Multi-image authentication method based on fourier pti and double logical mapping

Abstract

The application is based on a multi-image authentication method of Fourier single-pixel imaging and double-logic mapping, and the encryption process is as follows: selecting an initial iteration value and a bifurcation parameter, generating a sequence by using a logic mapping, randomly selecting Fourier space frequencies by using the sequence and averaging grouping, obtaining four groups of Fourier base patterns by four-step phase shifting and differential measurement, irradiating the original target image by using the Fourier base patterns to obtain four groups of illumination intensity values and synthesizing an illumination intensity value sequence, reselecting an initial iteration value and a bifurcation parameter, generating a sequence by using a logic mapping, and performing disordering on the illumination intensity value sequence to obtain a final ciphertext; the decryption process is as follows: performing inverse disordering on the ciphertext by using a second sequence, performing scanning in four groups of values, calculating Fourier frequency spectrum coefficients, performing inverse code on the Fourier frequency spectrum coefficients by using a first sequence, and performing two-dimensional inverse Fourier transform to recover the image, and performing nonlinear correlation authentication on the reconstruction result and the original target image. The problems of long imaging time and low imaging quality are solved.

Description

Technical Field

[0001] This invention belongs to the field of image imaging processing technology, specifically relating to a multi-image authentication method based on Fourier single-pixel imaging and dual logical mapping. Background Technology

[0002] The rapid development of the internet has led to an increasing amount of information being exchanged online. However, when information is transmitted in plaintext, it is highly vulnerable to cyberattacks, posing a significant threat to personal information security and national security. The "encryption-transmission-decryption" transmission model effectively solves this problem. Images, as a typical multimedia carrier, are favored for their intuitiveness and large information capacity, and are also transmitted in large quantities online. Therefore, how to effectively encrypt and decrypt images to ensure the secure transmission of information is receiving increasing attention from researchers.

[0003] Single-pixel imaging differs from traditional array imaging. An imaging system typically consists of a light source, a device capable of generating randomly distributed light intensity (such as a spatial light modulator (SLM), digital micromirror device (DMD), or projector), a lens, and a detector without spatial resolution (also known as a single-pixel detector or barrel detector). From an imaging system perspective, the most significant difference between single-pixel imaging and traditional imaging is that traditional imaging requires expensive pixelated array detectors using silicon as the photosensitive material, such as charge-coupled devices (CCDs) and complementary metal-oxide-semiconductor (CMOS) detectors. Compared to array detectors, single-pixel detectors offer advantages such as high sensitivity, a wide spectral range, and low cost. Therefore, single-pixel imaging technology has significant advantages in low-light and non-visible light band imaging.

[0004] Single-pixel imaging can be categorized into Random Light Single-Pixel Imaging (RLSPI) and Structured Light Single-Pixel Imaging (SLSPI) based on the light source type. RLSPI uses illumination light modulated by a random phase mask (RPM) to illuminate the object and reconstructs the image using an association algorithm. To reconstruct a high-quality image, this method requires multiple single-pixel measurements of the target object under different illumination lights, consuming a significant amount of time and resulting in low imaging efficiency. To reduce the number of measurements, researchers proposed Compressed Sensing Ghost Imaging (CGI), which, based on the principle of compressed sensing, encodes the target image in the sparse domain into a sequence of intensity values ​​using a sensing matrix and reconstructs the image using a convex optimization algorithm. However, common compressed sensing reconstruction algorithms require multiple iterations to solve for the optimal value, consuming considerable time. Therefore, both traditional RLSPI and CGI are methods that sacrifice time for quality and are inefficient. SLSPI uses illumination light modulated by a structured phase mask to illuminate the object; common examples include Hadamard single-pixel imaging, Fourier single-pixel imaging (FSI), and discrete cosine single-pixel imaging. Structured light (such as Hadamard basis patterns, Fourier basis patterns, and discrete cosine basis patterns) has a significantly better imaging quality than RLSPI for the same number of measurements due to its complete orthogonality. However, SLSPI still suffers from low imaging quality and long imaging time. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-image authentication method based on Fourier single-pixel imaging and dual logical mapping, which solves the problems of long imaging time and low imaging quality of existing methods.

