CN113115053B - Image encryption method based on integer wavelet transform and compressed sensing - Google Patents

Abstract

The present invention proposes an image encryption method based on integer wavelet transform and compressed sensing, which solves the problem of insufficient encryption security in the way of direct carrier embedding in the current spatial domain image encryption method based on compressed sensing. The image is preprocessed, and the random sequence generated by the chaotic system is associated with the plaintext image information, which can effectively resist the known plaintext attack and the chosen plaintext attack; then the preprocessed plaintext image is sparsely processed, and the scrambling operation is performed sequentially; Generate a measurement matrix, use the measurement matrix to perform compression sensing on the plaintext image after the scrambling operation, and perform a diffusion operation before embedding the carrier image to further improve the security of image encryption. Embedding operation, and then perform inverse integer wavelet transformation, reduce data loss caused by frequency domain transformation, and improve the encryption security of image information.

Description

An Image Encryption Method Based on Integer Wavelet Transform and Compressed Sensing

technical field

The present invention relates to the technical field of image encryption, and more specifically, relates to an image encryption method based on integer wavelet transform and compressed sensing.

Background technique

With the rapid development of Internet technology and social media, more and more multimedia information is generated and disseminated on the Internet. Among these digital information, digital image is an information format that can transmit information in a visual way, but there will be some private images in these digital images, and the transmission of private images on the network will have certain risks. In order to prevent these digital images containing a large amount of private information from being acquired or used by unauthorized people, image encryption has attracted great attention as an effective means.

According to the different encryption domains, digital image encryption can be divided into frequency domain encryption and air domain encryption. Spatial domain encryption refers to the digital image as a two-dimensional matrix, and the reversible transformation of the two-dimensional matrix from the perspective of space. Commonly used spatial domain image encryption schemes include two stages of scrambling and diffusion. The frequency domain is relative to the spatial domain of the image, and the image is processed from the frequency domain space. Generally, discrete cosine transform, fast Fourier transform and wavelet can be used. Transform and other transformation methods to realize the conversion between image space domain and frequency domain. The feature of the frequency domain encryption scheme is that the encryption speed is fast, but it is usually a lossy encryption, that is, there is a small difference between the decrypted image and the plaintext image.

Compressive sensing theory is a new signal sampling theory, which can efficiently capture and recover signals by setting up an underdetermined linear system. Compressed sensing theory explores how to achieve the same signal reconstruction accuracy at a lower sampling rate. Since digital images have high redundancy properties, some unnecessary processes will occur when processing images. Compressed sensing just happens to reduce data redundancy. Before data transmission, if the ciphertext image can be further compressed, it can not only improve the efficiency, but also be more suitable for the transmission channel with limited bandwidth. The encrypted image has texture-like or noise-like features, and these features will attract the attention of attackers, which increases the attack rate of encrypted image information during transmission. Image hiding technology may reduce this potential attack threat. Combining with information hiding technology, the original image is encrypted and embedded into the processed carrier image, realizing a visually meaningful image encryption technology. This reduces the possibility of the image being attacked to a certain extent.

On February 19, 2019, the Chinese invention patent with the publication number CN109360141A disclosed an image encryption method based on compressed sensing and three-dimensional cat mapping. First, the initial state value of the three-dimensional cat mapping chaotic system is calculated according to the pixel average value of the plaintext image and system parameters, then scramble the sparse coefficient matrix of the plaintext image, build a measurement matrix and perform compression measurement on the scrambled sparse coefficient matrix to obtain the ciphertext image, based on the carrier image, use the embedding algorithm to embed the ciphertext image into The visually secure image is obtained after the carrier image, which makes the ciphertext image visually safe, and avoids the disadvantages of the difference between the decrypted image and the plaintext image obtained by the frequency domain encryption method. However, in this method, the ciphertext The image is then embedded, and the encryption security still needs to be considered.

Contents of the invention

In order to solve the problem of insufficient encryption security in the current airspace image encryption method based on compressed sensing after compressed sensing, the present invention provides an image encryption method based on integer wavelet transform and compressed sensing, using integer wavelet transform It can achieve reversibility, reduce data loss caused by frequency domain transformation, and improve the encryption security of image information.

