Image filter device and program

Abstract

To provide an image filter device that applies filter processing to a classical image compatible with a quantum image so as to reduce the noise caused by the quantum image.SOLUTION: An image filter device 1, 7 applies filter processing to an input image or an output image so as to reduce the noise generated in the output image due to a state of a quantum image, in the case where the input image, which is a classical image, is encoded to form the quantum image and the output image, which is a classical image, is decoded by a result of measuring the quantum image. Encoding to form the quantum image includes basis encoding by associating position information in the classical image with each of multiple bases. The filter processing includes image sharpening by defining neighborhoods of each pixel position on the classical image in basis-encoded state.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to an image filter device and a program for reducing noise caused by quantum images in classical images.

Background Art

[0002] There exists quantum information technology that embeds and utilizes information in qubits (quantum bits). In particular, when image information is embedded, the information is called a quantum image. The technology of embedding information as a quantum image is explained in Non-Patent Document 1 and the like. In this specification, for the sake of comparison with quantum images, an image expressed as digital information (classical bits) of 0 / 1 depending on the presence or absence of conventional magnetism and charge is particularly called a classical image when it is distinguished from a quantum image. Qubits embedded with information can be transmitted over long distances by communicating with existing optical fibers for digital signals. This is called quantum communication.

[0003] Here, it is possible to enjoy the advantages of quantum communication by transmitting an image according to the following flow. Examples of the advantages include eavesdropping resistance due to the no-cloning theorem of quantum and the ability to transmit in parallel with existing optical communication within an optical fiber by dividing wavelength bands, which can contribute to the information and communication industry. For the sake of subsequent explanation, each procedure constituting the following flow is called transmission procedures 1 to 5. 1. The sender has the image information in the state of a classical image. 2. The sender encodes (enciphers) the classical image into a quantum image. 3. In quantum communication, the quantum image is transmitted to the receiver. 4. The receiver decodes (deciphers) the quantum image into a classical image. 5. The receiver views the image information on a display terminal such as a display.

[0004] These transmission procedures 1 to 5 can be realized using the following prior art.

[0005] ●FRQI (Flexible Representation of Quantum Images; Flexible Representation of Quantum Images) The FRQI disclosed in Non-Patent Document 2 etc. is a technique for encoding (encoding) classical image information with the number of pixels on one side being 2 to the power of n into 2n + 1 quantum bits using amplitude and basis, and it is possible to represent a grayscale (classical) image with 256 levels of brightness as quantum bits. Specifically, the encoding of classical image information into the quantum state |Img> by FRQI is represented as shown in Equation (1) described later in "Embodiments for Carrying Out the Invention".

[0006] ●Quantum Gate Machine The FRQI is a technique as an algorithm or agreement for handling image information as a quantum state, while a quantum gate machine prototype (quantum computer) as hardware that actually performs processing in a quantum state according to the agreement is disclosed in Non-Patent Document 3 etc. For example, IBM provides a service for using a quantum computer. A quantum computer can be used not only for applications that handle quantum images, but when used for applications of quantum images, the sender and receiver who execute the transmission procedures 2 and 4 can use the API (Application Programming Interface) of a classical computer provided as a service to program the operation of the quantum computer from the classical computer, thereby enabling encoding and decoding of quantum images in the quantum computer.

[0007] In addition, when particularly distinguishing from a quantum computer that handles quantum bits, a conventional computer that handles 0 / 1 digital information (classical bits) according to the presence or absence of magnetism or charge will be called a classical computer.

Prior Art Documents

Patent Documents

[0008]

Patent Document 1

Patent Document 2

[0009] [Non-Patent Document 1] SU, Jie, et al. A new trend of quantum image representations. IEEE Access, 2020, 8: 214520-214537. [Non-Patent Document 2] LE, Quang Phuc, et al. Flexible representation of quantum images and its computational complexity analysis. In: Proceedings of the 25th Fuzzy Systems Symposium of the Japanese Society for Fuzzy Theory and Intelligent Informatics. The Japanese Society for Fuzzy Theory and Intelligent Informatics, 2009. p. 185-185. [Non-Patent Document 3] SANTOS, Alan C. The IBM quantum computer and the IBM quantum experience. arXiv preprint arXiv:1610.06980, 2016. [Summary of the Invention] [Problems to be Solved by the Invention]

[0010] However, quantum gate machines (quantum computers) have a problem in that they have noise. It is known that noise occurs with a certain probability each time a gate is executed or a quantum state is measured, and this probability is generally provided as public information as part of the specifications when using a quantum computer as a service.

