CN113206732A - Method and device for safely transmitting and receiving medical image - Google Patents
Method and device for safely transmitting and receiving medical image Download PDFInfo
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Abstract
The invention provides a method and a device for safely transmitting and receiving a medical image, wherein the method is used for carrying out sparse representation on an original medical image to obtain a sparse matrix; generating two chaotic matrixes by adopting a logistic chaotic system, calculating tensor products, sampling and compressing a sparse matrix of the medical image according to the tensor products to obtain an observation matrix, and normalizing the observation matrix; generating a first chaotic sequence and a second chaotic sequence by adopting a chaotic system, carrying out spatial scrambling on the observation matrix after the normalization processing by adopting the first chaotic sequence, and carrying out digital hidden encryption on the observation matrix after the spatial scrambling by adopting the second chaotic sequence to obtain an encrypted image; sending the first initial parameter, the second initial parameter, the third initial parameter, the fourth initial parameter, the standard parameter in the normalization processing and the encrypted image to a receiving end; in the receiving process, the encryption process is reversed and the image is reconstructed based on the IRLS algorithm. The method generates the measurement matrix based on the two chat matrixes, and is large in key space and high in safety.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to a method and a device for safely transmitting and receiving a medical image.
Background
With the continuous increase of medical requirements, a large amount of medical data is generated in different medical care scenes, and the work of quickly and safely transmitting medical images faces challenges. Medical images generally involve the privacy of the patient, and the need for security is high during internet transmission. In addition, a large amount of medical image data has a large storage space and a low transmission speed, and meanwhile, in order to ensure the diagnosis effect, information of the medical image is not lost in the transmission process. Therefore, the confidentiality and integrity of medical data with medical images as main objects in the transmission process are increasingly required, and an efficient encryption and transmission method is urgently needed.
Disclosure of Invention
The embodiment of the invention provides a method and a device for safely transmitting and receiving a medical image, which aim to solve the problems of poor safety and low transmission speed of the medical image in the transmission process.
The technical scheme of the invention is as follows:
in one aspect, the present invention provides a method for safely transmitting a medical image, including:
acquiring an original medical image, and performing sparse representation on the medical image to obtain a corresponding sparse matrix;
generating a first chaotic matrix based on a first initial parameter and a second chaotic matrix based on a second initial parameter by adopting a logistic chaotic system, calculating a tensor product of the first chaotic matrix and the second chaotic matrix, sampling and compressing a sparse matrix of the medical image according to the tensor product to obtain an observation matrix, and normalizing the observation matrix;
generating a first chaotic sequence based on a third initial parameter and a second chaotic sequence based on a fourth initial parameter by adopting a chaotic system, carrying out spatial scrambling on the observation matrix after the normalization processing by adopting the first chaotic sequence, and carrying out digital hidden encryption on the observation matrix after the spatial scrambling by adopting the second chaotic sequence to obtain an encrypted image;
sending the first initial parameter, the second initial parameter, the third initial parameter, the fourth initial parameter, the standard parameter in the normalization process and the encrypted image to a receiving end; wherein the standard parameter is a maximum value, a minimum value and/or an average value in the observation matrix, the receiving end regenerates the first chaotic matrix based on the first initial parameter and the second chaotic matrix based on the second initial parameter by adopting a logistic chaotic system, regenerates the first chaotic sequence based on the third initial parameter and the second chaotic sequence based on the fourth initial parameter by adopting a chaotic system, performs digital hidden inverse operation on the encrypted image by adopting the second chaotic sequence, performs spatial scrambling inverse operation on the obtained image according to the first chaotic sequence and performs inverse normalization operation by adopting the standard parameter to obtain the observation matrix, and reconstructs the observation matrix by utilizing a preset reconstruction algorithm based on the first chaotic matrix and the second chaotic matrix to obtain a reconstructed image.
In some embodiments, the sparse representation of the medical image to obtain a corresponding sparse matrix comprises: and performing discrete wavelet transformation on the medical image to obtain a sparse matrix.