[0006] The technical solution adopted in this invention is a multi-image authentication method based on Fourier single-pixel imaging and dual logical mapping, including an encryption process and a decryption process;

[0007] The specific steps of the encryption process are as follows:

[0008] Step 1: Generate a random sequence X using a one-dimensional logical mapping, arrange the random sequence X in ascending order to obtain a new sequence X′, and map the random sequence X to the new sequence X′ to obtain the address code A;

[0009] Step 2, select the Fourier spatial frequency M SF and M SF The upper half is arranged from left to right and from top to bottom to obtain a tuple sequence V composed of spatial frequencies. The tuple sequence V is then mapped to the address code A obtained in step 1 to obtain the sequence V′. After dividing the sequence V′ into L equal groups, L groups of sequences V′ are obtained. (i) ;

[0010] Step 3, convert each sequence V′ obtained in Step 2 into a sequence V′. (i)The grayscale pattern is obtained through the Fourier basis pattern generation formula. An extended grayscale pattern is then obtained using bilinear interpolation. Finally, the Floyd-Steinberg error diffusion dithering algorithm is used to binarize each extended grayscale pattern, resulting in a binarized Fourier sine pattern P. (i) ;

[0011] Step 4, according to each sequence V′ obtained in Step 2 (i) The order is as follows: using the binarized Fourier sine mode P obtained in step 3. (i) For the original target image Q (i) Sequential illumination was performed, and the total response D was collected using a single-pixel detector. (i) ;

[0012] Step 5: Generate a random sequence Y using a one-dimensional logical mapping, sort the random sequence Y in ascending order to obtain a new sequence Y′, and map the random sequence Y to the new sequence Y′ to obtain the address code B;

[0013] Step 6, convert all the original target images Q obtained in Step 4 into... (i) The total response values ​​are concatenated to obtain a real-value sequence consisting of reflected light intensities. The real-value sequence is then mapped to the address code B obtained in step 5 to obtain the ciphertext C.

[0014] The specific steps of the decryption process are as follows:

[0015] Step S1: Generate a random sequence Y using a one-dimensional logical mapping, arrange the random sequence Y in ascending order to obtain a new sequence Y′, and map the random sequence Y to the new sequence Y′ to obtain the address code B;

[0016] Step S2: Perform inverse mapping on the ciphertext C based on the address code B obtained in step S1 to obtain the inverse mapped ciphertext. Divide the inverse mapped ciphertext into L groups, for the original target image Q. (i) The total response D, consisting of the intensity of reflected light, was obtained. (i) ;

[0017] Step S3, take the total response D obtained in step S2. (i) Perform a front-to-back scan, extracting four values ​​as a group, i.e., (D0, D... π / 2 D 3π / 2 D π The Fourier spectrum coefficients F of each extracted value are calculated using formula (7). (i) ;

[0018] F(f x ,f y )={D0(f x ,f y )-D π (fx ,f y )+j[D π / 2 (f x ,f y )-D 3π / 2 (f x ,f y )]} / (2bk) (7)

[0019] In equation (7), k is a factor that depends on the size and position of the detector, b is the contrast, (f x ,f y ) represents the spatial frequency M SF ;

[0020] Step S4: Generate a random sequence X using a one-dimensional logical mapping, and sort the random sequence X′ in ascending order to obtain a new sequence X′. Then, map the random sequence X to the new sequence X′ to obtain the address code A.

[0021] Step S5, take all the Fourier spectrum coefficients F obtained in step S3. (i) The sparse Fourier spectrum coefficient sequence F is obtained by concatenating the sequences. The sparse Fourier spectrum coefficient sequence F is then inversely mapped according to the address code A obtained in step S4 to obtain the inversely mapped sparse Fourier spectrum coefficient sequence. The Fourier spectrum coefficients are then arranged in order from left to right and from top to bottom according to the inversely mapped sparse Fourier spectrum coefficient sequence.

[0022] Step S6: Supplement the Fourier spectral coefficients arranged in step S5 to obtain complete sparse Fourier spectral coefficients. Perform a two-dimensional inverse Fourier transform on the complete sparse Fourier spectral coefficients to obtain a noisy reconstruction result containing information of the original target image.

[0023] Step S7: Perform nonlinear correlation verification on the reconstruction result obtained in step S6 and the original target image;

[0024] Step S8: Post-process the nonlinear correlation certification performed in step S7 to obtain the nonlinear correlation certification graph.

[0025] Step S9: Perform authentication based on the nonlinear correlation authentication map obtained in step S8. If the center of the authentication map has a clear peak or the center intensity value is very prominent compared to other positions, the authentication is successful. If the authentication map is in a chaotic state or there is no clear peak at the center position, the authentication fails, indicating that the image to be authenticated has no relation to the original target image.

[0026] The invention is further characterized in that,

[0027] The specific process of step 1 is as follows:

[0028] Step 1.1: Given the parameters x0 and μ1 of two one-dimensional logical mappings, generate a random sequence X = {x} using formula (1). i |i=1,2,...,MN / 2+K1}, and discard the first K1 values, as shown in formula (1):

[0029] x n+1 =μ1×x n ×(1-x n (1)

[0030] In equation (1), K1 is a positive integer, and MN is the original target image Q. (i) The number of pixels, that is, the length is M pixels and the width is N pixels;

[0031] Step 1.2: Arrange the random sequence X obtained in step 1.1 in ascending order to obtain a new sequence X′. Map the random sequence X to the new sequence X′ to obtain the address code A.