In order to achieve the above-mentioned technical effect, the technical scheme of the present invention is as follows:

An image encryption method based on integer wavelet transform and compressed sensing, including:

S1. Select the chaotic system, set the initial value of the chaotic system, determine the plaintext image P whose size is M×N and the pixel sum is S, and preprocess the plaintext image P;

S2. Substitute M, N, S and the initial value into the chaotic system to iterate, generate a random sequence, and obtain a quantized random sequence after preprocessing and quantization;

S3. Perform sparse processing on the preprocessed plaintext image P, and use a quantized random sequence to perform a scrambling operation on the sparsely processed plaintext image P;

S4. Generate a measurement matrix, use the measurement matrix to perform compressed sensing on the plaintext image P after the scrambling operation, and then quantize and merge to obtain D;

S5. Execute the diffusion operation on D to obtain the ciphertext image E;

S6. Introduce the carrier image Q, perform integer wavelet transform on the carrier image to obtain the frequency coefficient, split the ciphertext image E, embed it into the frequency coefficient, and then perform inverse integer wavelet transformation on the frequency coefficient to obtain the final visual security image F.

Preferably, the process of preprocessing the plaintext image P described in step S1 is: dividing the plaintext image P into four sub-images P _i , i=1, 2, 3, 4, i represents the serial number of the sub-image; wherein, Extract the odd rows and odd columns of the plaintext image P to form the first subimage _P1 , extract the odd rows and even columns of the plaintext image P to form the second subimage _P2 , and extract the even rows and odd columns of the plaintext image P to form the third subimage P _3. Extract even-numbered rows and even-numbered columns of the plaintext image P to form a fourth sub-image P ₄ .

Preferably, the initial value of the chaotic system is set to x ₀ , y ₀ , z ₀ , and in step S2, M, N, S and the initial value are substituted into the chaotic system for M×N+S iterations, starting from 1+S Start to take M×N numbers at , and generate three random sequences x, y and z of length M×N. The formula for preprocessing the random sequences x, y and z is:

Among them, x', y', z' represent the preprocessed random sequence, and the formula for continuing to quantify x', y', z' is:

Wherein, X, Y, and Z represent quantized random sequences obtained after quantization processing of x', y', and z'. Here, the random sequence x, y, and z is firstly preprocessed to make it more random, and the subsequent quantization process is mapping. The random sequence generated by the chaotic system is associated with the plaintext image information, which is powerful against known Plaintext attack and chosen plaintext attack.

Preferably, the preprocessed plaintext image P has been divided into four subgraphs P _i , i=1, 2, 3, 4, i represents the serial number of the subgraph, in step S3, for the ith subgraph P of the plaintext image P The formula for sparse processing of _i is:

A _i =Psi×P _i ×Psi'i=1,2,3,4

Among them, Psi represents the sparse basis, which is obtained through the DWT function, and A _i represents the ith subgraph after sparse processing.

Preferably, the process of performing a scrambling operation on the sparsely processed plaintext image P by using a quantized random sequence is:

Sort the quantized random sequence Y to obtain its index sequence SY;

Perform a scrambling operation on the plaintext image P after the sparse processing, and set the plaintext image P after the scrambling operation as _Bi , i=1, 2, 3, 4, satisfying the formula:

B _i (j) = A _i (SY (j));

Among them, j=1, 2, 3..., M/2×N/2.

Preferably, the process of generating the measurement matrix described in step S4 is:

Extract the first M/2 numbers from the quantized random sequence X to form a sequence X', sort the sequence X', and obtain its index sequence SX;

Assuming that the compression ratio of the chaotic system is CR, the Hadamard matrix H is used to generate the measurement matrix, and the formula is:

Phi=H(SX(1:CR*M/2),:)

Among them, Phi represents the measurement matrix, and the random sequence of the chaotic system is used to control the generation of the measurement matrix, which reduces the transmission of the measurement matrix.