In some embodiments, the first initial parameter comprises three parameters of a randomly generated first control value, a first initial value and a first sampling distance, the second initial parameter comprises three parameters of a randomly generated second control value, a second initial value and a second sampling distance, the value ranges of the first control value and the second control value are (3.5699457, 4), the value ranges of the first initial value and the second initial value are (0, 1), and the value ranges of the first sampling distance and the second sampling distance are [15, + ∞ ]; the third initial parameter and the fourth initial parameter both comprise 4 randomly generated chaotic system initial values and 1 chaotic system sampling distance, the value range of the chaotic system initial values is (0, 1), and the value range of the chaotic system sampling distance is [1, + ∞ ].
In some embodiments, the calculation formula for normalizing the observation matrix is:
wherein Y is an observation matrix, YmaxTo observe the maximum value in the matrix Y, YminIs the minimum value in the observation matrix Y, alpha is a positive integer, and N is the observation matrix after normalization processing.
In some embodiments, α has a value of 8.
In some embodiments, spatially scrambling the normalized observation matrix with the first chaotic sequence includes:
expanding the observation matrix after the normalization processing into a row vector, and marking a first sequence number for each element in the row vector according to the sequence from left to right;
marking a second sequence number for each element in the first chaotic sequence according to the sequence from left to right, rearranging the elements in the first chaotic sequence according to the sequence from small to large, and forming an index sequence by the second sequence numbers corresponding to the elements after rearrangement;
and rearranging and splicing the elements in the row vector according to the one-to-one correspondence relationship between the first sequence number and the index sequence to obtain the observation matrix after spatial scrambling.
In some embodiments, performing digital hidden encryption on the spatially scrambled observation matrix by using the second chaotic sequence to obtain an encrypted image, includes:
amplifying 10 elements in the second chaotic sequence15Multiplying the integer part and then taking 2αAdjusting the dimensionality according to the row number and the column number of the observation matrix to obtain an encryption sequence, wherein alpha is a positive integer;
and encrypting the observation matrix after spatial scrambling by adopting the encryption sequence, wherein the calculation formula is as follows:
N2m＝β·N1+(1-β)·C2m；
where N1 is the spatially scrambled observation matrix, C2mFor encrypting the sequence, N2mTo encrypt an image, β ∈ (0, 1).
In another aspect, the present invention further provides a method for safely receiving a medical image, including:
receiving a first initial parameter, a second initial parameter, a third initial parameter, a fourth initial parameter, a standard parameter and an encrypted image, wherein the encrypted image is obtained by encrypting and compressing the medical image security sending method, and the standard parameter is a maximum value, a minimum value and/or an average value of an observation matrix in the medical image security sending method;
regenerating the first visual matrix based on the first initial parameters and the second visual matrix based on the second initial parameters by adopting a logistic chaotic system;
regenerating the first chaotic sequence based on the third initial parameter and regenerating the second chaotic sequence based on the fourth initial parameter by adopting a chaotic system;
performing digital hidden inverse operation on the encrypted image by adopting the second chaotic sequence, performing inverse operation of spatial scrambling on the decrypted image according to the first chaotic sequence, and performing inverse normalization operation according to the standard parameter to obtain the observation matrix;
and reconstructing the observation matrix by utilizing an IRLS algorithm based on the first and second visual matrixes to obtain a reconstructed image.
In some embodiments, reconstructing the observation matrix based on the first and second chaotic matrices using an IRLS algorithm to obtain a reconstructed image includes:
definition of εnIn order to iterate the weights,
for iterating the ith column of the matrix at the nth time, xi (n)For the ith column of the reconstruction matrix at the nth iteration, ε is initialized0＝1，
The IRLS algorithm employs lρUpdating the weight of the norm, wherein rho is 0.8, and the reconstruction process comprises the following steps:
for each column vector yi in the observation matrix y, when ε > 10-9When, the following operations are performedThe method comprises the following steps:
updating
Order to
Updating
Updating epsilonn+1＝min(εn，[r(x(n+1))k+1]/q)；
At the end of the iteration, output x ═ x(n+1)。
Wherein, r (x)(n+1) k+1The absolute value of the (k + 1) th component arranged in descending order in the signal x of q rows and 1 columns is defined as k, the sparsity of the signal x is defined as k, the iteration number is defined as n, i is the serial number of the column in the matrix, x' is the reconstructed column vector, y is the observation matrix, phi is the first chaotic matrix, P is the second chaotic matrix, and T is the transposed matrix.
In another aspect, the present invention further provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and when the processor executes the computer program, the steps of the method are implemented.