[0011] Due to the presence of this noise, when the transmission procedures 1 to 5 are performed as the conventional technology, the decoded images obtained in the transmission procedures 4 and 5 are regarded as degraded versions of the original image prepared in the transmission procedure 1. As shown in Fig. 8, which shows an example of an original image of size 4x4 (a grayscale image whose luminance value is an integer value within the range of 0 to 255) and a decoded image obtained by applying the conventional technology to this original image, the degradation due to noise is evident. Note that Fig. 8 will be referred to again in "Embodiments of the Invention".

[0012] Here, there are various conventional technologies for removing noise in classical images rather than quantum images. For example, Patent Document 1 relates to the use of machine learning to remove noise in MRI images as an alternative to the task of taking multiple shots and taking the average. Patent Document 2 relates to performing analog-to-digital conversion of classical images that are nonlinearly blocked as a preprocessing step for noise reduction. Patent Document 3 relates to solving the nonlinearity of light-to-electrical conversion using a lookup table. Patent Document 4 relates to tone correction and edge enhancement processing for radiation imaging. Patent Document 5 discloses selecting decoding appropriate to the compression method when performing lossy compression at the sender and edge enhancement at the receiver in order to reduce transmission bandwidth.

[0013] The conventional noise reduction technology for classical images is not a technology that deals with noise specific to quantum images, and therefore cannot deal with noise specific to quantum images. For the same reason, even if the noise reduction technology for classical images could be applied to quantum images, the effect of noise reduction would be insufficient, although it may be possible to see some effect of noise reduction by chance depending on the image.

[0014] In view of the above problems of the prior art, an object of the present invention is to provide an image filter device and a program that apply a filter process for reducing noise caused by a quantum image to a classical image corresponding to the quantum image.

Means for Solving the Problems

[0015] To achieve the above object, the present invention provides an image filter device that applies a filter process for reducing noise generated in an output image due to the state of a quantum image when an input image, which is a classical image, is encoded into the quantum image and then the output image, which is a classical image, is decoded based on the measurement result of the quantum image. Encoding into the quantum image includes basis encoding by associating position information in the classical image with each of a plurality of bases. The first feature is that the filter process includes performing sharpening after defining a neighborhood in the basis-encoded state for each pixel position on the classical image.

[0016] Further, the present invention provides an image filter device that applies a filter process for reducing noise generated in an output image due to the state of a quantum image when an input image, which is a classical image, is encoded into the quantum image and then the output image, which is a classical image, is decoded based on the measurement result of the quantum image. Encoding into the quantum image includes amplitude encoding by associating pixel values in the classical image with the amplitudes of single qubits. The second feature is that the filter process includes saturating, for each pixel value of a target image with at least one of the input image and the output image as the target image for processing, the pixel values corresponding to the upper side and the lower side in the set of pixel values of the target image to the maximum value and the minimum value that can be taken by a pixel value predefined in the classical image. Further, it is characterized in that a computer functions as the image filter device.

Effects of the Invention

[0017] According to the first feature, noise reduction due to base encoding can be performed on classical images. According to the second feature, noise reduction due to amplitude encoding can be performed on classical images.

Brief Description of the Drawings

[0018]

Figure 1

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Figure 8

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Figure 10

Modes for Carrying Out the Invention

[0019] FIG. 1 is a functional block diagram of a quantum image processing system 100 according to an embodiment. The quantum image processing system 100 includes a preprocessing unit 1, an input IF (interface) unit 2, a quantum encoding unit 3, a quantum communication unit 4, a quantum decoding unit 5, an output IF (interface) unit 6, and a postprocessing unit 7.

[0020] Here, the preprocessing unit 1, the input IF (interface) unit 2, the output IF (interface) unit 6, and the postprocessing unit 7 can be realized by a classical computer (a form in which a plurality of classical computers communicate with each other via a network may also be used). The quantum encoding unit 3 and the quantum decoding unit 5 are a type of quantum computer and can be realized by a quantum gate machine disclosed in the aforementioned Non-Patent Document 3 and the like. The quantum communication unit 4 can be realized as communication equipment such as an optical fiber capable of transmitting a quantum state (a quantum image in this embodiment).

[0021] FIG. 2 is a flowchart of the operation of the quantum image processing system 100 according to an embodiment. In step S1, an original image to be processed by the quantum image processing system 100 is prepared manually or the like as a classical image. In step S2, the preprocessing unit 1 applies a filtering process to the original image prepared in step S1. In step S3, for the original image (classical image) filtered in step S2, each of the processing units 2 to 6 from the input IF unit 2 to the output IF unit 6 performs processing in the order of the codes, thereby encoding the original image as a classical image into a quantum image, transmitting the encoded quantum image remotely by quantum communication, and measuring the transmitted quantum image (quantum state) to obtain a decoded image obtained by decoding the original image as a classical image. In step S4, the postprocessing unit 7 applies a filtering process to the decoded image obtained in step S3. In step S5, the classical image obtained in step S4 is obtained as the final output from the quantum image processing system 100, and the flow of FIG. 2 is terminated.