Preferably, the plaintext image P after the scrambling operation is expressed as _Bi , i=1, 2, 3, 4, and the formula for performing compressed sensing on the plaintext image P after the scrambling operation is:

C _i =Phi×B _i

Among them, C _i represents the image after compressed sensing, i = 1, 2, 3, 4, and C _i is quantized and combined to obtain D _i , i = 1, 2, 3, 4, integrated into D, where, D _i The solution formula is:

D _i ＝255+255×(C _i -max(C _i (:)))/(max(C _i (:))-min(C _i (:))), although the image has been scrambled , but the total number of pixels has not changed, quantization and merging are performed, and the value of C _i is mapped to [0-255] to prepare for the subsequent embedding operation.

Preferably, the specific process of performing the diffusion operation on D in step S5 to obtain the ciphertext image E is as follows:

Let the size of D be md×nd, and recombine the random sequence Z into a matrix W with size md×nd. When performing the diffusion operation on D, first perform addition and modulo diffusion on D in the row direction, and then carry out the addition and modulo diffusion in the column direction. Add modulo diffusion to get the ciphertext image E, and the process satisfies the formula:

Wherein, p=1, 2, 3,..., md; k=1, 2, 3,..., nd, the diffusion operation further improves the security of image encryption.

Preferably, the size of the carrier image Q in step S6 is 2M×2N, and the integer wavelet transform performed on the carrier image is a two-stage integer wavelet transform, and the size after the two-stage integer wavelet transform is: M/2×N/2 , the obtained frequency coefficients are LL, HL, LH, HH;

Determine the size of the ciphertext image E according to the compression ratio CR of the chaotic system, split the ciphertext image E according to the size of the ciphertext image E, and embed the split ciphertext image E into LL, HL, LH, HH Among the corresponding frequency coefficients, an inverse integer wavelet transform is performed on the frequency coefficients to obtain the final visual safety image F.

Preferably, the inverse integer wavelet transform performed on the frequency coefficients is a quadratic inverse integer wavelet transform.

Here, combined with information hiding technology, the ciphertext image E is embedded into the carrier image Q, which improves the security hiding effect of the image information, and uses integer wavelet transform and inverse integer wavelet transform to achieve reversibility, which can reduce the loss caused by frequency domain transform. resulting in data loss.

Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

The present invention proposes an image encryption method based on integer wavelet transform and compressed sensing. The method preprocesses the plaintext image, then iterates in the chaotic system to generate a random sequence, and obtains a quantized random sequence after preprocessing and quantization. , so that the random sequence has stronger randomness. The random sequence generated by the chaotic system is associated with the plaintext image information, which can effectively resist the known plaintext attack and the chosen plaintext attack; then the preprocessed plaintext image is sparsely processed, and the quantitative The random sequence scrambles the sparsely processed plaintext image to generate a measurement matrix, uses the measurement matrix to perform compressed sensing on the scrambled plaintext image, uses the random sequence of the chaotic system to control the generation of the measurement matrix, and reduces the cost of the measurement matrix. Transmission, before embedding the carrier image, perform a diffusion operation to further improve the security of image encryption, and solve the problem of insufficient encryption security in the current airspace image encryption method based on compressed sensing directly embedding the carrier after compressed sensing. Integer wavelet transform is performed on the carrier image to obtain frequency coefficients, the ciphertext image is split and embedded into the frequency coefficients, and then inverse integer wavelet transformation is performed on the frequency coefficients. Integer wavelet transform can be used to achieve reversibility and reduce the loss caused by frequency domain transformation. Data loss, improving the encryption security of image information.

