1 p,q. DETAILED DESCRIPTION OF THE INVENTION

[0011] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

[0012] <Outline of the embodiment of the present invention> We will explain typical situations for noise removal, the regularization term, and the proximal operator, and then explain the details of the method of the embodiment of the present invention. Here, we will introduce an example where the signal is non-negative, but this can be easily extended to the case of real numbers. In the following, we will use the following notation.

[0013] JPEG2025166587000002.jpg20164 (1)

[0014] (Typical scenario) A sparse signal time series s, where signals occur with a Bernoulli distribution with probability α t Assume ≧0.

[0015] JPEG2025166587000003.jpg19111 (2)

[0016] Signal s at time t t and response function wφ τ The convolution of σ 2 The observed signal is added with normal noise.

[0017] JPEG2025166587000004.jpg20144 (3)

[0018] Here, w represents the signal strength.

[0019] At this time, ws t Estimate of x t Given that, the model gives x t and φ τ Convolution of y t and observations t The basic idea is to minimize the loss function f(x), which represents the squared error of

[0020] JPEG2025166587000005.jpg22164 (4)

[0021] A natural extension to this minimization problem of f(x) is to take advantage of the sparsity of the signal and introduce a regularization term g(x) into the objective function as shown in the following equation.

[0022] JPEG2025166587000006.jpg22122 (5)

[0023] To assess the quality of the estimated signal, we use the true signal s t The estimated signal x t Coefficient of determination R 2 We will use the following.

[0024] JPEG2025166587000007.jpg27164 (6)

[0025] (Proximal operator) For simplicity, the following notation is based on the condition that the signal to be estimated is non-negative, but it can be easily extended to all real numbers.

[0026] Consider an iterative solution method using a proximal operator for the optimization problem Eq (equation (5)) that includes a regularization term. The proximal operator for the regularization term g(x) is defined as follows:

[0027] JPEG2025166587000008.jpg19124 (7)

[0028] By setting an appropriate learning coefficient γ, the estimate of x will converge by the next iteration using the following proximal operator:

[0029] JPEG2025166587000009.jpg22117 (8)

[0030] (LASSO) A typical regularization term is the L1 regularization term, and an optimization problem that includes the L1 regularization term is called LASSO.

[0031] JPEG2025166587000010.jpg1255 (9) JPEG2025166587000011.jpg1479 (10)

[0032] Here, η is a predetermined coefficient representing the strength of the regularization term.

[0033] (Group LASSO) Similarly, group LASSO, which takes into account the sparsity of groups, is also well known.

[0034] JPEG2025166587000012.jpg1242 (11) JPEG2025166587000013.jpg2182 (12)

[0035] (Proposed regularization term) In terms of proximal operators, LASSO corresponds to penalizing all observations with the same strength, while group LASSO considers the overall strength of the signal and attenuates it by a certain ratio. In noise removal, it is desirable to remove noise components while preserving the signal.

[0036] First, we use the L1 regularization term L1 p Introduce.

[0037] JPEG2025166587000014.jpg2249 (13)

[0038] This proximal operator is

[0039] JPEG2025166587000015.jpg22109 (14)

[0040] This is similar to the structure of LASSO and group LASSO, but the relative signal strength σ p (y + ) t When is close to 1, no penalty is applied. In other words, the structure is such that the penalty is applied only to the noise part.

[0041] To emphasize this structure, we introduce a proximal operator with parameter q and a corresponding regularization term L1 p,q is used.

[0042] JPEG2025166587000016.jpg22129 (15) JPEG2025166587000017.jpg2291 (16) JPEG2025166587000018.jpg15164 (17)

[0043] where 2F1[ , , , ] is a hypergeometric function.

[0044] The proximal operator according to the method described in this embodiment can be generalized as follows, using a norm that calculates the overall signal strength and a scale function that converts the entire signal into a range from 0 to 1 while maintaining the relative strength relationship:

[0045] JPEG2025166587000019.jpg25143 (18)

[0046] The regularization term at this time can be calculated as follows:

[0047] JPEG2025166587000020.jpg23130 (19)

[0048] However, the regularization term itself is not necessary for the iteration of optimization, and is only used as reference information for convergence, so it is not necessarily necessary to obtain an analytical formula.

[0049] <System configuration> As shown in FIG. 1, an information processing device 10 according to an embodiment of the present invention includes a CPU 12, a ROM 14, a RAM 16, a HDD 18, a communication interface 20, and a bus 22 for interconnecting these components.

[0050] The CPU 12 executes various programs. The ROM 14 stores various programs, parameters, etc. The RAM 16 is used as a work area when the CPU 12 executes the various programs. The HDD 18, which serves as a recording medium, stores various programs and data, including a program for executing an estimation processing routine, which will be described later.