[0022] In the configuration of the above-described quantum image processing system 100, the processing contents of each of the processing units 2 to 6 from the input IF unit 2 that executes step S3 to the output IF unit 6 can be the same as the processing contents of FRQI disclosed in the aforementioned Non-Patent Document 1 and the like. When only applying the prior art FRQI as it is, as described with reference to FIG. 8, due to the fact that the quantum image is processed by a quantum gate machine, the final decoded image is obtained in a form in which the original image deteriorates.

[0023] In this embodiment, by applying a filter process to the original image before being processed as a quantum image by the preprocessing unit 1 that performs a pre-filter process and the postprocessing unit 7 that performs a post-filter process, respectively, and by applying a filter process to the decoded image decoded after being processed as a quantum image, it is possible to reduce noise caused by the quantum image in the state of a classical image.

[0024] Here, the filter processes performed by the preprocessing unit 1 and the postprocessing unit 7 are common, and both the preprocessing unit 1 and the postprocessing unit 7 can be configured as an image filter device 10 whose functional block is shown in FIG. 3. The image filter device 10 includes a first processing unit 11 that applies a filter related to amplitude and a second processing unit 12 that applies a filter related to position. In the image filter device 10, it is possible to perform both the filter processes of the first processing unit 11 and the second processing unit 12, or to perform only one of the filter processes. When applying both filter processes, the application order thereof may be arbitrary.

[0025] Also, in the quantum image processing system 100, the filter processing of both the preprocessing unit 1 and the postprocessing unit 7 (that is, the filter processing of both steps S2 and S4) may be performed, or only the filter processing of either one of them may be performed (that is, either the preprocessing unit 1 or the postprocessing unit 7 (step S2 or S4) is omitted). Whether both the preprocessing unit 1 and the postprocessing unit 7 are used or only one of them is used, the effect of reducing the noise caused by the quantum image can be obtained in the finally obtained decoded image. (Therefore, the configuration in which both the preprocessing unit 1 and the postprocessing unit 7 are omitted from the quantum image processing system 100 corresponds to a configuration in which each processing unit 2 to 6 from the input IF unit 2 to the output IF unit 6 executes the prior art FRQI as it is, and the transmission procedures 1 to 5 are executed as they are, and thus cannot cope with the noise caused by the quantum image.)

[0026] Note that, in reality, there is also noise when performing quantum communication in the quantum communication unit 4. However, the preprocessing unit 1 and the postprocessing unit 7 in the embodiment of the present invention do not cope with the noise of the quantum communication, but cope with the noise in the quantum encoding unit 3 and the quantum decoding unit 5 as quantum gate machines. For this reason, the quantum communication unit 4 may be regarded as performing ideal transmission without noise generation, or by adopting a configuration in which the quantum communication unit 4 is omitted in the quantum image processing system 100, the processing of the quantum encoding unit 3 and the quantum decoding unit 5 may be performed in this order within one quantum gate machine.

[0027] Hereinafter, as a premise for explaining the processing content of the image filter device 10 as common processing in the preprocessing unit 1 and the postprocessing unit 7, each processing from the input IF unit 2 that executes the prior art FRQI to the output IF unit 6 will be outlined.

[0028] FIG. 4 and FIG. 5 are diagrams showing schematic examples of the processing content of the prior art FRQI. In FRQI, a classical image to be processed is quantum-encoded by a quantum encoding unit 3 into a quantum image as a quantum state |Img(θ)> according to the following formula (1), and the quantum decoding unit 5 measures the encoded (and transmitted by the quantum communication unit 4) quantum image, so that a decoded image as a classical image can be obtained from the measurement result according to formula (2). In formulas (1) and (2), the operation symbol with a circle around "×" is a tensor product.

[0029]

Number

[0030] In formula (1), |0> and |1> are two-dimensional quantum basis states, and the luminance information of the position |i> of the classical image is amplitude-encoded (amplitude-coded) in the front 1-qubit "cosθ i |0> + sinθ i |1>" of the qubits that are added as superposition states. (The position |i> is based on the basis encoding described below.) That is, the luminance information of the classical image is embedded in the amplitude part of the front 1-qubit. Specifically, when the luminance value defined in advance in the classical image to be processed is within the range of 0 to 255 (hereinafter, 0 to 255, which is an example of the range defined by the luminance value, is also used as an example for explanation), the luminance y = [0, 255] of the classical image is linearly transformed into the phase θ = [0, π / 2], for example, "θ = (π / 2)*(y / 256)", etc., so that each phase θ i and each luminance y i have a correspondence relationship, and a quantum image corresponding to the classical image can be defined. Note that as long as the correspondence relationship between each phase θ i and each luminance y i can be defined, the conversion method is arbitrary, and a monotonically increasing function such as a sin function may be used in the middle.

