Data processing apparatus and data processing method

Abstract

To improve image quality.SOLUTION: A data processing device according to an embodiment comprises a processing unit having a complex neural network with an activation function whose gain changes according to a complex argument.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The embodiments disclosed in this specification and the drawings relate to a data processing apparatus and a data processing method.

Background Art

[0002] In machine learning using neural networks, real-valued neural networks are typically used.

[0003] However, in medical data processing apparatuses such as magnetic resonance imaging apparatuses and ultrasonic diagnostic apparatuses, signal processing using complex numbers is often used. Therefore, various applications are expected by using complex number neural networks.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] One of the problems to be solved by the embodiments disclosed in this specification and the drawings is to improve image quality. However, the problems to be solved by the embodiments disclosed in this specification and the drawings are not limited to the above problems. The problems corresponding to the respective effects of each configuration shown in the embodiments described later can also be regarded as other problems.

Means for Solving the Problems

[0006] The data processing apparatus according to the embodiment includes a processing unit having a complex number neural network provided with an activation function whose gain changes according to a complex argument.

Brief Description of the Drawings

[0007]

Figure 1

Figure 2

Figure 3

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Figure 7

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Figure 9

DETAILED DESCRIPTION OF THE INVENTION

[0008] (Embodiment) Hereinafter, embodiments of a data processing apparatus and a data processing method will be described in detail with reference to the drawings.

[0009] First, the configuration of a data processing apparatus 100 according to an embodiment will be described with reference to FIG. 1.

[0010] The data processing apparatus 100 is an apparatus that generates data using machine learning. As an example, the data processing apparatus 100 executes processing of analysis signal data obtained by converting a real signal into a complex number using orthogonality, generation of a learned model, execution of the learned model, and the like.

[0011] The data processing apparatus 100 includes a processing circuit 110, a memory 132, an input device 134, and a display 135. The processing circuit 110 includes a training data creation function 110a, a learning function 110b, an interface function 110c, a control function 110d, an application function 110e, and an acquisition function 110f.

[0012] In the embodiment, each processing function and the learned model (for example, a neural network) performed by the training data creation function 110a, the learning function 110b, the interface function 110c, the control function 110d, the application function 110e, and the acquisition function 110f are stored in the memory 132 in the form of a program executable by a computer. The processing circuit 110 is a processor that reads out and executes the program from the memory 132 to realize the function corresponding to each program. In other words, the processing circuit 110 in the state of having read out each program has each function shown in the processing circuit 110 of FIG. 1. Further, the processing circuit 110 in the state of having read out the program corresponding to the learned model (neural network) can perform processing according to the learned model. In FIG. 1, the function of the processing circuit 110 is described as being realized by a single processing circuit, but it may be configured that the processing circuit 110 is constituted by combining a plurality of independent processors, and each processor realizes the function by executing a program. In other words, each of the above-described functions may be configured as a program, and even when one processing circuit executes each program. Also, two or more of the functions of the processing circuit 110 may be realized by a single processing circuit. As another example, a specific function may be implemented in a dedicated independent program execution circuit.

[0013] In FIG. 1, the processing circuit 110, the training data creation function 110a, the learning function 110b, the interface function 110c, the control function 110d, the application function 110e, and the acquisition function 110f are each an example of a processing unit, a creation unit, an input unit (learning unit), a reception unit, a control unit, an application unit, and an acquisition unit.

[0014] As used in the above description, the term "processor" means, for example, a CPU (Central Processing Unit), a GPU (Graphical Processing Unit), or a circuit such as an application specific integrated circuit (ASIC), a programmable logic device (for example, a simple programmable logic device (SPLD), a complex programmable logic device (CPLD), and a field programmable gate array (FPGA)). The processor realizes its functions by reading and executing the programs stored in the memory 132.

[0015] Alternatively, instead of storing the program in the memory 132, the program may be directly incorporated into the circuit of the processor. In this case, the processor realizes its functions by reading and executing the program incorporated in the circuit. Therefore, for example, instead of storing the learned model in the memory 132, the program related to the learned model may be directly incorporated into the circuit of the processor.

[0016] The processing circuit 110 generates training data for learning based on the data, signals, and images acquired by the interface function 110c by the training data generation function 110a.

[0017] The processing circuit 110 performs learning using the training data generated by the training data creation function 110a by the learning function 110b, and generates a learned model.

[0018] The processing circuit 110 acquires data, signals, images, etc. for signal generation by the application function 110e from the memory 132 by the interface function 110c.

[0019] The processing circuit 110 controls the overall processing of the data processing apparatus 100 by the control function 110d. Specifically, the processing circuit 110 controls the processing of the processing circuit 110 based on various setting requests input from the operator via the input device 134, and various control programs and various data read from the memory 132 by the control function 110d.

[0020] Also, the processing circuit 110 generates a signal based on the result of the processing performed using the training data generation function 110a and the learning function 110b by the application function 110e. Further, the processing circuit 110 applies the learned model generated by the learning function 110b to the input signal and generates a signal based on the application result of the learned model.

[0021] The memory 132 is composed of a semiconductor memory element such as a RAM (Random Access Memory), a flash memory, a hard disk, an optical disk, etc. The memory 132 is a memory that stores data such as signal data for display and signal data for training generated by the processing circuit 110.

[0022] The memory 132 stores various data such as a control program for performing signal processing and display processing as necessary.

[0023] The input device 134 receives various instructions and information inputs from the operator. The input device 134 is, for example, a pointing device such as a mouse or a trackball, a selection device such as a mode switch, or an input device such as a keyboard.

[0024] The display 135 receives an input of imaging conditions through a GUI (Graphical User Interface) under the control of the control function 110d or the like, and displays signals generated by the control function 110d or the like. The display 135 is, for example, a display device such as a liquid crystal display. The display 135 is an example of a display unit. The display 135 has a mouse, a keyboard, buttons, a panel switch, a touch command screen, a foot switch, a trackball, a joystick, and the like.

[0025] Subsequently, with reference to FIGS. 2 to 4, the configuration of the neural network according to the embodiment will be described.

[0026] FIG. 2 shows an example of the inter-layer interconnection in the neural network 7 used for machine learning by the processing circuit 110 having the learning function 110b. The neural network 7 includes an input layer 1, an output layer 2, and intermediate layers 3, 4, 5, etc. between the input layer 1 and the output layer 2. Each intermediate layer is composed of a layer related to each input (hereinafter referred to as the input layer in each layer), a linear layer, and a layer related to processing using an activation function (hereinafter referred to as the activation layer). For example, the intermediate layer 3 is composed of an input layer 3a, a linear layer 3b, and an activation layer 3c, the intermediate layer 4 is composed of an input layer 4a, a linear layer 4b, and an activation layer 4c, and the intermediate layer 5 is composed of an input layer 5a, a linear layer 5b, and an activation layer 5c. Also, each layer is composed of a plurality of nodes (neurons).

