A Quantum Image Watermark Embedding Method Based on Quantum Haar Wavelet Transform

Abstract

The present invention discloses a quantum image watermark embedding method based on quantum Haar wavelet transform, which relates to the technical field of quantum image processing. Specifically, it includes steps of initializing a quantum image, processing and transforming the image, embedding watermark information, restoring image information, and extracting quantum watermark information. The design of the present invention only requires adding a device for generating quantum states to basic equipment; by decomposing the carrier image, the watermark information is embedded into the least significant bit of the color information in the diagonal sub-band of the decomposed image, so that the embedding effect of the watermark is good, with strong robustness and imperceptibility, enabling the watermark to be embedded without damaging the original image, and the fidelity of the carrier image can be guaranteed; the least significant bit embedding method is used to embed the watermark information to achieve the copyright protection of quantum images; its overall scheme is relatively simple and is easy to implement in an actual quantum computer.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum information transmission, and in particular to a quantum image watermark embedding method based on quantum Haar wavelet transform. Background Technique

[0002] Quantum image processing is a new sub-discipline that focuses on extending traditional image processing tasks and operations to the quantum computing framework. Different from classical image processing, images are stored in the qubits of a quantum computer. Utilizing the excellent parallel computing ability of quantum computing can greatly reduce the image storage space and the circuit size required for image processing, providing more possibilities for image processing.

[0003] As an important carrier for humans to transmit information in modern society, if images are wantonly spread on the Internet without considering the rights and interests of copyright owners, serious consequences will surely occur. By using image watermarking technology to process images, copyright information can be effectively embedded into the images, enabling the rights and interests of copyright owners to be technically protected.

[0004] To realize the embedding and extraction of quantum image watermarks, some theoretical algorithms have gradually become practical. The literature "Quantum watermarking scheme through Arnold scrambling and LSB steganography" proposed to realize the embedding and extraction of watermarks based on the Arnold transform and the LSB method, but the image effect after embedding the watermark is not as good as that of the corresponding classical watermark embedding algorithm; the literature "Quantum Image Watermarking Algorithm Based on Haar Wavelet Transform" proposed a method based on wavelet transform for the FRQI quantum image representation model to realize the embedding and extraction of watermarks, but it needs to convert each watermark information bit into a quantum gate, increasing the complexity of the algorithm. Currently, there is no high-performance watermark embedding and extraction technology for the NEQR quantum image representation method. In view of this, we propose a quantum image watermark embedding method based on quantum Haar wavelet transform. Summary of the Invention

[0005] In order to overcome the above problems existing in the prior art, the present invention proposes a quantum image watermark embedding method based on quantum Haar wavelet transform.

[0006] The technical solution adopted by the present invention to solve its technical problems is: a quantum image watermark embedding method based on quantum Haar wavelet transform, including the following steps:

[0007] S1. Initialize quantum information: Prepare a quantum image based on the NEQR model;

[0008] S2. Process the quantum image: Decompose the image using quantum Haar wavelet watermarking to obtain four sub-bands of the image;

[0009] S3. Embed watermark information: Embed the watermark information into the least significant bit of the color in the diagonal detail sub-band of the original image using the LSB watermark embedding method;

[0010] S4. Restore the image: Use quantum Haar wavelet watermarking to restore the image information;

[0011] S5. Extract the watermark: Use quantum wavelet transform and the original image to extract the watermark image.

[0012] In the above quantum image watermark embedding method based on quantum Haar wavelet transform, in step S1, the specific method for initializing quantum information includes the following steps:

[0013] S1.1. Convert the classical grayscale image into a quantum image representation method using the NEQR model;

[0014] S1.2. Use a quantum register to obtain the quantum state to be prepared by measuring the amplitude of each basis vector.

[0015] In the above quantum image watermark embedding method based on quantum Haar wavelet transform, in step S1.1, the specific algorithm formula of the NEQR model quantum image is as follows: Assume that a 2 n ×2 n grayscale image with a size of 2 q is prepared, then the color value and coordinate value of the image pixel can be encoded into a quantum state as:

[0016]

[0017]

[0018] |i> = |y>|x> = |y n-1 y n-2 …y0>|x n-1 x n-2 …x0>, x i , y i ∈{0,1}

[0019] where |I> represents the quantum image, |c i > represents the color information, |i> represents the position information, k represents any value between 0 and q - 1, |y> represents the coordinate information in the vertical direction, |x> represents the coordinate information in the horizontal direction, x iThe i-th encoded bit representing the horizontal coordinate information, y i The i-th encoded bit representing the vertical coordinate information.