Description of drawings

Fig. 1 represents the flow chart of the image encryption method based on integer wavelet transform and compressed sensing proposed in the embodiment of the present invention;

Fig. 2 shows a schematic diagram of a specific plaintext image House proposed in the embodiment of the present invention;

Fig. 3 represents the schematic diagram of the ciphertext image that utilizes the image encryption method that the present invention proposes to obtain after encrypting the plaintext image described in Fig. 2;

FIG. 4 shows a schematic diagram of a specific carrier image Pentagon proposed in an embodiment of the present invention;

Fig. 5 shows the schematic diagram of the final visual security image of embedding the ciphertext image into the carrier image in the embodiment of the present invention;

Fig. 6 represents the plaintext image diagram after decrypting the image encrypted by the encryption method proposed by the present invention;

Fig. 7 represents the histogram of the carrier image Pentagon corresponding to Fig. 4;

Figure 8 represents a histogram of the final visual security image;

Fig. 9 shows the histogram of the plaintext image House corresponding to Fig. 2;

Fig. 10 represents the histogram of the ciphertext image;

Fig. 11 shows a histogram of the decrypted plaintext image.

Detailed ways

The accompanying drawings are for illustrative purposes only and cannot be construed as limiting the patent;

In order to better illustrate this embodiment, some parts of the drawings will be omitted, enlarged or reduced, and do not represent the actual size;

For those skilled in the art, it is understandable that some well-known content descriptions in the drawings may be omitted.

The description of the positional relationship in the drawings is for illustrative purposes, and should not be construed as a limitation to this patent;

The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

Example

The image encryption method based on integer wavelet transform and compressed sensing as shown in Figure 1 includes:

S1. Select the chaotic system, set the initial value of the chaotic system, determine the plaintext image P whose size is M×N and the pixel sum is S, and preprocess the plaintext image P; in this embodiment, a specific one is selected The plaintext image is shown in Figure 2.

Specifically, the process of preprocessing the plaintext image P is: divide the plaintext image P into four sub-images Pi, i=1, 2, 3, 4, i represents the serial number of the sub-image; Columns form the first sub-image P ₁ , extract the odd-numbered rows and even-numbered columns of the plaintext image P to form the second sub-image P ₂ , extract the even-numbered rows and odd-numbered columns of the plaintext image P to form the third sub-image P ₃ , and extract the even numbers of the plaintext image P The fourth subgraph P ₄ is composed of rows with even columns; in addition, the initial value of the chaotic system is set to x ₀ =0.067, y ₀ =0.247, z ₀ =0.863;

S2. Substitute M, N, S and the initial value into the chaotic system to iterate, generate a random sequence, and obtain a quantized random sequence after preprocessing and quantization;

M, N, S and the initial value are substituted into the chaotic system for M×N+S iterations, and M×N numbers are taken from 1+S to generate three random sequences x, y of length M×N and z, the formula for preprocessing random sequences x, y and z is:

Among them, x', y', z' represent the preprocessed random sequence, and the formula for continuing to quantify x', y', z' is:

Wherein, X, Y, and Z represent quantized random sequences obtained after quantization processing of x', y', and z'. Here, the random sequence x, y, and z is firstly preprocessed to make it more random, and the subsequent quantization process is mapping. The random sequence generated by the chaotic system is associated with the plaintext image information, which is powerful against known Plaintext attack and chosen plaintext attack.

S3. Perform sparse processing on the preprocessed plaintext image P, and use a quantized random sequence to perform a scrambling operation on the sparsely processed plaintext image P. This step realizes the encryption and hiding of the first layer of image information;

In actual implementation, the four sub-images P _i (i=1, 2, 3, 4) obtained after the block are sparsely processed to obtain A _i (i = 1, 2, 3, 4), and the plaintext image P The formula for sparse processing of the i-th subgraph P _i is:

A _i =Psi×P _i ×Psi'i=1,2,3,4

Among them, Psi represents the sparse basis, which is obtained through the DWT function, and A _i represents the ith subgraph after sparse processing.

Sort the quantized random sequence Y to obtain its index sequence SY;

Perform a scrambling operation on the plaintext image P after the sparse processing, and set the plaintext image P after the scrambling operation as _Bi , i=1, 2, 3, 4, satisfying the formula:

B _i (j) = A _i (SY (j));

Among them, j=1, 2, 3..., M/2×N/2.