[0027] Here, the data processing apparatus 100 according to the embodiment applies a linear layer with complex coefficients and a non-linear activation (activation function) to medical data having complex values. That is, the processing circuit 110 generates a learned model by training the neural network 7 that applies a linear layer with complex coefficients and a non-linear activation (activation function) to medical data having complex values by the learning function 110b. The processing circuit 100 stores the generated learned model in, for example, the memory 132 as necessary.

[0028] Note that the data input to the input layer 1 is, for example, complex number data obtained by discretely sampling an electrical signal using quadrature detection.

[0029] Also, the data output from the output layer 2 is, for example, complex number data from which noise has been removed.

[0030] Note that when the neural network 7 according to the embodiment is, for example, a convolutional neural network (CNN), the data input to the input layer 1 is data represented by a two-dimensional array such as size 32×32, for example, and the data output from the output layer 2 is data represented by a two-dimensional array such as size 32×32, for example. The size of the data input to the input layer 1 and the size of the data output from the output layer 2 may be the same or different. Similarly, the number of nodes in the intermediate layer may be the same as or different from the number of nodes in the layers before and after it.

[0031] Subsequently, generation of the learned model according to the embodiment, that is, the learning step, will be described. The processing circuit 110 generates a learned model by performing, for example, machine learning on the neural network 7 by means of the learning function 110b. Here, performing machine learning means, for example, determining the weighting in the neural network 7 composed of the input layer 1, the intermediate layers 3, 4, 5, and the output layer 2. Specifically, it means determining a set of coefficients characterizing the connection between the input layer 1 and the intermediate layer 3, a set of coefficients characterizing the connection between the intermediate layer 3 and the intermediate layer 4,..., and a set of coefficients characterizing the connection between the intermediate layer 5 and the output layer 2. The processing circuit 150 determines these sets of coefficients by means of the learning function 110b, for example, by the backpropagation method.

[0032] The processing circuit 110 performs machine learning based on training data, which is teacher data composed of the data input to the input layer 1 and the data output to the output layer 12, by means of the learning function 110b, determines the weighting between the layers, and generates a learned model in which the weighting has been determined.

[0033] In deep learning, an autoencoder can be used. In this case, the data required for machine learning does not have to be supervised data.

[0034] Next, the process when applying the learned model according to the embodiment will be described. First, the processing circuit 110 inputs, for example, an input signal to the learned model by the application function 110e. For example, the processing circuit 110 inputs the input signal to the input layer 1 of the neural network 7, which is the learned model, by the application function 110e. Subsequently, the processing circuit 110 acquires, as an output signal, the data output from the output layer 2 of the neural network 7, which is the learned model, by the application function 110e. The output signal is a signal subjected to a predetermined process such as noise removal. In this way, the processing circuit 150 generates an output signal subjected to a predetermined process such as noise removal by the application function 150e. If necessary, the processing circuit 150 may cause the obtained output signal to be displayed on the display 135 by the control function 110d.

[0035] Returning to the description of the activation function and the activation layer, the activation function in the neural network 7 will be described with reference to FIG. 3. In FIG. 3, nodes 10a, 10b, 10c, and 10d are shown by cutting out a part of the nodes of the input layer in a certain layer. On the other hand, node 11 is one of the nodes of the linear layer, and node 12 is one of the nodes of the activation layer, which is a layer related to the process (activation) using the activation function.

[0036] Here, considering the case where the output values of nodes 10a, 10b, 10c, and 10d are complex numbers z1, z 2、 z 3、 z4 respectively, the output result to node 11 in the linear layer is Σ i=1 m (ω i z i +b). Here, ω iLet \(w_{i}\) be the weight coefficient between the \(i\)-th input layer and node 11, \(m\) be the number of nodes connected to node 11, and \(b\) be a predetermined constant. Subsequently, assuming the output result output to node 12, which is the activation layer, is \(y\), \(y\) is expressed as in the following formula (1) using the activation function \(A\).

[0037]

Number

[0038] Here, the activation function \(A\) is usually a non-linear function. For example, the sigmoid function, tanh function, ReLU (Rectified Linear Unit), etc. are selected as the activation function \(A\).

[0039] Figure 4 shows the processing using such an activation function. In Figure 4, the intermediate layer 5 is the \(n\)-th layer of the neural network 7, and consists of an input layer 5a, a linear layer 5b, and an activation layer 5c. The input layer 6a is the \((n + 1)\)-th layer of the neural network. Also, the input layer 5a has nodes 20a, 20b, 20c, 20d, etc., the linear layer 5b has nodes 21a, 21b, 21c, 21d, etc., and the linear layer 5c has nodes 22a, 22b, 22c, etc. Also, Figure 4 is a real-valued neural network where each node has a real value, and the input result \(z\) to the input layer 5a n,i and the output result \(z\) of the input layer 6a n+1、i are complex numbers.

[0040] Here, by performing a predetermined weighted addition for each node in the input layer 5a, the output result to the linear layer 5b is calculated. For example, the output result to the \(j\)-th node 21b in the linear layer 5b is \(\sum\) i=1 m \(\omega\) i,j \(z\) n,i \(+ b\) n,j given by. Here, \(\omega\) i,j is the weight coefficient between the \(i\)-th input layer and the \(j\)-th linear layer, \(b\) n,jis a predetermined constant known as a bias term. Subsequently, by applying the activation function A to each node of the linear layer 5b, the output result to the activation layer 5c is calculated. For example, the output to the j-th node 22b in the activation layer 5c is given by An,j(Σi=1mωi,jzn,i+bn,j) using the activation function An,j, as represented by the following equation (2).

[0041]

Number

[0042] Subsequently, based on the values output by the nodes of the activation layer 5c, the values of the nodes of the input layer 6a of the n-th layer are determined. As an example, the values of the nodes of the activation layer 5c are input as they are to the nodes of the input layer 6a. Also, as another example, a further non-linear function may be applied to the activation layer 5c to determine the nodes of the input layer 6a.

[0043] Subsequently, the background related to the embodiment will be described.

[0044] In machine learning using neural networks, real-valued neural networks are often used. However, in the field of signal processing, for example, in order to uniformly handle two components such as AC signal intensity and time, a complex number representation may be used. In such a case, various applications are expected by using a complex number neural network instead of a real number neural network.