[0031] On the other hand, in formula (1), |i> is a 2n-dimensional quantum state of the 2n qubits on the rear side that form qubits added as superposition states, 2 n ×2 nIt is possible to take a superposition state of individual ground states, and when measured, it will be determined as one of the ground states with a predetermined probability in accordance with quantum mechanics. Here, 2 n ×2 n Assuming that each of the 2×2 ground states corresponds to a pixel position in the classical image, position information base encoding can be performed. In the example EX1 of FIG. 4, when n = 1, the four ground states |i> = |00>, |01>, |10>, |11> (for example, when taking the sum of formula (1), i = 0, 1, 2, 3 can be respectively associated) are respectively associated with the positions (0, 0), (0, 1), (1, 0), (1, 1) of a classical image of size 2×2, showing an example of such encoding.

[0032] The quantum encoding unit 3 can realize the encoding of the quantum state |I(θ)> into a quantum image by the FRQI of formula (1) as the processing of a predetermined quantum circuit. In the example EX2 of FIG. 4, a schematic example of the quantum circuit when n = 1 is shown.

[0033] The quantum decoding unit 5 decodes the classical image by determining the luminance value y(I) of position I as shown in formula (2) from the results of measuring the quantum state |Img(θ)> multiple times. A schematic example of such decoding is example EX3 of FIG. 4, and more specifically, as shown in examples EX4 and EX400 - 411 of FIG. 5. For example, the luminance value of the position (0, 1) of the classical image is decoded based on the frequencies of the two ground quantum states |001> and |101> in which the position (0, 1) is encoded among the measurement results over multiple times. For example, referring to example EX401, |001> has the rear 2 qubits in the base |01> with the position (0, 1) encoded, and the front 1 qubit is measured with a frequency of 50% (relative frequency among all the measurement results of the position (0, 1)), and |101> has the rear 2 qubits in the base |01> with the position (0, 1) encoded, and the front 1 qubit is measured with a frequency of 50% (relative frequency among all the measurement results of the position (0, 1)).

[0034] From this result, since the maximum likelihood value of the encoding term at position (0, 1) in Equation (1) is determined as the phase θ = π / 4 with "(cosπ / 4·|0> + sinπ / 4·|1>)|01>", if the linear transformation "θ=(π / 2)*(y / 256)" is used, the corresponding luminance value y = 127 can be decoded in the amplitude encoding for the single qubit "cosθ i |0> + sinθ i |1>". That is, among all the measurement results where the measurement results of the two qubits at the back are the same position |I> = |01> (in the denominator on the right side of Equation (2), all of "the number of measurements where |i> = |I>"), the probability that |0> is measured by the front single qubit is the square of the amplitude |cosθ i | 2 = 50% = 1 / 2, the probability that |1> is measured by the front single qubit is the square of the amplitude |sinθ i | 2 = 50% = 1 / 2 Therefore, cosθ i = sinθ i = 1 / √2 can be calculated and decoded as described above.

[0035] Note that since it is necessary to perform measurement multiple times in Equation (2) in the quantum decoding unit 5, correspondingly, in the quantum encoding unit 3, the same quantum state |Img(θ)> should be generated multiple times and then measured by the quantum decoding unit 5.

[0036] The quantum encoding unit 4 and the quantum decoding unit 5 can be implemented as a series of quantum circuits. Implementation examples for n = 2 are shown as parts P1 to P10 in FIGS. 6 and 7. For n = 2, a classical image of size 4×4 can be converted (i.e., encoded) into a 5 - qubit quantum image and measured as shown in FIGS. 6 and 7.

[0037] Parts P1 to P9 are circuits of the quantum encoding unit 4, and the last part P10 is measured as the quantum decoding unit 5 to determine the quantum state to one of the basis states (with a predetermined probability corresponding to the original quantum state). According to the conventional notation of quantum circuits in the art, each of parts P1 to P10 represents that the operation of the quantum bit is performed from the left side to the right side. Parts P1 to P10 are processed in this order. For example, the right end (last) of part P1 is connected to the left end (first) of the next part P2. The six processing lines are, in order from top to bottom, the processing lines of the quantum bits for which the position information is encoded are pos0, pos1, pos2, pos3 in the figure, and the 4×4 = 16 position information of the classical image is associated with the 16 basis states from |0000> to |1111> as the 4-qubit |pos0, pos1, pos2, pos3>. The processing line of the 1 quantum bit for which the luminance information is encoded is gr in the figure, and the processing line of the 5 classical bits for storing the measurement result is meas in the figure.