[0032] The specific process of step 3 is as follows:

[0033] Step 3.1, take each sequence V′ obtained in step 2. (i) The Fourier pattern generation formula is as follows: A grayscale mode with M×N pixels is obtained by using the Fourier pattern generation formula.

[0034] P φ (x,y;f x ,f y )=a+b·cos(2πf x x+2πf y y+φ) (2)

[0035] In equation (2), (x, y) represents the spatial coordinates of the pattern; a is the DC term, which is equal to the average intensity value of the pattern; b is the contrast, (f x ,f y ) represents the spatial frequency M SF φ represents the phase;

[0036] Step 3.2: Use bilinear interpolation to upsample each grayscale pattern obtained in Step 3.1 by a factor of d, constructing an extended grayscale pattern with pixels W×H. The extended grayscale pattern is compared with the original target image Q. (i) Same size;

[0037] Step 3.3: Use the Floyd-Steinberg error diffusion jitter algorithm to binarize each extended grayscale mode obtained in Step 3.2, to obtain the binarized Fourier sine mode P. (i) ;

[0038] The expression for binarization using the Floyd-Steinberg error propagation jitter algorithm is:

[0039]

[0040] In equation (3), the pixel marked with * is the currently scanned pixel, and the blank pixel is the previously scanned pixel. After scanning an extended grayscale mode from left to right and from top to bottom, its average quantization error will be close to zero.

[0041] The specific process of step 4 is as follows:

[0042] Step 4.1, according to each sequence V′ obtained in Step 2 (i) The order is as follows: using the binarized Fourier sine mode P obtained in step 3. (i) For the original target image Q (i) Perform sequential irradiation;

[0043] Step 4.2, following the operation in Step 4.1, use formulas (4) and (5) to collect the total response D by the single-pixel detector. (i) ;

[0044] D φ (f x ,f y ) = D n +kE φ (f x ,f y (4)

[0045]

[0046] In equations (4) and (5), D n The response to ambient light illumination is represented by k, which is a factor that depends on the size and position of the detector, Ω represents the lighting scene, and Q(x,y) is the surface reflectance distribution function of the object image.

[0047] The specific process of step 5 is as follows:

[0048] Step 5.1: Given the parameters y0 and μ2 of two one-dimensional logical mappings, generate a random sequence Y = {y0, μ2 ... i |i=1,2,...,MN / 2+K2}, and discard the first K2 values, as shown in formula (6):

[0049] y n+1 =μ2×y n ×(1-y n (6)

[0050] Step 5.2: Arrange the random sequence Y obtained in step 5.1 in ascending order to obtain a new sequence Y′. Map the random sequence Y to the new sequence Y′ to obtain the address code B.

[0051] The specific process of step S1 is as follows:

[0052] Step S1.1: Given the parameters y0 and μ2 of two one-dimensional logical mappings, generate a random sequence Y = {y0, μ2, μ2, μ0 ... i |i=1,2,...,MN / 2+K2}, and discard the first K2 values;

[0053] Step S1.2: Arrange the random sequence Y obtained in step S1.1 in ascending order to obtain a new sequence Y′. Map the random sequence Y to the new sequence Y′ to obtain the address code B.

[0054] The specific process of step 4 is as follows:

[0055] Step S4.1: Given the parameters x0 and μ1 of two one-dimensional logical mappings, generate a random sequence X = {x} using formula (1). i |i=1,2,...,MN / 2+K1}, and discard the first K1 values;

[0056] Step S4.2: Arrange the random sequence X obtained in step S4.1 in ascending order to obtain a new sequence X′. Map the random sequence X to the new sequence X′ to obtain the address code A.

[0057] The specific process of step 6 is as follows:

[0058] Step S6.1: Retain the upper half of the Fourier spectrum coefficients arranged in step S5, and set the lower half coefficients to 0.

[0059] Step S6.2: Based on the upper half of the Fourier spectrum coefficients retained in step S6.1, the lower half of the Fourier spectrum coefficients in step S6.1 is supplemented by the conjugate symmetry of the Fourier spectrum coefficients to obtain the complete sparse Fourier spectrum coefficients.

[0060] Step S6.3: Perform an inverse Fourier transform on the sparse Fourier spectrum coefficients obtained in step S6.2 to obtain a noisy reconstruction result containing information of the original target image. The pixel size of the reconstruction result is M×N.

[0061] The expression for the inverse Fourier transform is:

[0062] O(x,y)=F -1 {F(μ,ν)} (8)

[0063] In equation (8), F -1{·} denotes the two-dimensional inverse Fourier transform, and (μ,ν) are the Fourier domain coordinates.