[0045] Here, as a method for handling complex numbers in a neural network, for example, there is a method of handling complex numbers in a neural network by dividing a complex number into a real part and an imaginary part and considering each as a node of a standard real-valued neural network. As an example, a method of handling complex numbers in a neural network can be considered by using a CReL activation function that applies ReLU to each of the real part and the imaginary part of a complex number as an activation function.

[0046] Also, as another example, there is a method of handling complex numbers in a neural network by expressing complex numbers using absolute value (or signed absolute value) and phase, and considering each as a node of a standard real-number neural network.

[0047] However, in the method of simply extending ReLu, which has been conventionally used in real-number neural networks, to complex numbers, since the activation function has a dependency on complex numbers, the image quality may not easily improve even with learning. For example, in the method of simply dividing a complex number into a real part and an imaginary part and applying ReLU to each, the rotational symmetry around the origin that the complex number originally had is broken, and data with a complex argument in the 0-degree direction and 90-degree direction is treated specially compared to other directions. As a result, artifacts may occur. Regarding this point, although the accuracy of the learned model can be improved by increasing the amount of training data, in the method of fixing the complex argument in one specific direction and decomposing the complex number into specific direction components, the learning efficiency with respect to the data volume may not be good.

[0048] The data processing apparatus 100 according to the embodiment is in view of such a background, and the data processing apparatus 100 according to the embodiment has a processing unit having a complex-number neural network equipped with a complex-sensitive activation function (CPSAF: Complex Sensitive Activation Function) that is an activation function whose gain changes according to the complex argument. Specifically, the activation function A used to calculate the output results to the activation layers 3c, 4c, 5c of the neural network 7, which is a complex-number neural network included in the processing circuit 110, is a complex-sensitive activation function whose gain changes according to the complex argument. By using, for example, a plurality of these complex-sensitive activation functions, it is possible to prevent the activation function from being biased toward a specific direction component, and as a result, the quality of the output signal can be improved.

[0049] Here, as a specific example of the above-described complex-sensitive activation function (CPSFA), for example The function A1 given by the following formula (3) can be mentioned.

[0050] [Number]

[0051] Here, z represents a complex number, phase(z) represents the complex argument of the complex number z, and α and β represent real parameters. The gain control function W β (x) is a function defined on the real number x. For example, it is a function that extracts an angle near x = 0 by a method characterized by the parameter β. Hereinafter, for example, the gain control function W β (x) will be explained by an example of a function that has a maximum value at x = 0 and whose value decreases as it moves away from x = 0. Since angles that differ by a constant multiple of 2π can be regarded as the same, for example, the gain control function W β can be selected as a periodic function with a period of 2π, and W β (x + 2nπ) = W β (x) holds.

[0052] In such a case, the activation function A1(z) is obtained by multiplying the complex number z by the gain control function W β (phase(z) - α). Therefore, the activation function A1(z) can obtain a large gain (signal value) when the complex argument of z is close to α to a certain extent, and the magnitude of the gain is controlled by the parameter β. Therefore, the activation function A1 represented by formula (3) αβ can be considered as a function represented by the product of a gain control function that extracts a signal component in a predetermined angular direction and the input complex number, and is an example of an activation function sensitive to the complex argument.

[0053] As another example of an activation function sensitive to the complex argument, the activation function A2(z) given by the following formula (4) can be mentioned.

[0054] [Number]

[0055] Here, the activation function A2(z) is a special case where, in Equation (3), the gain control function W β (x) is given by the following Equation (5).

[0056]

Equation

[0057] Here, the wrap function on the right side of Equation (5) is given by the following Equation (6), where n is a natural number.

[0058]

Equation

[0059] That is, the gain control function W β (x) is a function that returns 1 if the angle x is within the range of β with respect to 0, and 0 otherwise. That is, the activation function A2 αβ (z) is a function that extracts the complex number region within the range of angle β from the angle α direction. In other words, the activation function A2 αβ (z) represented by Equation (4) can be considered as a function that extracts the signal components within the range from a predetermined angle α to a predetermined angle β, and is an example of an activation function sensitive to the complex argument.

[0060] Note that the gain control function W β is not limited to the form shown in Equation (5) in the embodiment, and may be, for example, in the form shown by the following Equation (7) or Equation (8).

[0061]

Equation

[0062] Here, in Equation (7), a small value such as ε = 0.1 or ε = 0.01 is set as ε. This Equation (7) is an example of a function that realizes a function similar to LeakyReLU for complex inputs.

[0063] [Number]

[0064] Also, in Equation (8), ε has a meaning similar to the minimum output value for negative inputs in ELU, and for example, ε = 1 is adopted. Equation (8) is an example of a function that realizes a function similar to ELU for complex inputs.

[0065] Also, as another example of an activation function sensitive to the complex argument, activation functions A3(z) to A5(z) given by the following Equations (9) to (11) can be cited.

[0066] [Number]

[0067] [Number]

[0068] [Number]

[0069] Here, the activation function A3 given by Equation (9) αβ (z) is obtained by rotating the activation function A1 αβ (z) by an angle α in the clockwise direction and then taking the real part, and then rotating it by an angle α in the direction opposite to the previous rotation operation. That is, the activation function A3 αβ (z) is a function corresponding to an operation including a rotation operation around the origin, an operation of taking the real part of a complex number, and a rotation operation in the direction opposite to the rotation operation.

[0070] Also, the activation function A4 given by Equation (10) αβ (z) is obtained by adding to the activation function A3 αβ (z) the result of rotating the complex number z by an angle α in the clockwise direction, then taking the imaginary part, and then rotating it by an angle α in the direction opposite to the previous rotation operation.

[0071] Also, in Equation (11), A legacy is a standard activation function that returns a real value for a given real value. Examples of A legacy include, for example, the sigmoid function, soft sign function, softplus function, tanh function, ReLU, clipped power function, polynomial, radial basis function, wavelet, and the like. The activation function A αβ (z) given by Equation (11) is basically the same function as the activation function A αβ (z), but additionally includes an operation of taking the real part and then applying the activation function A legacy defined as a real number.

[0072] Note that the activation function A β expressed using the gain control function W αβ can also be written in an expression form using the gain function G β as shown in Equation (12) below. Here, the function G β is given by Equation (13) below. Here, γ = cosβ.

[0073]

Equation

[0074]

Equation

[0075] Note that here, the gain function G β corresponding to the gain control function W β in the form of Equation (5) has been described. However, for the gain control function W β in the forms of Equation (7) and Equation (8), the corresponding gain function G β can also be constructed in the same way.