S4. Generate a measurement matrix, use the measurement matrix to perform compressed sensing on the plaintext image P after the scrambling operation, and then quantize and merge to obtain D. This step realizes the encryption and hiding of the second layer of image information;

Extract the first M/2 numbers from the quantized random sequence X to form a sequence X', sort the sequence X', and obtain its index sequence SX;

Let the compression ratio of the chaotic system be CR. In this embodiment, CR is 0.5, and the Hadamard matrix H is used to generate the measurement matrix. The formula is:

Phi=H(SX(1:CR*M/2),:)

Among them, Phi represents the measurement matrix, and the random sequence of the chaotic system is used to control the generation of the measurement matrix, which reduces the transmission of the measurement matrix; the plaintext image P after the scrambling operation is expressed as Bi, _i =1, 2, 3, 4, for The formula for compressed sensing of the plaintext image P after the scrambling operation is:

C _i =Phi×B _i

Among them, C _i represents the image after compressed sensing, i = 1, 2, 3, 4, and C _i is quantized and combined to obtain D _i , i = 1, 2, 3, 4, integrated into D, where, D _i The solution formula is:

D _i ＝255+255×(C _i -max(C _i (:)))/(max(C _i (:))-min(C _i (:))), although the image has been scrambled , but the total number of pixels has not changed, quantization and merging are performed, and the value of C _i is mapped to [0-255] to prepare for the subsequent embedding operation.

S5. Perform a diffusion operation on D to obtain the ciphertext image E. This step realizes the encryption and hiding of the first layer of image information. The schematic diagram of the ciphertext image obtained after encryption is shown in FIG. 3 .

Due to the previous scrambling operation, only the position of the pixel in the single block is changed. In order to further improve security, here the integrated image D will be subjected to a diffusion operation, the diffusion operation in the row direction is performed first, and then the diffusion operation in the column direction is performed. Let the size of D be md×nd, and recombine the random sequence Z into a matrix W with size md×nd. When performing the diffusion operation on D, first perform addition and modulo diffusion on D in the row direction, and then carry out the addition and modulo diffusion in the column direction. Add modulo diffusion to get the ciphertext image E, and the process satisfies the formula:

Wherein, p=1, 2, 3,..., md; k=1, 2, 3,..., nd, the diffusion operation further improves the security of image encryption.

S6. Introduce the carrier image Q, perform integer wavelet transform on the carrier image to obtain the frequency coefficient, split the ciphertext image E, embed it into the frequency coefficient, and then perform inverse integer wavelet transformation on the frequency coefficient to obtain the final visual security image F.

In this embodiment, as shown in Figure 4, the carrier image Pentagon is used, and the size of the carrier image is 2M×2N, and the carrier image is subjected to two-level integer wavelet transform, and the integer wavelet transform performed on the carrier image is a second-level integer wavelet Transformation, the size after two-level integer wavelet transformation is: M/2×N/2, and the obtained frequency coefficients are LL, HL, LH, HH;

Determine the size of the ciphertext image E according to the compression ratio CR of the chaotic system, split the ciphertext image E according to the size of the ciphertext image E, and embed the split ciphertext image E into LL, HL, LH, HH Among the corresponding frequency coefficients, since the compression ratio CR=0.5, the size of the ciphertext image E obtained after encrypting the plaintext image P with a size of M×N is M/2×N, and the size of the carrier image Q after two-level integer wavelet transform is The size is M/2×N/2. Therefore, split the ciphertext image E into two matrices E_left and E_right of size M/2×N/2, embed E_left into LH, embed E_right into HH, set the embedding coefficient to α=0.1, and embed the formula for:

Perform inverse integer wavelet transform on LL, HL, LH', HH' to obtain the final visual security image F. This step is also to realize the encryption and hiding of the fourth layer of image information. Figure 5 shows the final visual image of embedding the ciphertext image into the carrier image. The schematic diagram of a secure image, combined with information hiding technology, embeds the ciphertext image E into the carrier image Q, which improves the security hiding effect of image information, and uses integer wavelet transform and inverse integer wavelet transform to achieve reversibility, which can reduce the frequency domain Data loss due to conversion.