[0064] The specific process of step S7 is as follows:

[0065] Step S7.1: Based on the reconstruction result obtained in step S6, perform d-fold downsampling on the original target image with pixels W×H;

[0066] Step S7.2: Perform nonlinear correlation authentication between the downsampled original target image obtained in step S7.1 and the original target image, expressed as:

[0067]

[0068] In equation (9), For the downsampled original target image, Q′ (i) This is the result of the reconstruction.

[0069] The expression for post-processing in step S8 is:

[0070] NC(NC<((MAX(NC)-MIN(NC))*0.6)+MIN(NC))=0 (10)

[0071]

[0072] In equations (10) and (11), MAX(·) and MIN(·) represent the maximum and minimum functions, respectively. This is the enhancement coefficient.

[0073] The beneficial effects of this invention are:

[0074] (1) The method of the present invention randomly samples the target image to be verified based on the spatial frequency distribution of a small size, and uses the Floyd-Steinberg error diffusion jitter algorithm to convert the Fourier sinusoidal mode generated at each frequency into a binarized illumination mode. In the process of ciphertext generation, two chaotic sequences are used to randomly select the spatial frequency of each object image and shuffle all the measurement values, which greatly improves the measurement efficiency.

[0075] (2) The method of the present invention uses the initial value, bifurcation parameter and discard value of the logical mapping as the key, which can greatly improve the security of the cryptographic system. Attached Figure Description

[0076] Figure 1 This is a framework diagram of the encryption process of the multi-image authentication method based on Fourier single-pixel imaging and dual logical mapping of the present invention;

[0077] Figure 2This is a framework diagram of the decryption process of the multi-image authentication method based on Fourier single-pixel imaging and dual logical mapping of the present invention;

[0078] Figure 3 The original target image is shown in the experimental diagram of the multi-image authentication method based on Fourier single-pixel imaging and dual logical mapping of this invention.

[0079] Figure 4 This is a ciphertext distribution diagram of the multi-image authentication method based on Fourier single-pixel imaging and dual logical mapping of the present invention;

[0080] Figure 5 This is a decryption image-correlation distribution diagram of the multi-image authentication method based on Fourier single-pixel imaging and dual logical mapping of the present invention. Detailed Implementation

[0081] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0082] This invention relates to a multi-image authentication method based on Fourier single-pixel imaging and dual logical mapping, including an encryption process and a decryption process;

[0083] like Figure 1 As shown, the specific steps of the encryption process are as follows:

[0084] Step 1: Generate a random sequence X using a one-dimensional logical mapping, arrange the random sequence X in ascending order to obtain a new sequence X′, and map the random sequence X to the new sequence X′ to obtain the address code A;

[0085] Step 1.1: Given the parameters x0 and μ1 of two one-dimensional logical mappings, generate a random sequence X = {x} using formula (1). i |i=1,2,...,MN / 2+K1}, and discard the first K1 values, as shown in formula (1):

[0086] x n+1 =μ1×x n ×(1-x n (1)

[0087] In equation (1), K1 is a positive integer, and MN is the original target image Q. (i) The number of pixels, that is, the length is M pixels and the width is N pixels;

[0088] Step 1.2: Arrange the random sequence X obtained in step 1.1 in ascending order to obtain a new sequence X′. Map the random sequence X to the new sequence X′ to obtain the address code A.

[0089] Step 2, select the Fourier spatial frequency M SF and M SFThe sequence is arranged to obtain a tuple sequence V composed of spatial frequencies. The tuple sequence V is then mapped to the address code A obtained in step 1 to obtain sequence V′. Sequence V′ is then processed as follows: Figure 3 After being divided into L groups as shown, L groups of sequences V′ are obtained. (i) ;

[0090] Step 2.1, select the Fourier spatial frequency M SF The upper half is arranged from left to right and from top to bottom to obtain a tuple sequence V composed of spatial frequencies. The tuple sequence V is then mapped to the address code A obtained in step 1 to obtain the sequence V′.

[0091] Step 2.2: Divide the sequence V′ obtained in Step 2.1 into L groups, specifically 4 groups, to obtain L groups of sequences V′. (i) Then V′ (i) Spatial frequencies are assigned to groups in the original target image Q. (i) ;

[0092] Step 3, convert each sequence V′ obtained in Step 2 into a sequence V′. (i) The grayscale pattern is obtained through the Fourier basis pattern generation formula. An extended grayscale pattern is then obtained using bilinear interpolation. Finally, the Floyd-Steinberg error diffusion dithering algorithm is used to binarize each extended grayscale pattern, resulting in a binarized Fourier sine pattern P. (i) ;

[0093] Step 3.1, take each sequence V′ obtained in step 2. (i) The Fourier pattern generation formula is as follows: A grayscale mode with M×N pixels is obtained by using the Fourier pattern generation formula.