[0076] Regarding the relationship between the activation functions described so far and the activation function of Complex ReLU, for a complex number z, the activation function of Complex ReLu is given by ReLu(Re(z)) + iReLU(Im(z)). The activation function A1 sensitive to the complex argument according to the embodiment αβ ~A5 αβ and Complex ReLU without a rotation operation have different ways of approaching the problem, but the activation function A1 sensitive to the complex argument according to the embodiment αβ ~A5 αβ includes processing similar to Complex ReLU (for example, α = π / 4, β = π / 4). Depending on the selection method of the gain control function, it is considered possible to perform processing equivalent to Complex ReLU.

[0077] In addition, when the processing circuit 110 according to the embodiment performs machine learning using the neural network 7 that uses an activation function whose gain changes according to the complex argument, the activation function may be applied while changing the parameters included in the activation function. Specifically, for example, considering the case of using the activation function A1 shown in Equation (3) αβ when using, the processing circuit 110, by the learning function 110b, while changing the angles α and β which are the parameters included in the activation function A1 αβ applies the activation function A1 αβ to the neural network 7 and may perform machine learning.

[0078] This case will be described with reference to FIGS. 5 and 6. Here, FIG. 5 is a diagram regarding the case of performing learning while changing the parameters included in the activation function for different nodes. On the other hand, FIG. 6 is a diagram for explaining the case of performing learning while changing the parameters included in the activation function for the same node, that is, while applying a plurality of activation functions to one node.

[0079] In FIG. 5, the processing circuit 110 performs machine learning by applying, using the learning function 110b, an activation function whose gain changes according to the complex argument while changing the parameters included in the activation function for different nodes, to the neural network 7. As an example, when A1 αβ is selected as the activation function, the processing circuit 110 uses the learning function 110b to change the angle α or β, which is a parameter included in the activation function A1 αβ , for different nodes, and applies the activation function 23 to the neural network 7 to perform machine learning.

[0080] For example, in the example of FIG. 5, the processing circuit 110 uses the learning function 110b to apply, to node 21a, the activation function 23 obtained by setting α = 0 degrees in the activation function A1 αβ to obtain the output result to node 22a in the activation layer 5c. Also, the processing circuit 110 uses the learning function 110b to apply, to node 21b, the activation function 23 obtained by setting α = 120 degrees in the activation function A1 αβ to obtain the output result to node 22b in the activation layer 5c. Also, the processing circuit 110 uses the learning function 110b to apply, to node 21c, the activation function 23 obtained by setting α = 240 degrees in the activation function A1 αβ to obtain the output result to node 22c in the activation layer 5c.

[0081] In the above example, for each node, the parameters included in the applied activation function A1 αβ are different, being α = 0 degrees, 120 degrees, and 240 degrees. Therefore, in the complex neural network, the directions of the activation functions can be dispersed, and the adverse effects caused by the activation functions depending on a specific angular direction can be reduced.

[0082] Next, some examples of how to select the parameters α and β in the activation function are given. For example, the processing circuit 110 may use the learning function 110b to fix β = π / 4 and use four types of angles α = {π / 4, 3π / 4, 5π / 4, 7π / 4} as the parameters of the activation function that changes, and apply the activation function to perform learning. Also, for example, the processing circuit 110 may use the learning function 110b to fix β = π / 3 and use three types of angles α = {π / 3, π, 5π / 3} as the parameters of the activation function that changes, and apply the activation function to perform learning. Also, as another example, the processing circuit 110 may use the learning function 110b to fix α = 0 and use three types of angles β = {π / 4, π / 3, π / 2} as the parameters of the activation function that changes, and apply the activation function to perform learning. Also, when the parameters α and β are not changed, the processing circuit 110 may perform learning with, for example, α = π / 3 and β = π / 3 by the learning function 110b.

[0083] Also, the processing circuit 110 may, by the learning function 110b, change the quantity corresponding to the angle that is a parameter included in the activation function while making it an integer multiple of the first angle that is a value obtained by dividing 360 degrees or 180 degrees by the golden ratio, and apply the activation function. Thereby, the activation function can have approximately the same value in any direction in the angular direction, the values can be dispersed, and artifacts and the like can be reduced. Also, by setting the number of nodes in each layer of the complex neural network to a Fibonacci value, the values of the activation function can be further dispersed in any direction, and artifacts and the like can be reduced.

[0084] In the example of FIG. 5, the case where the activation function is applied while changing the parameters related to the activation function for different nodes has been described, but the embodiment is not limited to this. The processing circuit 110 may perform learning by applying the activation function while changing the parameters related to the activation function for the same node by the learning function 110b. In other words, the processing circuit 110 may apply a plurality of activation functions to a plurality of nodes.

[0085] Such an example is shown in FIG. 6. The processing circuit 110 may perform learning by the learning function 110b by applying an activation function while changing the parameters related to the activation function for the same node.

[0086] Similar to FIG. 5, when the activation function is A1 represented by Equation (3) αβ it will be described. The processing circuit 110 uses the learning function 110b to apply, to the node 21a, the activation function A1 αβ with α = 60 degrees as the activation function 23a1 to the node 21a to obtain the output result to the node 22a1 of the activation layer 5c, and the activation function A1 αβ with α = 240 degrees as the activation function 23a2 to the node 21a to obtain the output result to the node 22a2 of the activation layer 5c. The processing circuit 110 uses the learning function 110b to apply, to the node 21b, the activation function A1 αβ with α = 60 degrees as the activation function 23b1 to the node 21b to obtain the output result to the node 22b1 of the activation layer 5c, and the activation function A1 αβ with α = 240 degrees as the activation function 23b2 to the node 21b to obtain the output result to the node 22b2 of the activation layer 5c. The processing circuit 110 uses the learning function 110b to apply, to the node 21c, the activation function A1 αβ with α = 60 degrees as the activation function 23c1 to the node 21c to obtain the output result to the node 22c1 of the activation layer 5c, and the activation function A1 αβ with α = 240 degrees as the activation function 23c2 to the node 21c to obtain the output result to the node 22c2 of the activation layer 5c.

[0087] As can be seen from the above description, in such an embodiment, a complex activation function is applied to the nodes of one linear layer and the output results are multiplexed. Thereby, the values of the activation function can be dispersed in the complex argument direction, and the image quality can be improved.

[0088] Also, as another example, the processing circuit 110 may apply the activation function while changing the parameters related to the activation function layer by layer of the neural network 7 by the learning function 110b. As an example, taking the golden angle as GA, the processing circuit 110, by the learning function 110b, in the first layer of the neural network 7, for the activation function A1 αβ in which those with α = GA, α = 2*GA, and α = 3*GA respectively are applied, and in the second layer of the neural network 7, for the activation function A1 αβ in which those with α = 4*GA, α = 5*GA, and α = 6*GA respectively are applied may be used. Here, as the parameter α of the activation function, through each layer of the neural network 7, the same angle may not appear twice, that is, all angles can be made different. Thereby, the value of the activation function can be further dispersed in the complex argument direction.