[0020] The above-mentioned quantum image watermark embedding method based on quantum Haar wavelet transform. In S2, the processing of the quantum image includes the following steps:

[0021] S2.1. Use swap gates to arrange and combine to form an overall displacement gate

[0022] S2.2. Use controlled gates and controlled Hadamard gates to form an effective quantum Haar wavelet transform circuit;

[0023] S2.3. Use the quantum Haar wavelet transform circuit to decompose the quantum image stored in the quantum register to obtain the approximation sub-band, horizontal sub-band, vertical sub-band and diagonal sub-band of the image.

[0024] The above-mentioned quantum image watermark embedding method based on quantum Haar wavelet transform. In S2.3, the specific expression of image decomposition is as follows:

[0025]

[0026] Among them, |C> represents the carrier image, |C D > represents the decomposed image, I2 represents the 2×2 identity operator represents q identity operators, H represents the Hadamard operator, q represents the number of quantum circuits representing color information, and n represents the number of quantum circuits representing position information. represents n identity operators, represents q + n - 1 identity operators, represents q + n identity operators, represents q + 2n - 1 identity operators.

[0027] The above-mentioned quantum image watermark embedding method based on quantum Haar wavelet transform. In S3, the specific watermark embedding method includes the following steps:

[0028] S3.1. Introduce a quantum image containing watermark information;

[0029] S3.2. Design a multi-dimensional quantum controlled-NOT gate to prepare for the subsequent watermark information embedding;

[0030] S3.3. Embed the watermark information into the least significant bit of the color bit in the diagonal sub-band of the carrier image.

[0031] For the above quantum image watermark embedding method based on quantum Haar wavelet transform, in S3.3, the specific method for embedding color information is expressed as follows:

[0032]

[0033]

[0034] where |C E > represents the quantum image after watermark embedding, |C D > represents the decomposed image, and |WI> represents the watermark image. is a multi-dimensional quantum controlled-NOT gate, and U EM represents the overall watermark information embedding operation, X represents the CNOT gate. represents the i-th longitudinal coordinate information of the carrier image that controls the CNOT gate. represents the i-th transverse coordinate information of the carrier image that controls the CNOT gate. represents the i-th transverse coordinate information of the watermark image that controls the CNOT gate. represents the i-th longitudinal coordinate information of the u watermark image that controls the CNOT gate.

[0035] For the above quantum image watermark embedding method based on quantum Haar wavelet transform, in S4, the specific method for restoring the image is as follows: The image with embedded watermark information is restored by using the inverse quantum Haar wavelet transform, and its calculation expression is as follows:

[0036]

[0037]

[0038] where |CW> represents the restored quantum image, |C E > represents the quantum image after watermark embedding, and I2 represents the 2×2 identity operator. represents q identity operators, H represents the hadamard operator, q represents the number of quantum circuits representing color information, and n represents the number of quantum circuits representing position information. represents n identity operators. represents q + n - 1 identity operators. represents q + n identity operators. represents q + 2n - 1 identity operators.

[0039] For the above quantum image watermark embedding method based on quantum Haar wavelet transform, in S5, the specific method for extracting watermark information includes the following steps:

[0040] S5.1. Decompose the image with embedded watermark by using quantum Haar wavelet transform;

[0041] S5.2. Design corresponding multi-dimensional quantum controlled gates to extract the watermark information in the carrier image.

[0042] For the above quantum image watermark embedding method based on quantum Haar wavelet transform, in S5.2, the calculation expression for extracting the watermark information is as follows:

[0043]

[0044]

[0045] Where, represents the operator for extracting the watermark information of the j-th pixel, represents the j-th longitudinal coordinate information of the carrier image that controls the CNOT gate, represents the j-th transverse coordinate information of the carrier image that controls the CNOT gate, represents the j-th transverse coordinate information of the watermark image that controls the CNOT gate, represents the j-th longitudinal coordinate information of the watermark image that controls the CNOT gate, represents the conjugate of the j-th transverse coordinate information of the carrier image that controls the CNOT gate, represents the conjugate of the j-th longitudinal coordinate information of the carrier image that controls the CNOT gate, |C WI > represents the watermark image, U EX represents the operator for extracting all the watermark information, |CW D > represents the carrier image embedded with the watermark.