[0094] P φ (x,y;f x ,f y )=a+b·cos(2πf x x+2πf y y+φ) (2)

[0095] In equation (2), (x, y) represents the spatial coordinates of the pattern; a is the DC term, which is equal to the average intensity value of the pattern; b is the contrast, (f x ,f y ) represents the spatial frequency M SF φ represents the phase;

[0096] Step 3.2: Use bilinear interpolation to upsample each grayscale pattern obtained in Step 3.1 by a factor of d, constructing an extended grayscale pattern with pixels W×H. The extended grayscale pattern is compared with the original target image Q. (i) They are the same size, i.e., W×H=M×N;

[0097] Step 3.3: Use the Floyd-Steinberg error diffusion jitter algorithm to binarize each extended grayscale mode obtained in Step 3.2, to obtain the binarized Fourier sine mode P. (i) ;

[0098] The expression for binarization using the Floyd-Steinberg error propagation jitter algorithm is:

[0099]

[0100] In equation (3), the pixel marked with * is the currently scanned pixel, and the blank pixel is the previously scanned pixel. After scanning an extended grayscale mode from left to right and from top to bottom, its average quantization error will be close to zero.

[0101] Step 4, according to each sequence V′ obtained in Step 2 (i) The order is as follows: using the binarized Fourier sine mode P obtained in step 3. (i) For the original target image Q (i) Sequential illumination was performed, and the total response D was collected using a single-pixel detector. (i) ;

[0102] Step 4.1, according to each sequence V′ obtained in Step 2 (i) The order is as follows: using the binarized Fourier sine mode P obtained in step 3. (i) For the original target image Q (i) Perform sequential irradiation, that is, in sequence V′ (i) Lighting P (i) model;

[0103] Step 4.2, following the operation in Step 4.1, use formulas (4) and (5) to collect the total response D by the single-pixel detector. (i) ;

[0104] D φ (f x ,f y ) = D n +kE φ (f x ,f y (4)

[0105]

[0106] In equations (4) and (5), D n The response to ambient light illumination is represented by k, which is a factor that depends on the size and position of the detector, Ω represents the illumination scene, and Q(x,y) is the surface reflectance distribution function of the object image.

[0107] Through the above steps, the original target image Q (i) Random sampling was implemented, that is, the Fourier spectrum of the target image was obtained randomly;

[0108] Step 5: Generate a random sequence Y using a one-dimensional logical mapping, sort the random sequence Y in ascending order to obtain a new sequence Y′, and map the random sequence Y to the new sequence Y′ to obtain the address code B;

[0109] Step 5.1: Given the parameters y0 and μ2 of two one-dimensional logical mappings, generate a random sequence Y = {y0, μ2 ... i |i=1,2,...,MN / 2+K2}, and discard the first K2 values, as shown in formula (6):

[0110] y n+1 =μ2×y n ×(1-y n (6)

[0111] Step 5.2: Arrange the random sequence Y obtained in step 5.1 in ascending order to obtain a new sequence Y′. Map the random sequence Y to the new sequence Y′ to obtain the address code B.

[0112] Step 6, convert all the original target images Q obtained in Step 4 into... (i) The total response values ​​are concatenated to obtain a real-valued sequence consisting of reflected light intensities. This real-valued sequence is then mapped to the address code B obtained in step 5 to obtain, as shown below. Figure 4 The ciphertext C shown is obtained by using parameter x as the key. 01 μ1, K1 and parameter x 02 μ2, K2;

[0113] like Figure 2 As shown, the specific steps of the decryption process are as follows:

[0114] Step S1: Generate a random sequence Y using a one-dimensional logical mapping, arrange the random sequence Y in ascending order to obtain a new sequence Y′, and map the random sequence Y to the new sequence Y′ to obtain the address code B;

[0115] Step S1.1: Given the parameters y0 and μ2 of two one-dimensional logical mappings, generate a random sequence Y = {y0, μ2, μ2, μ0 ... i |i=1,2,...,MN / 2+K2}, and discard the first K2 values;

[0116] Step S1.2: Arrange the random sequence Y obtained in step S1.1 in ascending order to obtain a new sequence Y′. Map the random sequence Y to the new sequence Y′ to obtain the address code B.