[0089] Also, for example, in the above embodiment, the angle of the parameter α is not limited to the golden angle. For example, taking θ as a certain angle, the processing circuit 110, by the learning function 110b, in the first layer of the neural network 7, for the activation function A1 αβ in which those with α = θ + rand(1), α = 2*θ + rand(1), and α = 3*θ + rand(1) respectively are applied, and in the second layer of the neural network 7, for the activation function A1 αβ in which those with α = 4*θ + rand(2), α = 5*θ + rand(2), and α = 6*θ + rand(2) respectively are applied may be used. Here, rand(i) is a random number determined for each i, and is a random number that takes a fixed value for each layer of the neural network.

[0090] Also, the embodiment is not limited thereto, and the processing circuit 110 may include a calculation unit (not shown in FIG. 1) that optimizes the parameters related to the activation function, and perform learning using the activation function based on the parameters optimized by the calculation unit by the learning function 110b to generate a learned model. An example of such processing is shown in FIG. 7.

[0091] As shown in FIG. 7, the processing circuit 110 includes a first neural network 7 that is a neural network for outputting an output signal / output data with respect to an input signal / input data, and a second neural network 8 for adjusting an activation function in the first neural network 7. The second neural network 8 is an example of the calculation unit described above. The second neural network 8 is connected to the activation layers 3c, 4c, and 5c of the first neural network 7 and controls the parameters of the activation function in the activation layer.

[0092] Similar to the above, when the activation function A1 αβ is used, the value of the parameter α of the activation function A1 αβ in the activation layers 3c, 4c, and 5c of the first neural network 7 is determined as α = α i + α init . Here, α init is the initial value of the parameter α, and α i is the correction value of the parameter α in the i-th layer and has a constant value for each layer. The value of α i is optimized by learning by the calculation unit.

[0093] As an example, the processing circuit 110 may alternately repeat and execute a first learning that is learning of the weight coefficients in the first neural network 7 executed by the learning function 110b, and a second learning that is learning of the values of the parameters of the activation function of the first neural network 7 executed by the calculation unit.

[0094] Also, as another example, after the processing circuit 110 executes a second learning that is learning of the values of the parameters of the activation function of the first neural network 7 executed by the calculation unit, the processing circuit 110 may perform a first learning that is learning of the weight coefficients in the first neural network 7 executed by the learning function 110b using the values of the parameters.

[0095] Further, the processing circuit 110 may execute the first learning and the second learning simultaneously.

[0096] Note that the configuration of the calculation unit is not limited to a neural network. For example, optimization of the parameter values of the activation function of the first neural network 7 may be performed using linear regression.

[0097] Also, as the above-described embodiment, the case where the correction value of the common parameter α is used for each layer and each node has been described. However, the embodiment is not limited to this, and the correction value of the common parameter α may be a common parameter for each layer, or may be different parameters for each layer and each node.

[0098] As an example using the data processing apparatus 100, a medical signal processing apparatus incorporating the data processing apparatus 100 according to the embodiment will be described with reference to FIGS. 8 and 9. The following description does not limit the use of the data processing apparatus 100 to a medical signal processing apparatus.

[0099] That is, the data processing apparatus 100 is connected to various medical image diagnostic apparatuses such as, for example, the magnetic resonance imaging apparatus shown in FIG. 8 and the ultrasonic diagnostic apparatus shown in FIG. 9, and processes signals received from the medical image diagnostic apparatuses, generates a learned model, executes the learned model, and the like. Note that examples of the medical image diagnostic apparatus to which the data processing apparatus 100 is connected are not limited to the magnetic resonance imaging apparatus and the ultrasonic diagnostic apparatus, and other apparatuses such as an X-ray CT apparatus and a PET apparatus may also be used. As an example, the data processing apparatus 100 may be an apparatus that processes magnetic resonance data that is not medical data.

[0100] Note that when the processing circuit 110 is incorporated in various medical image diagnostic apparatuses, or when processing is performed in cooperation with various medical image diagnostic apparatuses, it may have a function of executing related processes together.

[0101] FIG. 8 is an example of a magnetic resonance imaging apparatus 200 incorporating the data processing apparatus 100 according to the embodiment.

[0102] As shown in FIG. 8, the magnetic resonance imaging apparatus 200 includes a static magnetic field magnet 201, a static magnetic field power supply (not shown), a gradient magnetic field coil 203, a gradient magnetic field power supply 204, a bed 205, a bed control circuit 206, a transmission coil 207, a transmission circuit 208, a reception coil 209, a reception circuit 210, a sequence control circuit 220 (sequence control unit), and the data processing apparatus 100 described in FIG. 1. Note that the magnetic resonance imaging apparatus 200 does not include a subject P (for example, a human body). Also, the configuration shown in FIG. 8 is merely an example.

[0103] The static magnetic field magnet 201 is a magnet formed in a hollow substantially cylindrical shape and generates a static magnetic field in the internal space. The static magnetic field magnet 201 is, for example, a superconducting magnet or the like and is excited by receiving current supply from a static magnetic field power supply. The static magnetic field power supply supplies current to the static magnetic field magnet 201. As another example, the static magnetic field magnet 201 may be a permanent magnet, and in this case, the magnetic resonance imaging apparatus 200 may not include a static magnetic field power supply. Also, the static magnetic field power supply may be provided separately from the magnetic resonance imaging apparatus 100.

[0104] The gradient magnetic field coil 203 is a coil formed in a hollow substantially cylindrical shape and is disposed inside the static magnetic field magnet 201. The gradient magnetic field coil 203 is formed by combining three coils corresponding to the X, Y, and Z axes orthogonal to each other, and these three coils receive current supply individually from the gradient magnetic field power supply 204 to generate a gradient magnetic field whose magnetic field strength changes along the X, Y, and Z axes. The gradient magnetic fields of the X, Y, and Z axes generated by the gradient magnetic field coil 203 are, for example, a slice gradient magnetic field Gs, a phase encoding gradient magnetic field Ge, and a readout gradient magnetic field Gr. The gradient magnetic field power supply 204 supplies current to the gradient magnetic field coil 203.

[0105] The examination table 205 includes a top plate 205a on which the subject P is placed. Under the control of the examination table control circuit 206, the top plate 205a is inserted into the cavity (imaging opening) of the gradient magnetic field coil 203 with the subject P placed thereon. Usually, the examination table 205 is installed such that its longitudinal direction is parallel to the central axis of the static magnetic field magnet 201. The examination table control circuit 206 drives the examination table 205 under the control of the data collection device 100 to move the top plate 205a in the longitudinal direction and the vertical direction.