In order to further verify the effectiveness, security and the effect of decryption and reconstruction of the method proposed in the present invention, the present invention also continues to combine the visual security image shown in Figure 5, the carrier image shown in Figure 4, and the chaotic system based on the principle of symmetry. The required initial values x ₀ =0.067, y ₀ =0.247, z ₀ =0.863 are used as input for decryption, and the initial values are substituted into the chaotic system for iterative calculation to obtain the key stream, and the key stream is quantified according to the mathematical model. Then carry out the inverse operation, that is, carry out two-level integer wavelet transform on the visual security image F, combine the carrier image Q to extract the ciphertext image, and then perform inverse diffusion, inverse quantization, reconstruction, compressed sensing recovery, and the decrypted plaintext image is as follows: Figure 6 shows the security level, Figure 7 shows the histogram of the carrier image Pentagon in Figure 4, and Figure 8 shows the histogram of the visual security image. It can be seen that the histogram of the carrier image is almost the same as the histogram of the visual image, indicating that the ciphertext image of the present invention has a good hiding effect and strong visual expression. Figure 9 is the histogram of the plaintext image House, and Figure 10 is the ciphertext image The histogram of the text image, it can be seen that the histogram of the plaintext image is ups and downs, and the histogram of the ciphertext image is flat, so the method of the present invention has completely changed the statistical characteristics of the image data, and the encryption effect is good. process, Figure 11 shows the histogram of the decrypted image, it can be seen that it is similar to the histogram of the plaintext image shown in Figure 9, indicating that the decryption reconstruction effect of the present invention is good, in addition the abscissa in the histogram mentioned in the present invention Both represent gray levels, and the ordinate represents the number of pixels.

Apparently, the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limiting the implementation of the present invention. For those of ordinary skill in the art, other changes or changes in different forms can be made on the basis of the above description. It is not necessary and impossible to exhaustively list all the implementation manners here. All modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the claims of the present invention.

Claims (10)

1. An image encryption method based on integer wavelet transform and compressed sensing is characterized by comprising the following steps:

s1, selecting a chaotic system, setting an initial value of the chaotic system, determining a plaintext image P with the size of M multiplied by N, pixels and S, and preprocessing the plaintext image P;

s2, substituting M, N, S and the initial value into the chaotic system for iteration to generate a random sequence, and performing pretreatment and quantization to obtain a quantized random sequence;

s3, performing sparse processing on the preprocessed plaintext image P, and scrambling the sparse processed plaintext image P by using a quantized random sequence;

s4, generating a measurement matrix, performing compressed sensing on the disordered plaintext image P by using the measurement matrix, and then performing quantization and combination to obtain D;

s5, performing diffusion operation on the D to obtain a ciphertext image E;

s6, introducing a carrier image Q, carrying out integer wavelet transformation on the carrier image to obtain a frequency coefficient, splitting a ciphertext image E, embedding the ciphertext image E into the frequency coefficient, and then carrying out inverse integer wavelet transformation on the frequency coefficient to obtain a final visual security image F.

2. The image encryption method based on integer wavelet transform and compressed sensing according to claim 1, wherein the process of preprocessing the plaintext image P in step S1 is as follows: dividing a plaintext picture P into four sub-pictures P _i I =1,2,3,4,i denotes the number of the subgraph; wherein, odd rows and odd columns of the plaintext image P are extracted to form a first sub-image P ₁ Extracting odd-numbered rows and even-numbered columns of the plaintext image P to form a second sub-image P ₂ Extracting the even rows and odd columns of the plaintext image P to form a third sub-image P ₃ Extracting even rows and even columns of the plaintext image P to form a fourth sub-image P ₄ 。

3. The image encryption method based on integer wavelet transform and compressed sensing of claim 2, wherein the initial value of the chaotic system is set as x ₀ ,y ₀ ,z ₀ In step S2, the number of iterations performed by substituting M, N, S and the initial value into the chaotic system is M × N + S times, and M × N numbers are taken from 1+S to generate three random sequences x, y, and z with a length of M × N, where the formula for preprocessing the random sequences x, y, and z is:

wherein, x ', y', z 'represents the random sequence after the pretreatment, and the formula for continuously carrying out the quantization processing on x', y ', z' is as follows:

wherein X, Y and Z represent quantized random sequences obtained after the quantization processing of X ', Y ' and Z '.