[0038] A person skilled in the art can design circuits as shown in FIGS. 6 and 7 by implementing the FRQI method such as in formulas (1) and (2) in a quantum circuit. Therefore, although the detailed description is omitted, among the circuit symbols in the figures, the H existing at the first positions of pos0, pos1, pos2, and pos3 is a Hadamard gate, the X existing in the middle of pos0, pos1, pos2, and pos3 is a NOT gate, the filled cross existing in the middle of gr is a CNOT (controlled NOT) gate, the Unitary existing in the middle of gr means a phase rotation gate, and the meter-like icon positions existing at the last positions mean the measurement of each of the 5 qubits. These circuit symbols are as commonly used in the notation of quantum circuits. Also, the vertical line spanning all of the upper 5 lines among the 6 processing lines indicates a semantic separation of the processing content of the quantum circuit, and the processing content for each separated part is as follows. That is, the first part creates a superposition of all states as a preparation, and the last part is measurement. The intermediate parts between these first and last parts are, in order, the parts that encode the information at position 0000, the parts that encode the information at position 0001,..., the parts that encode the information at position 1110, and the parts that encode the information at position 1111, that is, they encode the information at each position |I>=|0000>, |0001>,..., |1110>, |1111> in order.

[0039] The input IF unit 2 performs a process (a process of controlling the operation of the quantization code unit 3 as a quantum computer from a classical computer) of setting the circuit configuration of the quantization code unit 3 and its input as in the examples of FIGS. 6 and 7 in accordance with the FRQI method of formula (1). The output IF unit 6, also in accordance with the FQRI method of formula (2), sets the circuit configuration of the quantum decoding unit 5 as in the examples of FIGS. 6 and 7, and after interpreting the measurement result on a classical computer, obtains the decoded classical image as data to be processed on the classical computer.

[0040] The above is an overview of the FQRI method. Since noise such as that illustrated in FIG. 8 occurs in the decoded image of the FQRI method, this noise can be reduced by the filter processing of the preprocessing unit 1 and the postprocessing unit 7. By preprocessing the preprocessing unit 1, the classical image at the stage before being processed as a quantum image can be artificially processed to enhance the resistance to noise caused by the quantum image. (However, the classical image itself of the processing result in the preprocessing unit 1 may be in a state with noise as a classical image. The decoded image after applying the FQRI method to the classical image processed by the preprocessing unit 1 will result in reduced noise.) Also, by applying the postprocessing of the postprocessing unit 7 to the decoded image obtained with the noise after being processed as a quantum image, the noise can be reduced. As described above, there is only a difference in whether the image to be processed is in the previous stage or the subsequent stage of the quantum image, and the filter processing contents of the preprocessing unit 1 and the postprocessing unit 7 are common, and can be configured as an image filter device 10 as shown in FIG. 3. Hereinafter, as the processing contents of this common image filter device 10, the first processing unit 11 and the second processing unit 12 will be described.

[0041] In the first processing unit 11, noise reduction processing due to the adoption of amplitude encoding in the FQRI method is applied to the classical image. Specifically, the first processing unit 11 obtains the filter processing result by converting the luminance value y(i) at each position i of the classical image to y'(i) by the following formula (3). Note that formula (3) is applied to the luminance value y(i) that is not the target of "saturation" as described later, and for the luminance value y(i) that is the target of saturation, it is saturated to y'(i)=0 or 255.

[0042]

Equation

[0043] Here, y top and y bottomEach represents, in the set of all luminance values of the image to be subjected to the filtering process, the luminance value corresponding to a predetermined percentile value from the upper side (the side with higher luminance values) and the luminance value corresponding to the predetermined percentile value from the lower side (the side with lower luminance values). As this predetermined percentile value, for example, 1% may be used. The predetermined percentile values adopted for the upper and lower sides may be different values.

[0044] 1 qubit term "cosθ i |0> + sinθ i |1>" The information amplitude-encoded as such, when a bit-flip error occurs within the quantum circuit, due to the attenuation of the original amplitude, the measurement probability pair of |0>, |1> is (|cosθ i | 2 , |sinθ i | 2 ) = (p, 1 - p), noise occurs in the direction of reducing the dynamic range (that is, for example, regardless of the value that the original measurement probability p = |cosθ i | 2 takes within 0% ≤ p ≤ 100%, when a bit-flip of |0>, |1> occurs, noise acts in the direction of averaging to (p, 1 - p) = (50%, 50%)). Therefore, this noise can be reduced by the filter process of Equation (3) by the first processing unit 11 corresponding to "contrast enhancement".