[0106] The transmission coil 207 is disposed inside the gradient magnetic field coil 203 and generates a high-frequency magnetic field upon receiving an RF pulse from the transmission circuit 208. The transmission circuit 208 supplies an RF pulse corresponding to the Larmor frequency determined by the type of the target atom and the magnetic field strength to the transmission coil 207.

[0107] The reception coil 209 is disposed inside the gradient magnetic field coil 203 and receives a magnetic resonance signal (hereinafter, referred to as "MR signal" as necessary) emitted from the subject P due to the influence of the high-frequency magnetic field. When the reception coil 209 receives the magnetic resonance signal, it outputs the received magnetic resonance signal to the reception circuit 210.

[0108] Note that the above-described transmission coil 207 and reception coil 209 are merely examples. It may be configured by combining one or more of a coil having only a transmission function, a coil having only a reception function, or a coil having a transmission and reception function.

[0109] The reception circuit 210 detects the magnetic resonance signal output from the reception coil 209 and generates magnetic resonance data based on the detected magnetic resonance signal. Specifically, the reception circuit 210 generates magnetic resonance data by digitally converting the magnetic resonance signal output from the reception coil 209. Further, the reception circuit 210 transmits the generated magnetic resonance data to the sequence control circuit 220. Note that the reception circuit 210 may be provided on the gantry device side including the static magnetic field magnet 201, the gradient magnetic field coil 203, etc.

[0110] The sequence control circuit 220 performs imaging of the subject P by driving the gradient magnetic field power supply 204, the transmission circuit 208, and the reception circuit 210 based on sequence information. Here, the sequence information is information that defines the procedure for performing imaging. In the sequence information, the strength of the current supplied by the gradient magnetic field power supply 204 to the gradient magnetic field coil 203, the timing of supplying the current, the strength of the RF pulse supplied by the transmission circuit 208 to the transmission coil 207, the timing of applying the RF pulse, the timing at which the reception circuit 210 detects the magnetic resonance signal, etc. are defined. For example, the sequence control circuit 220 is an integrated circuit such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array), or an electronic circuit such as a CPU (Central Processing Unit) or an MPU (Micro Processing Unit). The sequence control circuit 220 is an example of a scan unit.

[0111] Furthermore, when the sequence control circuit 220 drives the gradient magnetic field power supply 204, the transmission circuit 208, and the reception circuit 210 to image the subject P and receives magnetic resonance data from the reception circuit 210, the sequence control circuit 220 transfers the received magnetic resonance data to the data processing device 100. The data processing device 100 performs overall control of the magnetic resonance imaging device 200 in addition to the processing described in FIG. 1.

[0112] Returning to FIG. 1, regarding the processing performed by the data processing device 100, which is processing other than the processing described in FIG. 1, the processing circuit 110 transmits sequence information to the sequence control circuit 220 and receives magnetic resonance data from the sequence control circuit 220 through the interface function 110c. Also, when receiving the magnetic resonance data, the processing circuit 110 having the interface function 110c stores the received magnetic resonance data in the memory 132.

[0113] The magnetic resonance data stored in the memory 132 is arranged in the k-space by the control function 110d. As a result, the memory 132 stores k-space data.

[0114] The memory 132 stores magnetic resonance data received by the processing circuit 110 having the interface function 110c, k-space data arranged in the k-space by the processing circuit 110 having the control function 110d, image data generated by the processing circuit 110 having the generation function (or application function 110e), and the like.

[0115] The processing circuit 110 performs overall control of the magnetic resonance imaging apparatus 200 by the control function 110d, and controls imaging, image generation, image display, and the like. For example, the processing circuit 110 having the control function 110d receives input of imaging conditions (imaging parameters, etc.) on the GUI, and generates sequence information according to the received imaging conditions. Further, the processing circuit 200 having the control function 110d transmits the generated sequence information to the sequence control circuit 220.

[0116] The processing circuit 110 reads out k-space data from the memory 132 by a generation function (or application function 110e) not shown in FIG. 1, and performs reconstruction processing such as Fourier transform on the read k-space data to generate a magnetic resonance image.

[0117] FIG. 9 is a configuration example of an ultrasonic diagnostic apparatus 300 incorporating the data processing apparatus 100 according to the embodiment. The ultrasonic diagnostic apparatus according to the embodiment includes an ultrasonic probe 305 and an ultrasonic diagnostic apparatus main body 300. The ultrasonic diagnostic apparatus main body 300 includes a transmission circuit 309, a reception circuit 311, and the above-described data processing apparatus 100.

[0118] The ultrasonic probe 305 has a plurality of piezoelectric vibrators, and these piezoelectric vibrators generate ultrasonic waves based on a drive signal supplied from a transmission circuit 309 included in an ultrasonic diagnostic apparatus main body 300 described later. Further, the plurality of piezoelectric vibrators included in the ultrasonic probe 305 receive a reflected wave from the subject P and convert it into an electrical signal (reflected wave signal). The ultrasonic probe 305 also has a matching layer provided on the piezoelectric vibrator and a backing material or the like that prevents the propagation of ultrasonic waves backward from the piezoelectric vibrator. Note that the ultrasonic probe 305 is detachably connected to the ultrasonic diagnostic apparatus main body 300. The ultrasonic probe 305 is an example of a scan unit.

[0119] When ultrasonic waves are transmitted from the ultrasonic probe 305 to the subject P, the transmitted ultrasonic waves are successively reflected at the discontinuous surfaces of the acoustic impedance in the body tissues of the subject P, received by the plurality of piezoelectric vibrators included in the ultrasonic probe 305 as reflected waves, and converted into reflected wave signals. The amplitude of the reflected wave signal depends on the difference in acoustic impedance at the discontinuous surface where the ultrasonic waves are reflected. When the transmitted ultrasonic pulse is reflected at the surface of a moving blood flow or a heart wall, etc., the reflected wave signal undergoes a frequency shift depending on the velocity component of the moving object with respect to the ultrasonic transmission direction due to the Doppler effect.

[0120] The ultrasonic diagnostic apparatus main body 300 is an apparatus that generates ultrasonic image data based on the reflected wave signal received from the ultrasonic probe 305. The ultrasonic diagnostic apparatus main body 300 is an apparatus capable of generating two-dimensional ultrasonic image data based on a two-dimensional reflected wave signal and three-dimensional ultrasonic image data based on a three-dimensional reflected wave signal. However, the embodiment is applicable even when the ultrasonic diagnostic apparatus 10 is an apparatus dedicated to two-dimensional data.