[0117] Step S2: Perform inverse mapping on the ciphertext C based on the address code B obtained in step S1 to obtain the inverse mapped ciphertext. Divide the inverse mapped ciphertext into L groups on average. For the original target image Q... (i) The total response D, consisting of the intensity of reflected light, was obtained. (i) ;

[0118] Step S3, take the total response D obtained in step S2. (i) Perform a front-to-back scan, extracting four values ​​as a group, i.e., (D0, D... π / 2 D 3π / 2 D π The Fourier spectrum coefficients F of each extracted set of values ​​are calculated using formula (7). (i) ;

[0119] F(f x ,f y )={D0(f x ,f y )-D π (f x ,f y )+j[D π / 2 (f x ,f y )-D 3π / 2 (f x ,f y )]} / (2bk) (7)

[0120] In equation (7), k is a factor that depends on the size and position of the detector, b is the contrast, (f x ,f y ) represents the spatial frequency M SF ;

[0121] Step S4: Generate a random sequence X using a one-dimensional logical mapping, and sort the random sequence X′ in ascending order to obtain a new sequence X′. Then, map the random sequence X to the new sequence X′ to obtain the address code A.

[0122] Step S4.1: Given the parameters x0 and μ1 of two one-dimensional logical mappings, generate a random sequence X = {x} using formula (1). i |i=1,2,...,MN / 2+K1}, and discard the first K1 values;

[0123] Step S4.2: Arrange the random sequence X obtained in step S4.1 in ascending order to obtain a new sequence X′. Map the random sequence X to the new sequence X′ to obtain the address code A.

[0124] Step S5, take all the Fourier spectrum coefficients F obtained in step S3. (i)The sparse Fourier spectrum coefficient sequence F is obtained by concatenating the sequences. The sparse Fourier spectrum coefficient sequence F is then inversely mapped according to the address code A obtained in step S4 to obtain the inversely mapped sparse Fourier spectrum coefficient sequence. The Fourier spectrum coefficients are then arranged in order from left to right and from top to bottom according to the inversely mapped sparse Fourier spectrum coefficient sequence.

[0125] Step S6: Supplement the Fourier spectral coefficients arranged in step S5 to obtain complete sparse Fourier spectral coefficients. Perform a two-dimensional inverse Fourier transform on the complete sparse Fourier spectral coefficients to obtain a noisy reconstruction result containing information of the original target image.

[0126] Step S6.1: Retain the upper half of the Fourier spectrum coefficients arranged in step S5, and set the lower half coefficients to 0.

[0127] Step S6.2: Based on the upper half of the Fourier spectrum coefficients retained in step S6.1, the lower half of the Fourier spectrum coefficients in step S6.1 is supplemented by the conjugate symmetry of the Fourier spectrum coefficients to obtain the complete sparse Fourier spectrum coefficients.

[0128] Step S6.3: Perform an inverse Fourier transform on the sparse Fourier spectrum coefficients obtained in step S6.2 to obtain a noisy reconstruction result containing information of the original target image. The pixel size of the reconstruction result is M×N.

[0129] The expression for the inverse Fourier transform is:

[0130] O(x,y)=F -1 {F(μ,ν)} (8)

[0131] In equation (8), F -1 {·} denotes the two-dimensional inverse Fourier transform, and (μ,ν) are the Fourier domain coordinates;

[0132] Step S7: Perform nonlinear correlation verification on the reconstruction result obtained in step S6 and the original target image;

[0133] Step S7.1: Based on the reconstruction result obtained in step S6, the original target image with pixels W×H is downsampled by a factor of d, where W×H=M×N;

[0134] Step S7.2: Perform nonlinear correlation authentication between the downsampled original target image obtained in step S7.1 and the original target image, expressed as:

[0135]

[0136] In equation (9), For the downsampled original target image, Q′ (i) The result of the reconstruction;

[0137] Step S8: Post-process the nonlinear correlation certification performed in step S7 to obtain a nonlinear correlation certification map. In this certification map, only the relative value of each pixel is changed to highlight the maximum peak value in the map.

[0138] The post-processing expression is:

[0139] NC(NC<((MAX(NC)-MIN(NC))*0.6)+MIN(NC))=0 (10)

[0140]

[0141] In equations (10) and (11), MAX(·) and MIN(·) represent the maximum and minimum functions, respectively. For enhancement coefficient;

[0142] Step S9: Perform authentication based on the nonlinear correlation authentication map obtained in step S8. If the center of the authentication map has a clear peak or the center intensity value is very prominent compared to other positions, the authentication is successful. If the authentication map is in a chaotic state or there is no clear peak at the center position, the authentication fails, indicating that the image to be authenticated has no relation to the original target image.

[0143] In the experiment, Fourier single-pixel imaging was used on the original target image, with a sampling ratio less than 5% of the Nyquist limit, to verify the reconstructed object image. Figure 5 As can be seen, there is a distinct spike in the center of each of the authentication images, indicating that all four sets of images were successfully authenticated.

