CN108846816B - Ciphertext domain image restoration method - Google Patents

Ciphertext domain image restoration method Download PDF

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CN108846816B
CN108846816B CN201810634763.XA CN201810634763A CN108846816B CN 108846816 B CN108846816 B CN 108846816B CN 201810634763 A CN201810634763 A CN 201810634763A CN 108846816 B CN108846816 B CN 108846816B
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damaged
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CN108846816A (en
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孙佳忆
秦川
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University of Shanghai for Science and Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
    • G06F21/60—Protecting data
    • G06F21/602—Providing cryptographic facilities or services
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/10—Image enhancement or restoration by non-spatial domain filtering

Abstract

The invention provides a ciphertext domain image repairing method, which is used for repairing a damaged image generated by the damage of a mask image in a ciphertext domain, and has the following characteristics that: step one, obtaining an encrypted image E to be repairedPAuxiliary encrypted image EJAnd a mask image θ; step two, treating the repaired encrypted image E through the mask image thetaPMarking to obtain a damaged region omega and a complete region phi; step three, calculating the priority of the pixel c to be repaired in the damaged region omega by taking a block as a unit to obtain a target block with the highest priority
Figure DDA0001700846190000011
Step four, in the auxiliary encryption image EJWith the aid of a target block
Figure DDA0001700846190000013
All candidate blocks B with good area phiSPerforming block matching to obtain the best matching block
Figure DDA0001700846190000014
Step five, using the best matching block
Figure DDA0001700846190000012
For target block
Figure DDA0001700846190000015
Repairing to select initial repairing encrypted image EP1(ii) a Step six, respectively carrying out pair of auxiliary encrypted images EJUpdating the damaged region omega and the intact region phi; step seven, repeatStep two to step six, until all the damaged regions omega are repaired to obtain a repaired encrypted image E'P。

Description

Ciphertext domain image restoration method
Technical Field
The invention relates to an image restoration method, in particular to a ciphertext domain image restoration method.
Background
Image restoration techniques are used in many applications. Such as removing unwanted objects or regions, filling in missing parts of images, and is also widely used in computer vision, including image restoration, compression, editing, and merging. Image inpainting techniques are also extended to image-related applications, such as composite video and animation. The current image restoration techniques are mainly classified into three categories: interpolation-based methods (e.g., FMM algorithms), partial differential equation-based methods (e.g., TV algorithms), and sample/block-based methods (e.g., Criminisi algorithms).
Today, as the internet evolves, cloud storage and computing become prevalent. Due to limited storage space and computing capacity, a user can upload own multimedia data (such as images, videos and the like) to the cloud end and outsource various data processing work to the cloud server to realize the data processing. However, although cloud computing brings convenience, since users generally desire to protect data privacy, security issues are also raised. Thus, one safe and reasonable solution is to encrypt the data before it is uploaded to the cloud, and the cloud server can process the data in the ciphertext domain. Then, after the user decrypts the received data from the cloud server, the data can obtain an ideal effect in a clear text domain. Based on such application scenarios and requirements, in recent years, processing of ciphertext domain signals has been extensively studied. However, research on restoration of images has been focused on the plaintext field, and has not been related to the ciphertext field.
Disclosure of Invention
The invention aims to solve the problem of how to repair an encrypted image in a ciphertext domain, and provides a ciphertext domain image repairing method.
The invention provides a ciphertext domain image repairing method, which is used for repairing a damaged image generated by the damage of a mask image in a ciphertext domain, and has the following characteristics that: step one, obtaining an encrypted image E to be repairedPAuxiliary encrypted image EJAnd a mask image θ; step two, treating the repaired encrypted image E through the mask image thetaPMarking to obtain the omega sum of the damaged areaA good area phi; step three, calculating the priority of the pixel c to be repaired in the damaged region omega by taking a block as a unit to obtain a target block with the highest priority
Figure BDA0001700846170000021
Step four, in the auxiliary encryption image EJWith the aid of a target block
Figure BDA0001700846170000022
All candidate blocks B with good area phiSPerforming block matching to find the best matching block in the good region phi
Figure BDA0001700846170000023
Step five, using the best matching block
Figure BDA0001700846170000024
For target block
Figure BDA0001700846170000025
Repairing is performed so that the encrypted image E to be repaired isPUpdating to an initial repair encrypted image EP1(ii) a Step six, respectively carrying out pair of auxiliary encrypted images EJUpdating the damaged region omega and the intact region phi; step seven, repeating the step two to the step six until all the damaged areas omega are repaired to obtain a repaired encrypted image E'PRepair encrypted image E'PEncrypting an image E for repairPThe repair result of (1).