[0051] The information processing device 10 according to this embodiment estimates signal data, which is spatial data or time-series data of signals included in observed data, by solving an optimization problem that optimizes an objective function including a loss function and a regularization term.

[0052] As shown in FIG. 2, the information processing device 10 according to this embodiment functionally comprises a data reading unit 30, an initial setting unit 32, a calculation unit 34, a convergence determination unit 36, and an output unit 42.

[0053] The data reading unit 30 reads observation data. The observation data is spatial data or time-series data of signals, and includes noise. For example, the data read in is time-series data representing changes in the average calcium concentration in a region of interest (ROI) representing a cell shape, obtained from video data obtained by observing, with a two-photon microscope, light emitted from a fluorescent protein due to an increase in the calcium concentration in the cell when an action potential is generated at a certain time t.

[0054] The initial setting unit 32 initializes signal data included in the observation data. The signal data included in the observation data is, for example, data obtained by removing noise from time-series data representing changes in the average calcium concentration in a ROI representing a cell shape.

[0055] The calculation unit 34 updates the estimated values ​​of the signals included in the observed data so as to optimize an objective function including a loss function and a regularization term.

[0056] Here, in the updating in the calculation unit 34, a regularization term is defined so that the estimated value of the signal after updating is corrected depending on the magnitude of the signal data, which is the spatial data or time series data of the signal, and whether the value of the normalized signal is close to 1.

[0057] Specifically, the regularization term is determined so as to correct the updated signal using a fraction whose denominator is a value representing the magnitude of the signal data and whose numerator is a value corresponding to the difference between 1 and the normalized signal value. More specifically, the value representing the magnitude of the signal data is the p-norm (p is an integer equal to or greater than 2), and the value corresponding to the difference between 1 and the normalized signal is the difference between 1 and the normalized signal value raised to the qth power (q is an integer equal to or greater than 1).

[0058] For example, in updating in the calculation unit 34, the regularization term is determined as in equation (16) so as to correct the updated signal y using the proximal operator expressed in equation (15) above. The calculation unit 34 updates the signal estimate value according to equation (8) above using the proximal operator expressed in equation (15) above.

[0059] The convergence determination unit 36 ​​repeats the update in the calculation unit 34 until a predetermined convergence determination condition is met. The convergence determination condition can be that a predetermined upper limit of the number of iterations has been reached, or that the change in the objective function shown in the above equation (5) is equal to or less than a threshold. The upper limit of the number of iterations and the threshold value can be determined empirically.

[0060] The output unit 42 outputs the final estimation result of the signal data obtained.

[0061] <Operation of information processing device> Next, the operation of the information processing device 10 according to this embodiment will be described.

[0062] First, when observation data is input to the information processing device 10, the information processing device 10 executes an estimation processing routine shown in FIG.

[0063] In step S100, the data reading unit 30 reads the observation data.

[0064] Next, in step S102, the initial setting unit 32 initializes the signal data included in the observation data.

[0065] Next, in step S104, the calculation unit 34 obtains signal data by updating the estimated value of each signal according to the above equation (8) using the proximal operator expressed by the above equation (15).

[0066] Next, in step S106, the convergence determination unit 36 ​​determines whether or not the process has converged. For example, if the change in the objective function shown in the above equation (5) is equal to or less than a threshold, the convergence determination unit 36 ​​determines whether or not the process has converged. In step S108, the output unit 42 outputs the signal data estimation result, and the process ends. If it is determined in step S106 that the process has not converged, the process returns to step S104.

[0067] When the above process is repeated and convergence is reached, signal data from which noise contained in the observation data has been removed is obtained, and the output unit 42 can output these values ​​as the noise removal results.

[0068] <Experimental Example> In order to evaluate the method described in the above embodiment, we used R 2 The actual waveform was evaluated as follows. τ A double exponential function was set to , and five signals were placed in a time series of length 1000, with a signal-to-noise ratio of 5. LASSO, group LASSO, L1 ∞ , L1 p,q For each, the parameters that maximized the average value of R2 were adopted and evaluated (see Figure 4). With LASSO (L1), as the coefficients were increased, the signal quickly became undetectable, and it was difficult to adjust to improve the state without regularization terms. The parameters adopted were η = 0.000006 for LASSO, η = 0.05 for group LASSO, and L1 ∞ Then η=0.003, L1 p,q In this case, p = 3, q ​​= 150, and η = 0.028. It can be seen that the method described in the above embodiment has higher accuracy than LASSO and group LASSO.