Claims

1. A multi-image authentication method based on Fourier ptychographic imaging and double logistic mapping, characterized in that, The encryption process and the decryption process are included; The specific steps of the encryption process are: Step 1, generate a random sequence using one-dimensional logical mapping X and arrange the random sequence X in ascending order to obtain a new sequence and map the random sequence X with the new sequence to obtain an address code A; Step 2, select the Fourier space frequency and The upper half is arranged in the order of left to right and top to bottom to obtain a tuple sequence composed of space frequencies , and the tuple sequence is mapped according to the address code A obtained in step 1 to obtain a sequence , the sequence is divided into L groups on average to obtain L group sequences ; Step 3: obtaining each group of sequences from step 2 The gray scale pattern is obtained by a Fourier base pattern generation formula, the extended gray scale pattern is obtained by using a bilinear interpolation algorithm on the gray scale pattern, and the binary Fourier sine pattern is obtained by using a Floyd-Steinberg error diffusion dithering algorithm on each extended gray scale pattern ; Step 4, each set of sequences obtained in step 2 is subjected to the binary Fourier sine pattern obtained in step 3 in sequence The original target image is sequentially illuminated and the total response is collected with a single pixel detector ; Step 5, generate random sequence using one-dimensional logical mapping Y and sort the random sequence Y in ascending order to get a new sequence and map the random sequence Y with the new sequence to get address code B; Step 6: Combine all the original target images obtained in Step 4. The total response values ​​are concatenated to obtain a real-valued sequence consisting of reflected light intensities. This real-valued sequence is then mapped to the address code B obtained in step 5 to obtain the ciphertext. ; The specific steps of the decryption process are: Step S1, generate a random sequence using one-dimensional logical mapping Y , and arrange the random sequence Y in ascending order to obtain a new sequence , and map the random sequence Y with the new sequence to obtain an address code B; Step S2: Pair the ciphertext with the address code B obtained in step S1. Perform an inverse mapping to obtain the inverse-mapped ciphertext. Divide the inverse-mapped ciphertext into L groups for the original target image. The total response, consisting of the intensity of reflected light, was obtained. ; Step S3, calculating the Fourier spectrum coefficients of each group of values extracted from the total response obtained in step S2 The forward-to-backward scan is performed, extracting a group of four values at a time, i.e. The Fourier spectrum coefficients of each group of values extracted are calculated by equation (7) ; （7） In formula (7), is a factor depending on the size and position of the detector, is the contrast, is the spatial frequency ; Step S4, generating a random sequence using one-dimensional logical mapping X , and arranging the random sequence in ascending order to obtain a new sequence , and mapping the random sequence X with the new sequence to obtain an address code A; Step S5: Calculate all the Fourier spectrum coefficients obtained in step S3. By concatenating the series, a sparse Fourier spectral coefficient sequence is obtained. F Based on the address code A obtained in step S4, the sparse Fourier spectrum coefficient sequence F Perform an inverse mapping to obtain the sparse Fourier spectrum coefficient sequence after inverse mapping. Arrange the Fourier spectrum coefficients from left to right and from top to bottom according to the sparse Fourier spectrum coefficient sequence after inverse mapping. Step S6, the Fourier spectrum coefficients arranged in step S5 are supplemented to obtain complete sparse Fourier spectrum coefficients, and inverse two-dimensional Fourier transform is performed on the complete sparse Fourier spectrum coefficients to obtain a noisy reconstruction result containing original target image information; Step S7, the reconstruction result obtained in step S6 is subjected to nonlinear correlation authentication with the original target image; Step S8, the nonlinear correlation authentication performed in step S7 is post-processed to obtain a nonlinear correlation authentication graph; Step S9, authentication is performed according to the nonlinear correlation authentication graph obtained in step S8, if there is a sharp peak in the center of the authentication graph or the center intensity value is very prominent relative to other positions, the authentication is successful; if the authentication graph is in a chaotic state or there is no obvious peak in the center position, the authentication fails, indicating that the image to be authenticated has no correlation with the original target image. 2.The multi-image authentication method based on Fourier ptychographic imaging and double-logic mapping of claim 1, wherein, The specific process of step 1 is: Step 1.1, given the parameters of two one-dimensional logical mappings and , generate a random sequence by equation (1) and discard the first values, equation (1) is as follows: （1） In formula (1), is a positive integer, MN is the pixel number of the original target image , that is, M pixels in length and N pixels in width; Step 1.