The ciphertext domain image restoration method provided by the invention also has the following characteristics: wherein, in the fourth step, the target block is divided into
Figure BDA0001700846170000026
And candidate block BSPerforming block matching to obtain the best matching block
Figure BDA0001700846170000027
The process comprises the following steps: according to the auxiliary encrypted image EJCalculating a target block by the following formula
Figure BDA0001700846170000028
With each candidate block BSThe distance between the two or more of the two or more,
Figure BDA0001700846170000031
(x, y) represents candidate block BSRelative to the target block
Figure BDA0001700846170000038
Coordinate displacement of (B)S∈Φ，
Figure BDA0001700846170000032
Figure BDA0001700846170000033
And
Figure BDA0001700846170000037
respectively representing auxiliary encrypted images EJTwo middle pixels m (i)1,j1) And m (i)2,j2) Selecting a distance target block from the encrypted value
Figure BDA0001700846170000039
The most recent candidate block BSAs the best matching block
Figure BDA00017008461700000310
The ciphertext domain image restoration method provided by the invention also has the following characteristics: wherein, in the third step, the target block is obtained from the damaged region omega
Figure BDA00017008461700000311
The process comprises the following steps: block priority O centered on pixel c to be repairedcIs composed of
Figure BDA0001700846170000034
Representing a block B of size l x l centred on the pixel c to be repairedcThe number of the medium good pixels,
Figure BDA0001700846170000035
indicating that the pixel c to be repaired is located at the boundary of the damaged region omega
Figure BDA0001700846170000036
Up, select block priority OcBlock B with the largest valuecAs a target block
Figure BDA00017008461700000312
The ciphertext domain image restoration method provided by the invention also has the following characteristics that: step eight, restoring the encrypted image E'PCarrying out local weighted mean filtering processing to obtain an optimized encrypted image E ″P。
The ciphertext domain image restoration method provided by the invention also has the following characteristics: wherein the encrypted image E to be repairedPIs composed of damaged image IdAnd carrying out encryption processing by a Paillier encryption algorithm to obtain an image.
The ciphertext domain image restoration method provided by the invention also has the following characteristics: wherein the auxiliary encrypted image EJIs composed of damaged image IdAnd (3) obtaining an image after Johnson Lindenstaus transformation encryption processing.
The ciphertext domain image restoration method provided by the invention also has the following characteristics: wherein, the damaged image IdObtaining an auxiliary encrypted image EJThe process comprises the following steps: will be damaged image IdEach pixel m (i, j) of the image sensor, and s-1 pixels around the pixel m (i, j) form an s-pixel block; constructing an s-dimensional vector N for pixels in an s-pixels blocki,j(ii) a Using the key kJRandom matrix of size kxs
Figure BDA0001700846170000041
And random k-dimensional noise vector σ vs vector Ni,jThe vector L is obtained by encryptioni,jThe vector Li,jAs an encryption result of one pixel m (i, j),
Figure BDA0001700846170000042
will be damaged image IdAll pixels m (i, j) of (a) to (b) correspond to a vector Li,jAs an auxiliary encrypted image EJ。
Action and Effect of the invention
According to the ciphertext domain image restoration method, the encrypted image E to be restored is obtainedPAuxiliary encrypted image EJAnd after masking the image theta, treating the repaired encrypted image E through the mask image thetaPMarking to obtain a damaged region omega and a sound region phi, and determining a target block of the damaged region omega
Figure BDA0001700846170000043
In the auxiliary encryption image EJWith the assistance of (1) finding the best matching block of good region phi by block matching
Figure BDA0001700846170000044
Then using the best matching block
Figure BDA0001700846170000045
For target block
Figure BDA0001700846170000046
Repairing to update encrypted image E to be repairedPAuxiliary encrypted image EJDamaged region omega and sound region phi, repeating the repair process until a repaired encrypted image E 'is obtained'PThe process is completely carried out in the ciphertext domain, the plaintext information of the image cannot be leaked, the privacy is strong, a good image restoration effect can be obtained, the method has a wide application prospect, and the method is particularly suitable for transmission and restoration of the image information in the cloud computing process.