[0045] Note that the grayscale image obtained as a result of the filter process of the first processing unit 11 saturates values of y top and above to the maximum luminance value of 255, and saturates values of y bottom and below to the minimum luminance value of 0. Therefore, it will necessarily include pixels composed of luminance values of the minimum value 0 and the maximum value 255 within the defined range [0, 255] (in the case of 8 bits) which is the range within which luminance values can be taken. Note that saturation means that for luminance values of y top and above, y top , y top + 1, y topPixels with luminance values of +2, … rewrite all their luminance values to the maximum value of 255, that is, saturate them to the maximum value. Similarly, for luminance values of y bottom where y is bottom , y bottom , y - 1 bottom , y - 2, … rewrite all their luminance values to the minimum value of 0, that is, it means saturating them to the minimum value. For pixels that are not subject to saturation, pixel values within the range of 0 to 255 are assigned according to Equation (3).

[0046] Therefore, for the image before the filtering process in the first processing unit 11, by using in advance an image that includes pixel values of the maximum luminance value 255 and the minimum luminance value 0, it is possible to prevent the appearance of the image from changing significantly before and after the filtering process. When filtering an image that does not include pixel values of the maximum luminance value 255 and the minimum luminance value 0, the image may be expanded to the outer peripheral side so that the expanded region includes pixel values of the maximum luminance value 255 and the minimum luminance value 0, or after detecting a region where applying object recognition by deep learning or the like is determined to have no significant impact on the appearance of the image, performing a process of rewriting the luminance value of the region to the maximum luminance value 255 or the minimum luminance value 0 and then applying the filtering process.

[0047] In Equation (3), luminance values excluded from the saturation target on the maximum value 255 side or the minimum value 0 side will be linearly mapped to the range of [1, 254], but it is also possible to use a predetermined function to non-linearly map them to the range of [1, 254]. At this time, non-linear mapping may be performed so as to expand the region where human perception is sensitive. The Weber-Fechner law may be used as a criterion for specifying the region where perception is sensitive.

[0048] In addition, when using the FQRI method as the quantum image method, since the luminance value is amplitude-encoded, a filter process for saturating the larger and smaller sides of the luminance value according to Equation (3) is applied. However, when using the QSNC method as the quantum image method, since the coordinate information is amplitude-encoded, the same saturation process may be applied to the coordinate information. When using the NAQSS method as the quantum image method, since the segmentation information is amplitude-encoded, the same saturation process may be applied to the segmentation information.

[0049] Also, although the case where the classical image is composed of grayscale images is used as an explanatory example, when dealing with color images such as RGB and YUV, the amplitude encoding of this embodiment can be similarly applied. That is, similar to the luminance value in the case of grayscale images, for a color image composed of general pixel values to which a luminance value or a color difference value etc. defined in advance for each channel is assigned, within the predetermined range defined for the signal of the pixel value of the channel, saturation can be performed in the same manner as Equation (3), and for pixels that are not saturated, linear or non-linear mapping can be applied. In this case, for example, in the case of an RGB image, 1 qubit can be assigned to each of the three channels of R, G, and B, and the pixel values of each of the three channels can be amplitude-encoded. Alternatively, the amplitude encoding may remain 1 qubit, and in addition to the 2n qubit position information for the basis encoding, 2 qubit channel information may be added.

[0050] As a predetermined arrangement for assigning this added 2 qubit channel information to the RGB three channels, for example, the following may be done. (1) If the measurement result of the 2 qubits at the basis encoding location for the channel information is 00, the result of the 1 qubit of the amplitude encoding is treated as the number of measurement times for the R channel. (2) If the measurement result of the 2 qubits at the basis encoding location for the channel information is 01, the result of the 1 qubit of the amplitude encoding is treated as the number of measurement times for the G channel. (3) If the measurement result of two qubits at the base encoding location for channel information is 10, the result of the single qubit of amplitude encoding is treated as the number of measurement times of the B channel. (4) If the measurement result of two qubits at the base encoding location for channel information is 11, the result is discarded as an error (no corresponding RGB channel).

[0051] In this case, the single qubit of amplitude encoding can reduce noise and suppress image degradation by applying the filter processing of the first processing unit 11 as "contrast enhancement processing" in the same way as above. Since the measurement result in the above (4) can be used as information separate from the image information, after estimating the error rate of the system (quantum circuit system by the quantum encoding unit 3 and the quantum decoding unit 5) from the measurement result, the degree of contrast enhancement (y top and y bottom as which percentile value) may be set according to the estimated error rate.