[0046] The beneficial effects of the present invention are: (1) Compared with other watermark embedding methods, the quantum image watermark embedding method based on quantum Haar wavelet transform does not require changing some basic devices, but only needs to add devices for generating quantum states;

[0047] (2) In the quantum image watermark embedding method based on quantum Haar wavelet transform, by decomposing the carrier image, the watermark information is embedded into the least significant bit of the color information of the diagonal subband of the decomposed image, so that the embedding effect of the watermark is good, with strong robustness and imperceptibility, and the watermark can be embedded without destroying the original image, and the fidelity of the carrier image can be guaranteed;

[0048] (3) In the quantum image watermark embedding method based on quantum Haar wavelet transform, the transmission of watermark information is realized by using quantum algorithms, which has the property of non-replicability itself and is the key to realizing secure information transmission.

[0049] (4) The overall scheme of the quantum image watermark embedding method based on quantum Haar wavelet transform is relatively simple. The integrity of the algorithm ensures simple hardware operations and easy implementation in actual quantum computers. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The present invention will be further described below with reference to the drawings and embodiments.

[0051] Figure 1 It is a flowchart of the watermark embedding method of the present invention;

[0052] Figure 2 They are the watermarked image and the carrier image obtained by using the quantum image watermark embedding method based on quantum Haar wavelet transform, where (q) is watermark image 1, (r) is watermark image 2, (s) is watermark image 3, (a)-(d) are carrier images; (e)-(h) are the images after embedding watermark 1; (i)-(l) are the images after embedding watermark 2; (m)-(p) are the images after embedding watermark 3;

[0053] Figure 3 It is a complete circuit diagram of the watermark embedding algorithm. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0054] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be described in detail below with reference to the drawings and specific embodiments.

[0055] This embodiment provides a quantum image watermark embedding method based on quantum Haar wavelet transform, and the specific process is as Figure 1 shown, including the following steps:

[0056] S1. Initialize the quantum information: Prepare a quantum image based on the NEQR model;

[0057] S2. Process the quantum image: Use the quantum Haar wavelet watermark to decompose the image to obtain four sub-bands of the image;

[0058] S3. Embed the watermark information: Use the LSB watermark embedding method to embed the watermark information into the lowest significant bit of the color of the diagonal detail sub-band of the original image;

[0059] S4. Restore the image: Use the quantum Haar wavelet watermark to restore the image information;

[0060] S5. Extract the watermark: Similar to the watermark embedding method, use the quantum wavelet transform and the original image to extract the watermark image.

[0061] Among them, the overall transmission scheme of this embodiment is mainly divided into five parts: the initialization stage, the quantum image processing stage, the watermark information embedding stage, the image restoration stage, and the watermark extraction stage. It can be pre-assumed that the noise effects are divided into depolarizing noise and bit-flip noise, and the probabilities of the two types of noise affecting quantum information transmission are different.

[0062] In this embodiment, in S1, the quantum information is initialized: The specific method for preparing a quantum image based on the NEQR model includes the following steps:

[0063] S1.1. Use the NEQR model to convert the classical grayscale image into a quantum image representation method;

[0064] S1.2. Use quantum registers to obtain the quantum state to be prepared by measuring the amplitude of each basis vector;

[0065] Specifically, in S1.1, the specific algorithm formula for preparing the quantum image is:

[0066]

[0067]

[0068] |i> = |y>|x> = |y n-1 y n-2 …y0>|x n-1 x n-2 …x0>, x i , y i ∈{0, 1};

[0069] In the formula, |I> represents the quantum image; |c i > represents the color information, where 8-bit quantum bits represent the color information of the grayscale image; |y>|x> represents the position information, where n quantum bits |y n-1 y n-2 …y0> are used to store the ordinate information, and similarly, |x n-1 x n-2 …x0> stores the abscissa information.

[0070] In this embodiment, in S2, the quantum image is processed: The specific method for decomposing the image using the quantum Haar wavelet watermark includes the following steps:

[0071] S2.1. Use swap gates to arrange and combine to form an overall displacement gate Its specific expression is as follows:

[0072]

[0073] S2.2. Use controlled The gate and the controlled Hadamard gate (H gate) constitute an effective quantum Haar wavelet transform circuit, and its specific expression is as follows:

[0074]

[0075] S2.3. Decompose the quantum image stored in the quantum register by using the quantum Haar wavelet transform circuit to obtain the approximation sub-band, horizontal sub-band, vertical sub-band, and diagonal sub-band of the image, and its specific expression is as follows:

[0076]

[0077] where |C> represents the carrier image, and |C D > represents the decomposed image.