Drawings
FIG. 1 is a flow chart of a ciphertext domain image restoration method in an embodiment of the invention;
FIG. 2 is a graph comparing the repairing effect of the experimental group 1;
FIG. 3 is a graph comparing the repairing effect of experiment group 2; and
fig. 4 shows 7 images selected from the image library.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the present invention easy to understand, the following embodiments specifically describe the ciphertext domain image restoration method of the present invention with reference to the accompanying drawings.
An image restorer (such as a cloud server with strong computing power) treats the restored encrypted image E according to the ciphertext domain image restoration method related to the embodimentPThe encrypted image E to be repaired needs to be obtained from the image owner before being repaired in the ciphertext domainPAuxiliary encrypted image EJAnd a mask image theta.
The image owner holds a damaged image IdAnd a mask image theta. Wherein the mask image theta is based on the damaged image IdDerived images I for marking damaged imagesdImages of damaged and sound areas. Since the image owner wants the image restorer to correct the damaged image I in the ciphertext domaindRepair is performed, so an image owner is required for the damaged image IdEncryption is carried out, and the specific process of encryption is as follows:
firstly, the damaged image IdEncrypted image E to be repaired is obtained by encrypting through Paillier encryption algorithmPThe encrypted image to be restored EPAs the object of the repair. In the present embodiment, the damaged image IdThe Paillier encryption algorithm is adopted for encryption, so that the Paillier encryption algorithm is also adopted for decryption in subsequent decryption. In practical application, damaged image IdOther algorithms can be used for encryption, and the subsequent decryption process also adopts the corresponding algorithm for decryption.
Secondly, the damaged image IdThe auxiliary encryption image E is obtained by encrypting through Johnson Lindenstaus graphic transformation algorithm (JL algorithm for short)J。
Wherein, the damaged image IdObtaining an auxiliary encrypted image EJThe process comprises the following steps:
(1) will be damaged image IdIs given by pixel m (i, j)An s-pixel block is formed for the center and the surrounding s-1 pixels.
(2) Constructing an s-dimensional vector N for pixels in an s-pixels blocki,j。
(3) Key kappa using JL algorithmJRandom matrix of size kxs
Figure BDA0001700846170000061
And random k-dimensional noise vector σ vs vector Ni,jThe vector L is obtained by encryptioni,j，
Figure BDA0001700846170000062
Vector Li,jIs a k-dimensional vector representing the result of the encryption for one pixel m (i, j).
(4) Will be damaged image IdAll pixels m (i, j) of (a) to (b) correspond to a vector Li,jAs an auxiliary encrypted image EJ。
Fig. 1 is a flowchart of a ciphertext domain image restoration method in an embodiment of the present invention.
As shown in fig. 1, the ciphertext domain image restoration method according to the embodiment includes the following steps:
step S1, the image restorer obtains the encrypted image E to be restoredPAuxiliary encrypted image EJAnd a mask image theta.
Step S2, treat the repair encrypted image E through the mask image θPMarking is carried out to obtain a damaged region omega and a good region phi.
Step S3, calculating the priority of the pixel c to be repaired in the damaged region omega by taking the block as the unit to obtain the target block with the highest priority
Figure BDA0001700846170000063
The block priority calculation takes into account the following two conditions:
(1) the center pixel of the block having the higher priority should be located at the boundary of the target region Ω.
(2) A block with a higher priority should have more good pixels.
These two conditions may ensure that the more perfect blocks in the repair process are repaired first and are biased towards those blocks that are continuous, strong-edged, and high-confidence pixels around.
Thus, the block B centered on the pixel c to be repairedcBlock priority O ofcIs composed of
Figure BDA0001700846170000071
Wherein the content of the first and second substances,
Figure BDA0001700846170000072
representing a block B of size l x l centred on the pixel c to be repairedcThe number of the medium good pixels,
Figure BDA0001700846170000073
indicating that the pixel c to be repaired is located at the boundary of the damaged region omega
Figure BDA0001700846170000074
The above.