[0121] As illustrated in FIG. 9, the ultrasonic diagnostic apparatus 10 includes a transmission circuit 309, a reception circuit 311, and a medical image processing apparatus 100.

[0122] The transmission circuit 309 and the reception circuit 311 control the ultrasonic transmission and reception performed by the ultrasonic probe 305 based on the instructions of the data processing device 110 having a control function. The transmission circuit 309 includes a pulse generator, a transmission delay unit, a pulsar, etc., and supplies a drive signal to the ultrasonic probe 305. The pulse generator repeatedly generates rate pulses for forming transmitted ultrasonic waves at a predetermined pulse repetition frequency (PRF: Pulse Repetition Frequency). Further, the transmission delay unit gives the delay time for each piezoelectric vibrator necessary for focusing the ultrasonic waves generated from the ultrasonic probe 305 into a beam shape and determining the transmission directivity to each rate pulse generated by the pulse generator. Also, the pulsar applies a drive signal (drive pulse) to the ultrasonic probe 305 at the timing based on the rate pulse.

[0123] That is, the transmission delay unit arbitrarily adjusts the transmission direction of the ultrasonic waves transmitted from the piezoelectric vibrator surface by changing the delay time given to each rate pulse. Also, the transmission delay unit controls the position of the focusing point (transmission focus) in the depth direction of ultrasonic wave transmission by changing the delay time given to each rate pulse.

[0124] In addition, the receiving circuit 311 includes an amplifier circuit, an A / D (Analog / Digital) converter, a reception delay circuit, an adder, a quadrature detection circuit, etc., and performs various processes on the reflected wave signal received from the ultrasonic probe 305 to generate a reception signal (reflected wave data). The amplifier circuit amplifies the reflected wave signal for each channel and performs gain correction processing. The A / D converter performs A / D conversion on the gain-corrected reflected wave signal. The reception delay circuit gives the reception delay time necessary for determining the reception directivity to the digital data. The adder performs an addition process on the reflected wave signals to which the reception delay time has been given by the reception delay circuit. By the addition process of the adder, the reflection component from the direction corresponding to the reception directivity of the reflected wave signal is emphasized. Then, the quadrature detection circuit converts the output signal of the adder into an in-phase signal (I signal, I: In-phase) and a quadrature signal (Q signal, Q: Quadrature-phase) in the baseband band. Then, the quadrature detection circuit transmits the I signal and the Q signal (hereinafter referred to as IQ signals) to the processing circuit 110 as reception signals (reflected wave data). Note that the quadrature detection circuit may convert the output signal of the adder into an RF (Radio Frequency) signal and then transmit it to the processing circuit 110. The IQ signals and the RF signal are reception signals having phase information.

[0125] When scanning a two-dimensional region in the subject P, the transmission circuit 309 causes the ultrasonic probe 305 to transmit an ultrasonic beam for scanning the two-dimensional region. Then, the receiving circuit 311 generates a two-dimensional reception signal from the two-dimensional reflected wave signal received from the ultrasonic probe 305. Also, when scanning a three-dimensional region in the subject P, the transmission circuit 309 causes the ultrasonic probe 305 to transmit an ultrasonic beam for scanning the three-dimensional region. Then, the receiving circuit 311 generates a three-dimensional reception signal from the three-dimensional reflected wave signal received from the ultrasonic probe 305. The receiving circuit 311 generates a reception signal based on the reflected wave signal and transmits the generated reception signal to the processing circuit 110.

[0126] The transmission circuit 309 causes the ultrasonic probe 305 to transmit an ultrasonic beam from a predetermined transmission position (transmission scanning line). The reception circuit 311 receives, from the ultrasonic probe 305, a signal due to the reflected wave of the ultrasonic beam transmitted by the transmission circuit 309 at a predetermined reception position (reception scanning line). When parallel simultaneous reception is not performed, the transmission scanning line and the reception scanning line are the same scanning line. On the other hand, when parallel simultaneous reception is performed, when the transmission circuit 309 causes the ultrasonic probe 305 to transmit one ultrasonic beam on one transmission scanning line, the reception circuit 311 simultaneously receives, as a plurality of reception beams, signals due to the reflected waves derived from the ultrasonic beam transmitted by the transmission circuit 309 to the ultrasonic probe 1, through the ultrasonic probe 305 at a plurality of predetermined reception positions (reception scanning lines).

[0127] The data processing device 100 is connected to the transmission circuit 309 and the reception circuit 311, and in addition to the functions already shown in FIG. 1, performs processing of the signal received from the reception circuit 311, control of the transmission circuit 309, generation of a learned model, execution of the learned model, and various image processes. The processing circuit 110 includes a B-mode processing function, a Doppler processing function, a generation function, etc., in addition to the functions already shown in FIG. 1. Hereinafter, returning to FIG. 1, a configuration that the data processing device 100 incorporated in the ultrasonic diagnostic apparatus 10 may have in addition to the configuration already shown in FIG. 1 will be described.

[0128] Each processing function and the learned model performed by the B-mode processing function, the Doppler processing function, and the generation function are stored in the memory 132 in the form of a program executable by a computer. The processing circuit 110 is a processor that reads a program from the memory 132 and executes it to realize the functions corresponding to the respective programs. In other words, the processing circuit 110 in the state of having read each program has these respective functions.

[0129] The B-mode processing function and the Doppler processing function are examples of a B-mode processing unit and a Doppler processing unit.

[0130] The processing circuit 110 performs various signal processes on the reception signal received from the reception circuit 311.

[0131] The processing circuit 110 receives data from the receiving circuit 311 by means of the B-mode processing function, performs logarithmic amplification processing, envelope detection processing, logarithmic compression processing, etc., and generates data (B-mode data) in which the signal intensity is expressed by the brightness of luminance (Brightness).

[0132] Also, the processing circuit 110 frequency-analyzes velocity information from the received signal (reflected wave data) received from the receiving circuit 311 by means of the Doppler processing function, and generates data (Doppler data) in which moving object information such as velocity, variance, and power due to the Doppler effect is extracted for multiple points.

[0133] Note that in the B-mode processing function and the Doppler processing function, processing can be performed on both two-dimensional reflected wave data and three-dimensional reflected wave data.

[0134] Also, the processing circuit 110 controls the entire processing of the ultrasonic diagnostic apparatus by means of the control function 110d. Specifically, the processing circuit 110 controls the processing of the transmission circuit 309, the receiving circuit 311, and the processing circuit 110 based on various setting requests input from the operator via the input device 134 and various control programs and various data read from the memory 132 by means of the control function 110d. Also, the processing circuit 110 controls the display of the ultrasonic image data for display stored in the memory 132 on the display 135 by means of the control function 110d.