[0052] In the second processing unit 12, as a noise reduction process due to adopting the base encoding of position information in the FQRI method, a sharpening filter process (edge enhancement filter process) is applied to the classical image.

[0053] FIG. 9 is a diagram schematically showing the (quantum) sharpening filter process by the second processing unit 12 in comparison with the (classical) sharpening filter process in the case of dealing with classical noise of a classical image. The upper side shows an example of the classical sharpening filter process as a conventional method, and the lower side shows an example of the quantum sharpening filter process of the method of the second processing unit 12.

[0054] In classical sharpening filter processing, in order to deal with noise such as blurring, for each pixel position, sharpening is realized by referring to the pixel values in its spatial neighborhood, and an example of its filter coefficient is shown as Example EX50. Quantum sharpening filter processing also performs sharpening in the same way, but as the spatial neighborhood that may be affected by noise, instead of the spatial neighborhood on the classical image, the neighborhood in the base-encoding state as shown in Example EX51 is used.

[0055] For example, in a 4×4 classical image as shown (with the upper left coordinate being (0,0) and the lower right coordinate being (3,3)), when applying a quantum sharpening filter to the black-filled position (1,2), since the position (1,2) corresponds to the 4-qubit base |1001>, |0001>, |1000>, |1011>, |1101> (each character takes one of the two values 0 and 1 representing the bases |0> and |1>, and when representing the base |1001> as a character string with a fixed length of 4 that matches the number of qubits 4 of 4 qubits, the neighborhood where the Hamming distance representing the difference between the character strings is within a predetermined range, for example, 1 or less) corresponding to the neighborhood in the base-encoding state can be used for sharpening. For the filter coefficient for sharpening, the same concept as in the classical case can be used, and for example, the results of sharpening can be obtained as shown in the following equations (4A), (4B) and Example EX51 of FIG. 9. That is, when there is a difference in the pixel values between the target pixel to be filtered and its neighboring pixels, a predetermined filter coefficient can be set as the coefficient of the weighted sum of the target pixel and its neighboring pixels so as to emphasize this difference. In equations (4A) and (4B), the value of the target pixel is emphasized by a constant multiple of 5, and a certain amount of subtraction is performed by multiplying the values of the four neighboring pixels by 1 each, thereby realizing sharpening that emphasizes the difference from the neighboring pixels of the target pixel. Similarly, when sharpening considering n neighbors, filter coefficients such as multiplying the value of the target pixel by (n + 1) and multiplying each of the n neighboring pixels by 1 and then subtracting can be used for sharpening. y'(|1001>)=5*y(|0001>)-y(|1000>)-y(|1011>)-y(|1101>) …(4A) y'(1,2) = 5 * y(1,2) - y(1,0) - y(0,2) - y(3,2) - y(1,3) …(4B)

[0056] Equations (4A) and (4B) are identical. Equation (4A) represents the pixel value y(i) by indicating the position information i in the 4 - qubit basis state, while equation (4B) represents the pixel value y(i) by indicating the position information i in the normal two - dimensional spatial coordinates in a classical image. The pixel value of the result of applying the filter to the pixel value at the pixel position i = |1001>=(1,2) being focused on is y'(i) on the left - hand side.

[0057] As shown in the example of Figure 9, the neighborhood of the pixel position in the basis encoding state does not necessarily coincide with the neighborhood in the normal spatial coordinates of a classical image (such as the neighborhood above, below, left, and right).

[0058] Note that for one of the multiple basis encoding states, when the original position is, for example, |i>=|1001>, due to a single bit - flip occurring as noise in the 4 - qubit being basis - encoded, the quantum state (one of the superposition quantum states) can change as follows. (cosθ i |0> + sinθ i |1>)|1001> → (cosθ i |0> + sinθ i |1>)|0001> (cosθ i |0> + sinθ i (cosθ i |0> + sinθ i |1>)|1001> → (cosθ (cosθ i |0> + sinθ i (cosθ i |0> + sinθ i |1>)|1001> → (cosθ (cosθ i |0> + sinθ i (cosθ i |0> + sinθ i |1>)|1001> → (cosθ

[0059] That is, the original pixel value of the original position |i>=|1001> is amplitude-encoded as the term "cosθ i |0> + sinθ i |1>". When a bit flip occurs once within the position information |i>=|1001>, it "mixes" and exists in one of the neighboring positions |0001>, |1000>, |1011>, |1101> different from the original position, and the result that should be measured at the original position |i>=|1001> will be counted at the neighboring positions, which causes deterioration corresponding to blurring in the case of classical images. Therefore, sharpening as in equations (4A) and (4B) is effective for noise reduction. When considering n bit flips of two or more times, a neighborhood with a Hamming distance of n or less as the string may be used.