[0078] In this embodiment, in S3, the specific method for embedding the watermark information includes the following steps:

[0079] S3.1. Introduce a quantum image containing the watermark information;

[0080] S3.2. Design a multi-dimensional quantum controlled NOT gate to prepare for the subsequent embedding of the watermark information. The specific expression of the controlled NOT gate is as shown below;

[0081]

[0082] S3.3. Embed the watermark information into the least significant bit of the color bit in the diagonal sub-band of the carrier image. The specific expression of the method for embedding the color information is as expressed by the following formula:

[0083]

[0084] In this embodiment, in S4, the method for restoring the image with the embedded watermark information is as follows: Restore the image with the embedded watermark information by using the inverse quantum Haar wavelet transform. Its calculation expression is as follows:

[0085]

[0086]

[0087] where |CW> represents the restored quantum image.

[0088] In this embodiment, in S5, the specific method for extracting the quantum watermark image includes the following steps:

[0089] S5.1. Decompose the image with the embedded watermark by using the quantum Haar wavelet transform;

[0090] S5.2. Design the corresponding multi-dimensional quantum controlled gate to extract the watermark information in the carrier image. The calculation expression for extracting the watermark information is as follows:

[0091]

[0092]

[0093] Through the above method steps, in this embodiment, for the first time, the least significant bit (LSB) watermark embedding method and the quantum Haar wavelet transform are combined to perform quantum image watermark embedding. Without the overhead of additional auxiliary qubits, and taking advantage of the non-replicability of the quantum image itself, while ensuring the image copyright, the security of information transmission is also protected.

[0094] Those of ordinary skill in the art can understand that the process of implementing all or part of the steps of the above embodiment can be completed by hardware or by a program instructing relevant hardware. The program can be stored in a computer-readable storage medium, and the above-mentioned storage medium can be a read-only memory, a magnetic disk, an optical disk, etc.

[0095] The specific implementation circuit of the above method is as Figure 3 shown, where |C> represents the carrier image, and |WI> represents the watermark image. First, the QHWT is used to decompose the image, then the multi-quantum controlled-NOT gate is used to embed the watermark information into the carrier image, and finally the inverse QHWT is used to restore the carrier image to complete the embedding of the watermark.

[0096] By adopting the above method, the following effect diagrams can be obtained as Figure 2 shown, where (q) is the watermark image 1, (r) is the watermark image 2, (s) is the watermark image 3, and (a)-(d) are the carrier images; (e)-(h) are the images after embedding watermark 1; (i)-(l) are the images after embedding watermark 2; (m)-(p) are the images after embedding watermark 3.

[0097] The above embodiments are only exemplary embodiments of the present invention and are not used to limit the present invention. The protection scope of the present invention is defined by the claims. Those skilled in the art can make various modifications or equivalent replacements within the essence and protection scope of the present invention, and such modifications or equivalent replacements should also be regarded as falling within the protection scope of the present invention.

Claims

1. A quantum image watermark embedding method based on quantum Haar wavelet transform, characterized in that, It includes the following steps: S1. Initialize the quantum information: Prepare a quantum image based on the NEQR model; S2. Process the quantum image: Use quantum Haar wavelet watermarking to decompose the image and obtain four sub-bands of the image; S3. Embed the watermark information: Use the LSB watermark embedding method to embed the watermark information into the lowest significant bit of the color in the diagonal detail sub-band of the original image; S4. Restore the image: Use quantum Haar wavelet watermarking to restore the image information; S5. Extract the watermark: Use quantum wavelet transform and the original image to extract the watermark image; In S3, the specific method of watermark embedding includes the following steps: S3.

1. Introduce a quantum image containing watermark information; S3.

2. Design a multi-dimensional quantum controlled-NOT gate to prepare for the subsequent watermark information embedding; S3.