[0135] Also, the processing circuit 110 generates ultrasonic image data from the data generated by the B-mode processing function and the Doppler processing function by means of a generating function (not shown). The processing circuit 110 generates two-dimensional B-mode image data in which the intensity of the reflected wave is represented by luminance from the two-dimensional B-mode data generated by the B-mode processing function by means of the generating function. Also, the processing circuit 110 generates two-dimensional Doppler image data representing moving object information from the two-dimensional Doppler data generated by the Doppler processing function 110b by means of the generating function. The two-dimensional Doppler image data is velocity image data, variance image data, power image data, or image data combining these.

[0136] Further, the processing circuit 110 converts (scan-converts) the scan line signal sequence of the ultrasonic scan into a scan line signal sequence in a video format typified by a television or the like by a generation function, and generates ultrasonic image data for display. Further, by the generation function, the processing circuit 110 performs various image processes other than scan conversion, for example, an image process (smoothing process) of regenerating an average value image of luminance using a plurality of image frames after scan conversion, an image process (edge enhancement process) using a differential filter within the image, and the like. Further, the processing circuit 110 performs various rendering processes on the volume data in order to generate two-dimensional image data for displaying the volume data on the display 135 by the generation function.

[0137] The memory 132 can also store the data generated in the B-mode processing function and the Doppler processing function. The B-mode data and Doppler data stored in the memory 132 can be called by an operator, for example, after diagnosis, and become ultrasonic image data for display via the processing circuit 110. Further, the memory 132 can also store the reception signal (reflected wave data) output by the reception circuit 311.

[0138] In addition, the memory 132 stores a control program for performing ultrasonic transmission / reception, image processing, and display processing as necessary, diagnostic information (for example, patient ID, doctor's findings, etc.), diagnostic protocols, and various data such as various body marks.

[0139] Returning to FIG. 2, in FIG. 2, the data input to the input layer 1 may be a medical image or medical image data acquired from a medical image diagnostic apparatus. When the medical image diagnostic apparatus is the magnetic resonance imaging apparatus 200, the data input to the input layer 1 is, for example, a magnetic resonance image. Further, when the medical image diagnostic apparatus is, for example, the ultrasonic diagnostic apparatus 300, the data input to the input layer 1 is, for example, an ultrasonic image.

[0140] In addition, the input data input to the input layer 1 may be a medical image, or may be various image data, projection data, intermediate data, or raw data at the stage before the medical image is generated. For example, when the medical image diagnostic apparatus is a PET apparatus, the input data input to the input layer 10 may be a PET image, or may be various data before the reconstruction of the PET image, such as time series data of coincidence coefficient information.

[0141] In addition, the data output from the output layer 2 is a medical image or medical image data, and similar to the data input to the input layer 1, it may also be various projection data, intermediate data, or raw data at the stage before the medical image is generated. When the purpose of the neural network 7 is noise processing, the data output from the output layer 2 is, for example, an image with noise removed and high image quality compared to the input image.

[0142] According to at least one of the embodiments described above, the image quality can be improved.

[0143] Regarding the above embodiments, the following appendices are disclosed as one aspect and selective features of the invention.

[0144] (Appendix 1) A magnetic resonance imaging apparatus provided in one aspect of the present invention has a data processing apparatus having a processing unit having a complex neural network equipped with an activation function whose gain changes according to a complex argument.

[0145] (Appendix 2) An ultrasonic diagnostic apparatus provided in one aspect of the present invention has a data processing apparatus having a processing unit having a complex neural network equipped with an activation function whose gain changes according to a complex argument.

[0146] Although several embodiments have been described, these embodiments are presented by way of example and are not intended to limit the scope of the invention. These embodiments can be implemented in various other forms, and various omissions, replacements, changes, and combinations of the embodiments can be made without departing from the gist of the invention. These embodiments and their modifications are included in the scope and gist of the invention, as well as in the invention described in the claims and the equivalent scope thereof.

Explanation of Reference Numerals

[0147] 110 Processing circuit 132 Memory 134 Input device 135 Display

Claims

1. A processing unit having a complex neural network with an activation function whose gain changes according to a complex argument, The activation function is a data processing device that is a function represented by the product of a gain control function that extracts a signal component in a predetermined angular direction and a complex number input.

2. The activation function is a function that extracts the signal component in a predetermined angular range from the predetermined angular direction, and the data processing device according to claim 1.

3. A processing unit having a complex neural network with an activation function whose gain changes according to a complex argument, The activation function is a data processing device that is a function corresponding to an operation including a rotation operation around the origin, an operation of taking the real part of a complex number, and a rotation operation in the opposite direction to the rotation operation.

4. The processing unit applies the activation function while changing a parameter included in the activation function, and the data processing device according to claim 1 or 3.

5. The processing unit applies the activation function while changing the parameter for different nodes, and the data processing device according to claim 4.

6. The processing unit applies the activation function while changing the parameter for the same node, and the data processing device according to claim 4.

7. The processing unit applies the activation function while changing the parameter for each layer of the complex neural network, and the data processing device according to claim 4.

8. The parameter is an amount corresponding to an angle, and the processing unit changes the parameter so as to be an integer multiple of a first angle, and the data processing device according to claim 4.

9. A processing unit having a complex neural network with an activation function whose gain changes according to a complex argument, The processing unit applies the activation function while changing a parameter included in the activation function, The parameter is an amount corresponding to an angle, and the processing unit changes the parameter so as to be an integer multiple of a first angle, The first angle is a value obtained by dividing 360 degrees or 180 degrees by the golden ratio, and the data processing device.

10. The number of nodes in each layer of the complex neural network is a Fibonacci value, and the data processing device according to claim 9.

11. The processing unit, Comprises a calculation unit for optimizing the parameters related to the activation function, The data processing apparatus according to claim 1 or 3, which performs learning using the activation function based on the parameters optimized by the calculation unit to generate a learned model.

12. The data processing apparatus according to claim 1 or 3, wherein the processing unit applies the complex neural network to magnetic resonance data or ultrasonic data.

13. A learned model is generated by a processing circuit using a complex neural network having an activation function whose gain changes according to a complex argument, The activation function is a data processing method that is a function represented by the product of a gain control function that extracts a signal component in a predetermined angular direction and a complex number input.

14. A learned model is generated by a processing circuit using a complex neural network having an activation function whose gain changes according to a complex argument, The activation function is a function corresponding to an operation including a rotation operation around the origin, an operation of taking the real part of a complex number, and a rotation operation in the opposite direction to the rotation operation.

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