[0069] Next, we will look at the specific estimated signals (see Figure 5). Here, we compare the R 2 This shows an example where L1 was the lowest. With LASSO, there is almost no difference from simple optimization. With group LASSO, the noise component is attenuated, but the signal peak is estimated lower than the original signal. ∞ Although the noise component is even less than in group LASSO, there is still a reduction in signal intensity at the peaks. p,q In this case, the noise is almost completely removed, and the signal intensity at the peak is close to that of the original signal.

[0070] As described above, according to an information processing device according to an embodiment of the present invention, signal data, which is spatial data or time-series data of a signal included in observation data, is estimated by solving an optimization problem that optimizes an objective function including a loss function and a regularization term. When updating an estimate of a signal included in the observation data to optimize the objective function, the regularization term is determined so that the updated estimate of the signal is corrected depending on the magnitude of the signal data, which is spatial data or time-series data of the signal, and whether the normalized signal value is close to 1. This makes it possible to suppress a decrease in signal intensity at peaks and remove noise included in the observation data.

[0071] Furthermore, it is possible to define a regularization term that imposes a penalty according to the frequency of the signal rather than the signal strength, thereby eliminating noise while preventing attenuation of the signal portion.

[0072] The present invention is not limited to the above-described embodiment, and various modifications and applications are possible without departing from the spirit and scope of the present invention.

[0073] The program of the present invention may be provided in a form stored on a storage medium. [Explanation of symbols]

[0074] 10. Information processing equipment 12 CPU 14 ROM 16 RAM 18 HDD 30 Data reading section 32 Initial setting section 34 Arithmetic section 36 Convergence judgment section 42 Output section

Claims

1. An information processing device that estimates signal data, which is spatial data or time-series data of signals included in observation data, by solving an optimization problem that optimizes an objective function including a loss function and a regularization term, a calculation unit that updates an estimated value of a signal included in the observation data so as to optimize the objective function; a convergence determination unit that repeats updating in the calculation unit until a predetermined convergence determination condition is satisfied; Including, In the updating in the calculation unit, the regularization term is determined so that the estimated value of the signal after updating is corrected depending on the magnitude of the signal data, which is spatial data or time series data of the signal, and whether the value of the normalized signal is close to 1. Information processing device.

2. 2. The information processing device according to claim 1, wherein the regularization term is determined so as to correct the updated signal using a fraction having a value representing the magnitude of the signal data as a denominator and a value corresponding to the difference between 1 and the value of the normalized signal as a numerator.

3. the value representing the magnitude of the signal data is a p-norm, 3. The information processing apparatus according to claim 2, wherein the value corresponding to the difference between 1 and the value of the normalized signal is a value obtained by raising the difference between 1 and the value of the normalized signal to the qth power.

4. In the updating in the calculation unit, the regularization term L is calculated so as to correct the updated signal y using a approximate operator expressed by the following equation: １ ｐ，ｑ 4. The information processing apparatus according to claim 3, wherein: where η is a predetermined coefficient, ２ F １ [ , , , ] is a hypergeometric function.

5. In the updating in the calculation unit, the regularization term L is calculated so as to correct the updated signal y using a approximate operator expressed by the following equation: １ ＊，ｑ 4. The information processing apparatus according to claim 3, wherein: where η is a predetermined coefficient, norm is a function that calculates the intensity of the entire signal, scale is a function that converts the entire signal into a range from 0 to 1 while maintaining the relative intensity relationship, and scale( ) ｔ indicates the value at time t.

6. An information processing method for estimating signal data, which is spatial data or time-series data of signals included in observation data, by solving an optimization problem that optimizes an objective function including a loss function and a regularization term, comprising: The computer updating estimates of signals included in the observed data so as to optimize the objective function; The estimated value of the signal included in the observation data is repeatedly updated until a predetermined convergence determination condition is satisfied. This includes: The regularization term is determined so that, in updating the estimated value of the signal included in the observation data, the estimated value of the signal after updating is corrected depending on the magnitude of the signal data, which is spatial data or time series data of the signal, and whether the value of the normalized signal is close to 1. Information processing methods.

7. A program for estimating signal data, which is spatial data or time series data of signals included in observation data, by solving an optimization problem that optimizes an objective function including a loss function and a regularization term, updating estimates of signals included in the observed data so as to optimize the objective function; The estimated value of the signal included in the observation data is repeatedly updated until a predetermined convergence determination condition is satisfied. It is a program that makes a computer execute The regularization term is determined so that, in updating the estimated value of the signal included in the observation data, the estimated value of the signal after updating is corrected depending on the magnitude of the signal data, which is spatial data or time series data of the signal, and whether the value of the normalized signal is close to 1. program.

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