2. Arrange the random sequence X obtained in step 1.1 in ascending order to obtain a new sequence Map the random sequence X with the new sequence to obtain the address code A. 3.The multi-image authentication method based on Fourier ptychographic imaging and double-logic mapping of claim 1, wherein, The specific process of step 3 is: Step 3.1, each set of sequences obtained in Step 2 is subjected to the following operation The gray pattern of pixels is obtained by the Fourier base pattern generation formula The Fourier base pattern generation formula is as follows; （2） In formula (2), represents the spatial coordinates of the pattern; is the direct current term, equal to the average intensity value of the pattern; is the contrast, is the spatial frequency , is the phase; Step 3.2: Use the bilinear interpolation algorithm to process each grayscale pattern obtained in Step 3.

1. Double upsampling, constructing a pixel with Extended grayscale mode, extended grayscale mode and original target image Same size; Step 3.3, binarize each extended gray scale pattern obtained in step 3.2 using Floyd-Steinberg error diffusion dithering algorithm to obtain a binarized Fourier sinusoidal pattern ; The expression for using the Floyd-Steinberg error diffusion dithering algorithm for binarization is: （3） In formula (3), The marked pixel is the pixel currently being scanned, and the blank pixel is the pixel previously scanned, and the average quantization error of which will be close to zero after scanning an extended gray scale mode from left to right and from top to bottom. 4.The multi-image authentication method based on Fourier ptychographic imaging and double-logic mapping of claim 1, wherein, The specific process of step 4 is: Step 4.

1. For each set of sequences obtained in step 2 in sequence, the binary Fourier sinusoidal patterns obtained in step 3 are sequentially illuminated on the original target image are sequentially illuminated on the original target image Step 4.

2. Collect total response from single-pixel detector following the procedure of Step 4.1 using Equation (4) and Equation (5) ; （4） （5） in formula (4) and formula (5), a response indicative of ambient lighting, is a factor dependent on the size and position of the detector, is a lighting scene, is a surface reflectance distribution function of the object image; indicates that the pixel is in a gray scale mode, indicates that the pixel is in a binary mode. 5.The multi-image authentication method based on Fourier ptychographic imaging and double-logic mapping of claim 1, wherein, The specific process of step 5 is: Step 5.1, given the parameters of two one-dimensional logical mappings y 0 and , generate a random sequence by formula (6) , and discard the first values, MN is the number of pixels of the original target image , formula (6) is as follows: （6） Step 5.

2. Map the random sequence obtained in step 5.1 Y In ascending order, obtaining a new sequence Map the random sequence Y with the new sequence obtaining the address code B. 6.The multi-image authentication method based on Fourier ptychographic imaging and double-logic mapping of claim 5, wherein, The specific process of step S1 is: Step S1.1, given the parameters of two one-dimensional logical mappings y 0 and , generate a random sequence by equation (6) and discard the first values; Step S1.

2. mapping the random sequence obtained in step S1.1 Y in ascending order, obtaining a new sequence Step S1.

3. mapping the random sequence Y with the new sequence obtaining the address code B. 7.The multi-image authentication method based on Fourier ptychographic imaging and double-logic mapping of claim 2, wherein, The specific process of step S4 is: Step S4.1, given the parameters of two one-dimensional logical mappings and generate a random sequence by equation (1) and discard the first values; Step S4.

2. mapping the random sequence obtained in step S4.1 X in ascending order, obtaining a new sequence mapping the random sequence X with the new sequence obtaining an address code A. 8.The multi-image authentication method based on Fourier ptychographic imaging and double-logic mapping of claim 1, wherein, The specific process of step S6 is: Step S6.1, the upper half of the Fourier spectrum coefficients arranged in step S5 is retained, and the lower half of the coefficients is set to 0; Step S6.2, the lower half of the Fourier spectrum coefficients in step S6.1 is supplemented according to the upper half of the Fourier spectrum coefficients retained in step S6.1 through the conjugate symmetry of the Fourier spectrum coefficients to obtain complete sparse Fourier spectrum coefficients; Step S6.3, inverse Fourier transform the sparse Fourier spectrum coefficients obtained in step S6.2 to obtain a noisy reconstruction result containing the original target image information, the pixel size of the reconstruction result being ; The expression of inverse Fourier transform is: （8） In formula (8), denotes a two-dimensional inverse Fourier transform, is a Fourier domain coordinate. 9.The multi-image authentication method based on Fourier ptychographic imaging and double-logic mapping of claim 1, wherein, The specific process of step S7 is: Step S7.1: Based on the reconstruction result obtained in step S6, for pixels... The original target image is processed Downsampling; Step S7.2, the original target image obtained in step S7.1 is subjected to nonlinear correlation authentication with the original target image, and the expression is: （9） In formula (9), is a down-sampled original target image, is a reconstruction result.

10. The multi-image authentication method based on Fourier ptychographic imaging and double-logic mapping of claim 1, wherein, The expression of post-processing in step S8 is: （10） （11） In formula (10) and formula (11), and respectively represent the maximum function and the minimum function, is an enhancement coefficient.

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