Will border the boundary
Figure BDA0001700846170000075
Solving the block priority O of all the pixels c to be repairedcPost-selection block priority OcBlock B with the largest valuecAs a target block
Figure BDA0001700846170000077
In step S4, the auxiliary encrypted image EJWith the aid of a target block
Figure BDA0001700846170000078
All candidate blocks B associated with the good area phi (or within a specified range)SPerforming block matching to select the best matching block from the good region phi
Figure BDA0001700846170000079
The specific process is as follows:
maintaining the characteristic of Euclidean distance based on JL transformation and according to the auxiliary encryption image EJCalculating a target block by the following formula
Figure BDA00017008461700000710
With each candidate block BSThe distance between the two or more of the two or more,
Figure BDA0001700846170000076
wherein (x, y) represents a candidate block BSRelative to the target block
Figure BDA00017008461700000711
Coordinate displacement of (B)S∈Φ，
Figure BDA0001700846170000081
Figure BDA0001700846170000082
And
Figure BDA0001700846170000083
respectively representing auxiliary encrypted images EJTwo middle pixels m (i)1,j1) And m (i)2,j2) Cryptographic values of, i.e. k-dimensional vectors EJ(i1,j1) And EJ(i2,j2)。D[EJ(i1,j1),EJ(i2,j2)]Representing an auxiliary encrypted image EJTwo pixels apart.
Since the Euclidean distance between two ciphertext vectors in the JL transformation is approximate to the Euclidean distance between corresponding plaintexts, the distance target block is selected
Figure BDA0001700846170000085
The most recent candidate block BSAs the best matching block
Figure BDA0001700846170000086
Figure BDA0001700846170000084
Step S5, using the best matching block
Figure BDA0001700846170000087
Corresponding patch Ψ insFor target block
Figure BDA0001700846170000088
Defective block Ψ incFilling to complete the target block
Figure BDA0001700846170000089
Repair of damaged pixels in the image to be repaired, and then encrypting the image to be repaired EPUpdating to an initial repair encrypted image EP1，
EP1(i,j)＝EP(i+x*,j+y*)，
(i,j)∈Ψc，
Wherein (x)*,y*) Representing best matching blocks
Figure BDA00017008461700000810
Relative to the target block
Figure BDA00017008461700000811
Coordinate displacement of (E)P1(i, j) is the encrypted marred pixel EP(i, j) filling result.
Step S6, respectively for the auxiliary encrypted image EJThe damaged region Ω and the good region Φ.
Wherein the auxiliary encrypted image EJUpdated as an auxiliary encrypted image EJ1，
EJ1(i,j)＝EJ(i+x*,j+y*)，
(i,j)∈Ψc。
The damaged region Ω is updated to a damaged region Ω', Ω
Figure BDA00017008461700000812
Updating the sound region phi to sound region phi' representing
Figure BDA00017008461700000813
Step S7, repeating steps S2-S6 until all damaged regions omega are repaired to obtain repaired encrypted image E'PRepair encrypted image E'PEncrypting an image E for repairPThe repair result of (1).
Step S8, repairing the encrypted image EPCarrying out local weighted mean filtering processing to obtain an optimized encrypted image E ″P。
For weighted mean filtering in the plain text domain, pixel c, m (i, j), in the corrupted region Ω should be replaced by a weighted mean of m (i, j) itself and its neighboring pixels:
m′(i，j)＝wi-1，j·m(i-1，j)+wi+1，j·m(i+1，j)+wi，j·m(i，j)+wi，j-1·m(i，j-1)+wi，j+1·m(i，j+1)，
the weights may be set as: w is ai-1，j＝wi+1，j＝wi，j-1＝wi，j+1＝1/(4+ω)、wi，jω/(4+ ω), where ω may be a small positive integer.
However, in order to realize weighted mean filtering in the encrypted domain, the weight w is based on the homomorphic propertyi，jShould be modified to be an integer:
w′i，j＝(4+ω)·wi，j，
according to the homomorphism property, the image restorer can execute the following operations to realize the weighted mean filtering of the damaged region Ω in the ciphertext domain:
Figure BDA0001700846170000091
wherein ρ '(i, j) represents E'PThe cryptographic value of the pixel at the middle coordinate (i, j), ρ "(i, j) is the result of a weighted mean filtering of ρ' (i, j) located in the cryptographic domain, thus obtaining the final optimized encrypted image E ″P。
In the above, the image restorer treats the restored encrypted image E according to the ciphertext domain image restoring method of the embodimentPThe optimized encrypted image E' is obtained by repairing in the ciphertext domainPAll the processes of (1).
After the repair is complete, the image repairer will send the optimized encrypted image E ″PAnd sending the image to the image owner or a receiver authorized by the image owner. And the image owner or the authorized receiver decrypts the image by the private key of the paillier encryption algorithm, and m '(i, j) represents the decryption result of rho' (i, j).
Due to the weight rounding process in the weighted mean filtering process, the decrypted result m' (i, j) of the pixels in the damaged region Ω should be further processed:
Figure BDA0001700846170000101
and correspondingly obtaining a final repaired image.