3. Embed the watermark information into the lowest significant bit of the color bit in the diagonal sub-band of the carrier image; In S3.3, the specific expression of the method for embedding color information is expressed as follows: Among them represents the quantum image after watermark embedding, represents the decomposed image, represents the watermark image, is a multi-dimensional quantum controlled-NOT gate, represents the overall watermark information embedding operation, represents the CNOT gate, represents the i-th longitudinal coordinate information of the carrier image that controls the CNOT gate, represents the i-th transverse coordinate information of the carrier image that controls the CNOT gate, represents the i-th transverse coordinate information of the watermark image that controls the CNOT gate, represents the i-th longitudinal coordinate information of the watermark image that controls the CNOT gate.

2. A quantum image watermark embedding method based on quantum Haar wavelet transform according to claim 1, characterized in that, In S1, the specific method for initializing the quantum information includes the following steps: S1.

1. Use the NEQR model to convert the classical grayscale image into a quantum image representation method; S1.

2. Use a quantum register to obtain the quantum state to be prepared by measuring the amplitude of each basis vector.

3. A quantum image watermark embedding method based on quantum Haar wavelet transform according to claim 2, characterized in that, In the above S1.1, the specific algorithm formula of the NEQR model quantum image is as follows: Assume that a -sized grayscale image is prepared, and the gray value is . Then, the color value and coordinate value of the image pixels can be encoded into quantum states as: ； wherein represents a quantum image, represents color information, represents position information, and k represents any value between 0 and q - 1, represents the coordinate information in the vertical direction, represents the coordinate information in the horizontal direction, represents the i-th encoded bit of the horizontal coordinate information, represents the i-th encoded bit of the vertical coordinate information.

4. A quantum image watermark embedding method based on quantum Haar wavelet transform according to claim 1, characterized in that, In S2, the processing of the quantum image includes the following steps: S2.

1. Use swap gates to arrange and combine to form an overall displacement gate S2.

2. Use the controlled gate and the controlled Hadamard gate to form an effective quantum Haar wavelet transform circuit; S2.

3. Use the quantum Haar wavelet transform circuit to decompose the quantum image stored in the quantum register to obtain the approximate sub-band, horizontal sub-band, vertical sub-band, and diagonal sub-band of the image.

5. A quantum image watermark embedding method based on quantum Haar wavelet transform according to claim 4, characterized in that, In S2.3, the specific expression of the image decomposition is as follows: Among them, represents the carrier image, represents the decomposed image, represents the identity operator of represents q identity operators, H represents the Hadamard operator, q represents the number of quantum circuits for color information, and n represents the number of quantum circuits for position information. represents n identity operators, represents q + n - 1 identity operators, represents q + n identity operators, represents q + 2n - 1 identity operators.

6. The quantum image watermark embedding method based on quantum Haar wavelet transform according to claim 1, characterized in that: In S4, the specific method for restoring the image is: Use the inverse quantum Haar wavelet transform to restore the image with the watermark information embedded, and its calculation expression is as follows: Among them represents the restored quantum image, represents the quantum image after watermark embedding, represents q identity operators, H represents the Hadamard operator, q represents the number of quantum circuits for color information, and n represents the number of quantum circuits for position information, represents n identity operators, represents q + n - 1 identity operators, represents q + n identity operators, represents q + 2n - 1 identity operators.

7. The quantum image watermark embedding method based on quantum Haar wavelet transform according to claim 1, characterized in that: In S5, the specific method for extracting the watermark information includes the following steps: S5.

1. Use the quantum Haar wavelet transform to decompose the image with the watermark embedded; S5.

2. Design a corresponding multi-dimensional quantum controlled gate to extract the watermark information in the carrier image.

8. The quantum image watermark embedding method based on quantum Haar wavelet transform according to claim 7, characterized in that: In S5.2, the calculation expression for extracting the watermark information is as follows: Among them, denotes the operator for extracting the watermark information of the j-th pixel, denotes the j-th longitudinal coordinate information of the carrier image that controls the CNOT gate, denotes the j-th horizontal coordinate information of the carrier image that controls the CNOT gate, denotes the j-th horizontal coordinate information of the watermark image that controls the CNOT gate, denotes the j-th longitudinal coordinate information of the watermark image that controls the CNOT gate, denotes the conjugate of the j-th horizontal coordinate information of the carrier image that controls the CNOT gate, denotes the conjugate of the j-th longitudinal coordinate information of the carrier image that controls the CNOT gate, denotes the watermark image, denotes the operator for extracting all watermark information, denotes the carrier image embedded with the watermark.

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