4. The method of claim 3The image encryption method based on integer wavelet transform and compressed sensing is characterized in that a preprocessed plaintext image P is divided into four sub-images P _i I =1,2,3,4,i indicates the number of sub-pictures, and in step S3, for the i-th sub-picture P of the plaintext picture P _i The formula for performing the sparse processing is as follows:

A _i ＝Psi×P _i ×Psi' i＝1,2,3,4

where Psi denotes the sparse basis, obtained by DWT function, A _i The ith sub-map after the thinning-out process is shown.

5. The image encryption method based on integer wavelet transform and compressed sensing according to claim 4, characterized in that the process of scrambling the sparsely processed plaintext image P by using the quantized random sequence is as follows:

sequencing Y of the quantized random sequence to obtain an index sequence SY;

scrambling operation is carried out on the plaintext image P after sparse processing, and the plaintext image P after scrambling operation is set to be represented as B _i I =1,2,3,4, satisfying the formula:

B _i (j)＝A _i (SY(j))；

wherein j =1,2,3 …, M/2 × N/2.

6. The image encryption method based on integer wavelet transform and compressed sensing according to claim 5, wherein the process of generating the measurement matrix in step S4 is:

extracting the front M/2 number from the X of the quantized random sequence to form a sequence X ', and sequencing the sequence X' to obtain an index sequence SX;

the compression ratio of the chaotic system is set as CR, a Hadamard matrix H is utilized to generate a measurement matrix, and the formula is as follows:

Phi＝H(SX(1:CR*M/2),:)

where Phi denotes a measurement matrix.

7. The image encryption method based on integer wavelet transform and compressive sensing as claimed in claim 6, whereinThen, the plaintext image P after scrambling operation is represented as B _i I =1,2,3,4, and the expression for compressed sensing of the plaintext image P after scrambling operation is:

C _i ＝Phi×B _i

wherein, C _i Represents the compressed perceived image, i =1,2,3,4, for C _i Carrying out quantization combination to obtain D _i I =1,2,3,4, integrated as D, where D _i The solving formula of (2) is as follows:

D _i ＝255+255×(C _i -max(C _i (:)))/(max(C _i (:))-min(C _i (:)))。

8. the image encryption method based on integer wavelet transform and compressed sensing of claim 7, wherein the step S5 of performing diffusion operation on D to obtain the ciphertext image E comprises the following specific processes:

and (2) setting the size of D as md × nd, recombining the quantized random sequence Z into a matrix W with the size of md × nd, and performing modulo diffusion on D in the row direction and then in the column direction to obtain a ciphertext image E when performing diffusion operation on D, wherein the process meets the formula:

wherein p =1,2,3, …, md; k =1,2,3, …, nd.

9. The image encryption method based on integer wavelet transform and compressed sensing of claim 8, wherein the size of the carrier image Q in step S6 is 2 mx 2N, the integer wavelet transform performed on the carrier image is a secondary integer wavelet transform, and the size of the carrier image Q after the secondary integer wavelet transform is: m/2 XN/2, and the obtained frequency coefficients are LL, HL, LH and HH;

determining the size of a ciphertext image E according to the compression ratio CR of the chaotic system, splitting the ciphertext image E according to the size of the ciphertext image E, embedding the split ciphertext image E into corresponding frequency coefficients of LL, HL, LH and HH, and performing inverse integer wavelet transform on the frequency coefficients to obtain a final visual security image F.

10. The integer wavelet transform and compressed sensing-based image encryption method of claim 9, wherein the inverse integer wavelet transform performed on the frequency coefficients is a quadratic inverse integer wavelet transform.

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