[0060] As described above, according to the embodiment of the present invention, noise caused by a quantum image can be reduced by performing a filtering process on a classical image. Hereinafter, various supplementary examples and the like regarding the embodiment of the present invention will be described.

[0061] (1) According to the embodiment of the present invention, by enabling noise reduction regarding the use of a quantum image, which is a novel technology in a quantum computer, which is a novel technology, it is possible to contribute to technological innovation and contribute to Goal 9, "Build the infrastructure for industry and technological innovation", of the Sustainable Development Goals (SDGs) led by the United Nations.

[0062] (2) FIG. 10 is a diagram showing an example of the hardware configuration in a general (classical) computer device 70. The constituent parts (functional parts 1, 2, 6, 7) as a classical computer device in the quantum image processing system 100 can be realized as one or more computer devices 70 having such a configuration. When realizing the classical constituent parts with two or more computer devices 70, information necessary for processing may be transmitted and received via a network. The computer device 70 includes a CPU (Central Processing Unit) 71 that executes a predetermined instruction, a GPU (Graphics Processing Unit) 72 as a dedicated processor that executes some or all of the execution instructions of the CPU 71 instead of or in cooperation with the CPU 71, a RAM 73 as a main storage device that provides a work area for the CPU 71 (and the GPU 72), a ROM 74 as an auxiliary storage device, a communication interface 75, a display 76 that performs display output, an input interface 77 that receives user input by a mouse, a keyboard, a touch panel, etc., a speaker 78 that performs voice output, and a bus BS for exchanging data between these components.

[0063] The classical constituent parts (functional parts 1, 2, 6, 7) can be realized by the CPU 71 and / or the GPU 72 that reads and executes a predetermined program corresponding to the function of each part from the ROM 74. Note that both the CPU 71 and the GPU 72 are a type of arithmetic unit (processor). Here, when display-related processing is performed, the display 76 operates in conjunction, and when communication-related processing related to data transmission and reception is performed, the communication interface 75 operates in conjunction, and when voice output-related processing is performed, the speaker 78 operates in conjunction.

Explanation of Signs

[0064] 100... Quantum image processing system, 1... Preprocessing unit (10... Image filter device), 2... Input IF unit, 3... Quantum encoding unit, 4... Quantum communication unit, 5... Quantum decoding unit, 6... Output IF unit, 7... Postprocessing unit (10... Image filter device), 11... First processing unit, 12... Second processing unit

Claims

1. An image filter device that applies a filter process for reducing noise generated in an output image due to the state of a quantum image, to at least one of an input image or the output image, in a case where an input image that is a classical image is encoded into a quantum image and then an output image that is a classical image is decoded based on a measurement result of the quantum image, wherein the encoding into the quantum image includes basis encoding by associating position information in the classical image with each of a plurality of bases, and the filter process includes performing sharpening after defining a neighborhood in the basis-encoded state for each pixel position on the classical image. The image filter device is characterized by this.

2. The image filter device according to claim 1, wherein the basis-encoded state is a state that can be expressed as a character string in which each character takes one of two values, and the neighborhood is defined in the state that can be expressed as the character string.

3. wherein the encoding into the quantum image includes amplitude encoding by associating a pixel value in the classical image with the amplitude of one qubit, and the filter process includes saturating, for each pixel value of a target image with the input image or the output image as the target image for processing, pixel values corresponding to those on the upper side and the lower side in a set of pixel values of the target image, to the maximum value and the minimum value that can be taken by a pixel value predefined in the classical image. The image filter device according to claim 1 is characterized by this.

4. The image filter device according to claim 3, wherein the filter process includes mapping pixel values corresponding to those not corresponding to the upper side and the lower side linearly or non-linearly.

5. An image filter device that applies a filter process for reducing noise generated in an output image due to the state of a quantum image, to at least one of an input image or the output image, in a case where an input image that is a classical image is encoded into a quantum image and then an output image that is a classical image is decoded based on a measurement result of the quantum image, wherein the encoding into the quantum image includes amplitude encoding by associating a pixel value in the classical image with the amplitude of one qubit, The filter processing includes saturating, in the filter processing of at least one of the input image and the output image as a target image for processing, pixel values corresponding to pixel values on the upper side and the lower side in the set of pixel values of the target image to the maximum value and the minimum value within the range of pixel values that can be taken in a classical image, respectively. An image filter device.

6. The filter processing includes mapping, linearly or non-linearly, pixel values corresponding to pixel values that do not correspond to the upper side and the lower side. The image filter device according to claim 5, characterized in that.

7. A program characterized by causing a computer to function as the image filter device according to any one of claims 1 to 6.

Images