The effect of the method according to the present embodiment is examined by comparing the image to be repaired, the damaged image, and the repaired image.
FIG. 2 is a graph comparing the repairing effect of the experimental group 1.
FIG. 3 is a graph comparing the repairing effect of experiment group 2.
As shown in fig. 2, fig. 2(a) shows an image to be repaired having a size of 512 × 512; FIG. 2(b) shows a randomly generated mask image; FIG. 2(c) shows a damaged image generated by the destruction of FIG. 2(a) according to FIG. 2 (b); fig. 2(d) shows that fig. 2(c) is encrypted by Paillier algorithm and JL transform respectively, wherein the ciphertext of each pixel after being encrypted by the JL transform is a multidimensional vector, so that the ciphertext cannot be displayed in an image form, while the ciphertext encrypted by the Paillier algorithm may exceed the value range of the gray value, so as to facilitate understanding of the encrypted result, which is obtained by modulo 256; fig. 2(e) shows a diagram after the optimized encrypted image is restored by the method of the present embodiment, modulo 256; fig. 2(f) shows a restored picture obtained by decrypting fig. 2 (e). Comparing fig. 2(f) with the image to be repaired like fig. 2(a), the peak signal-to-noise ratio PSNR of experimental group 1 is 44.65dB, and SSIM is 0.9826. SSIM is an index for measuring the structural similarity of two pictures, and the closer the value is to 1, the higher the similarity of the two pictures is.
As shown in fig. 3, (a) to (f) in fig. 3 have the same meanings as (a) to (f) in fig. 2, and when fig. 3(f) is compared with the image to be restored, like fig. 3(a), the peak signal-to-noise ratio PSNR of the experimental group 2 is 42.56dB, and SSIM is 0.9615.
In summary, the results of experiment 1 and experiment 2 both show the repairing effect of the method according to the present embodiment.
Fig. 4 shows 7 images selected from the image library.
In addition, as shown in fig. 4, we select 7 images from the image library for experiments, respectively and randomly damage, then repair in the ciphertext domain by using the method related to this embodiment, compare the obtained decrypted repair image with the repair results of three classic plaintext domain image repair algorithms (TV algorithm, BSCB algorithm, criiniisi algorithm), and obtain PSNR and SSIM results as shown in table 1,
TABLE 1 Algorithm repair results comparison Table
Figure BDA0001700846170000111
Figure BDA0001700846170000121
The results in table 1 show that the ciphertext domain image restoration method according to the present embodiment can be effectively applied in the cloud computing environment, and the restoration quality reaches a level equivalent to some advanced restoration methods for plaintext images, and the method can effectively protect image privacy, which is not possessed by these restoration methods for plaintext images.
Effects and effects of the embodiments
According to the ciphertext domain image restoration method of the embodiment, the encrypted image E to be restored is acquiredPAuxiliary encrypted image EJAnd after masking the image theta, treating the repaired encrypted image E through the mask image thetaPMarking to obtain a damaged region omega and a sound region phi, and determining a target block of the damaged region omega
Figure BDA0001700846170000122
In the auxiliary encryption image EJWith the assistance of (1) finding the best matching block of good region phi by block matching
Figure BDA0001700846170000123
Then using the best matching block
Figure BDA0001700846170000124
For target block
Figure BDA0001700846170000125
Repairing to update encrypted image E to be repairedPAuxiliary encrypted image EJDamaged region omega and sound region phi, repeating the repair process until a repaired encrypted image E 'is obtained'PThe process is completely carried out in the ciphertext domain, the plaintext information of the image cannot be leaked, the privacy is strong, a good image restoration effect can be obtained, the method has a wide application prospect, and the method is particularly suitable for transmission and restoration of the image information in the cloud computing process.
Further, the restored encrypted image E'PPerforming local weighted mean filtering can avoid restoring the encrypted image E'PThe mosaic effect appears, so that the obtained optimized encrypted image E ″)PHas more excellent image effect.
Further, the optimized encrypted image E ″ obtained by the method according to the present embodimentPThe restored image obtained after decryption and three classicsThe comparison of the repair results of the repair algorithm of the plaintext field image shows that, in terms of repair quality, the method according to the embodiment can reach a level equivalent to that of some advanced repair methods of the plaintext image.
The above embodiments are preferred examples of the present invention, and are not intended to limit the scope of the present invention.

Claims (6)

1. A ciphertext domain image repairing method is used for repairing damaged images in a ciphertext domain, and is characterized by comprising the following steps:
step one, obtaining an encrypted image E to be repairedPAuxiliary encrypted image EJAnd a mask image θ;
secondly, the encrypted image E to be repaired is processed by the mask image thetaPMarking to obtain a damaged region omega and a complete region phi;
thirdly, calculating the priority of the pixel c to be repaired in the damaged region omega by taking a block as a unit to obtain a target block with the highest priority
Figure FDA0003173924040000011
Step four, in the auxiliary encryption image EJWith the aid of the target block
Figure FDA0003173924040000012
All candidate blocks B with the good region ΦSPerforming block matching to find the best matching block in the good region phi
Figure FDA0003173924040000013
Step five, using the optimal matching block
Figure FDA0003173924040000014
For the target block
Figure FDA0003173924040000015
Repairing to repair the encrypted image E to be repairedPUpdating to an initial repair encrypted image EP1；
Step six, respectively carrying out comparison on the auxiliary encrypted images EJUpdating the damaged region omega and the intact region phi;
step seven, repeating the step two to the step six until all the damaged regions omega are repaired to obtain a repaired encrypted image E'PRepair encrypted image E'PEncrypting the image E to be repairedPAs a result of the repair of (a),
wherein, in the fourth step, the target block is processed
Figure FDA0003173924040000016
And the candidate block BSPerforming block matching to obtain the best matching block
Figure FDA0003173924040000017
The process comprises the following steps:
according to the auxiliary encrypted image EJCalculating the target block by the following formula
Figure FDA0003173924040000018
With each of said candidate blocks BSThe distance between the two or more of the two or more,
Figure FDA0003173924040000021
(x, y) represents the candidate block BSRelative to the target block
Figure FDA0003173924040000022
Coordinate displacement of (B)S∈Φ，
Figure FDA0003173924040000023
Figure FDA0003173924040000024
And
Figure FDA0003173924040000025
respectively representing said auxiliary encrypted images EJTwo middle pixels m (i)1,j1) And m (i)2,j2) The encrypted value of (a) is determined,
selecting the distance to the target block
Figure FDA0003173924040000026
The most recent candidate block BSAs the best matching block
Figure FDA0003173924040000027
2. The ciphertext domain image restoration method of claim 1, wherein:
wherein, in step three, the target block is obtained from the damaged region omega
Figure FDA0003173924040000028
The process comprises the following steps:
block priority O centered on the pixel c to be repairedcIs composed of
Figure FDA0003173924040000029
Figure FDA00031739240400000210
Representing a block B of size l x l centred on said pixel c to be repairedcThe number of the medium good pixels,
Figure FDA00031739240400000211
indicating that the pixel c to be repaired is located at the damagedThe boundary of region omega
Figure FDA00031739240400000212
In the above-mentioned manner,
selecting block priority OcBlock B with the largest valuecAs a target block
Figure FDA00031739240400000213
3. The ciphertext domain image restoration method according to claim 1, further comprising:
step eight, the repaired encrypted image E'PCarrying out local weighted mean filtering processing to obtain an optimized encrypted image E ″P。
4. The ciphertext domain image restoration method of claim 1, wherein:
wherein the encrypted image E to be repairedPIs composed of the damaged image IdAnd carrying out encryption processing by a Paillier encryption algorithm to obtain an image.
5. The ciphertext domain image restoration method of claim 1, wherein:
wherein the auxiliary encrypted image EJIs composed of the damaged image IdAnd (3) obtaining an image after Johnson Lindenstaus transformation encryption processing.
6. The ciphertext domain image restoration method of claim 5, wherein:
wherein the damaged image IdObtaining the auxiliary encrypted image EJThe process comprises the following steps:
the damaged image IdEach pixel m (i, j) of the image sensor, and s-1 pixels around the pixel m (i, j) form an s-pixel block;
constructing an s-dimensional vector N for pixels in the s-pixels blocki,j；
Using the key kJRandom matrix of size kxs
Figure FDA0003173924040000031
And a random k-dimensional noise vector σ versus the vector Ni,jThe vector L is obtained by encryptioni,jThe vector Li,jAs an encryption result of one pixel m (i, j),
Figure FDA0003173924040000032
the damaged image IdAll pixels m (i, j) of (a) to (b) correspond to a vector Li,jAs an auxiliary encrypted image EJ。
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