The invention has the beneficial effects that:
according to the safe transmitting and receiving method and device for the medical image, two chat matrixes are generated based on the logistic chaotic system in the transmitting process, and the tensor product is calculated to serve as the measuring matrix. In the compressed sensing technology, the same measurement matrix and user encryption sequence are required for the steps of image compression and image restoration, and in the transmission process, except for the encrypted images, only the initial parameters for generating the first chat matrix, the second chat matrix, the first chaotic sequence and the second chaotic sequence are transmitted, so that the data volume is greatly reduced, and the transmission speed is improved.
Furthermore, the compressed sensing technology has the characteristic that the image is compressed and simultaneously has the encryption property, the measurement matrix can be regarded as a key for image decryption, the image can be restored by the correct key, two Chaotic matrices can be regarded as encryption based on the tensor product technology, the adopted Chaotic matrices are generated by a Chaotic system, and the system has the characteristic that the output is greatly changed due to the tiny change of input parameters, so the tensor products of the two Chaotic matrices are much larger than the key space of one measurement matrix, and the safety in the image transmission process is greatly improved.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
It will be appreciated by those skilled in the art that the objects and advantages that can be achieved with the present invention are not limited to the specific details set forth above, and that these and other objects that can be achieved with the present invention will be more clearly understood from the detailed description that follows.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
fig. 1 is a logic diagram of a method for securely transmitting and receiving a medical image according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of a medical image transmission system used in a method for securely transmitting and receiving a medical image according to an embodiment of the present invention;
fig. 3 is a flowchart illustrating a method for securely transmitting a medical image according to an embodiment of the present invention;
fig. 4 is a flowchart illustrating a medical image security receiving method according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the following embodiments and accompanying drawings. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention, but not to limit the present invention.
It should be noted that, in order to avoid obscuring the present invention with unnecessary details, only the structures and/or processing steps closely related to the scheme according to the present invention are shown in the drawings, and other details not so relevant to the present invention are omitted.
It should be emphasized that the term "comprises/comprising" when used herein, is taken to specify the presence of stated features, elements, steps or components, but does not preclude the presence or addition of one or more other features, elements, steps or components.
It is also noted herein that the term "coupled," if not specifically stated, may refer herein to not only a direct connection, but also an indirect connection in which an intermediate is present.
Medical images refer to techniques and procedures for obtaining images of internal tissues of a human body or a part of the human body in a non-invasive manner for medical treatment or medical research, and mainly include x-ray radiation, nuclear magnetic resonance images, and the like. Medical images are generally diagnostic images of patients, which involve the privacy of the patient and therefore require high security for transmission. Meanwhile, in order to obtain higher definition, the amount of data of the medical image is generally larger, which results in a slower transmission speed in the transmission process. With the improvement of medical requirements of people, the increase of requirements of remote consultation, research and the like, the requirements of transmission of medical images are gradually improved, and higher requirements are put forward on safety and speed in the transmission process.
The invention is applied to a medical image transmission system as shown in fig. 2, and the system comprises three parts: the system comprises a sending end, a transmission line and a receiving end, wherein the sending end and the receiving end can adopt electronic equipment capable of storing and operating programs such as a computer and a single chip microcomputer, the transmission line can adopt a special communication line, and the transmission line can also adopt the Internet of things for transmission. The medical image transmission method is based on CS (compressed sensing) model construction and mainly comprises a compression process, an encryption process, a decryption process and a reconstruction process. The sending end carries out a compression process and an encryption process, and the receiving end carries out a decryption process and a reconstruction process. The method comprises the following steps that in the compression process, two probability matrixes are generated based on a logistic chaotic system, tensor products are calculated, and measurement matrixes are generated for sampling compression; the encryption process is based on a Chen chaotic system to generate two chaotic sequences, wherein one chaotic sequence is used for spatial scrambling, and the other chaotic sequence is used for digital hiding. The decryption process is the inverse operation of the encryption process, and the reconstruction process adopts a preset reconstruction algorithm for processing.
On one hand, the invention provides a medical image security sending method which runs on a sending end or medical image generation equipment, and can compress pictures at a low rate and upload and download the pictures by solving the tensor product of two chat matrixes as a measurement matrix for compression and sampling, so that the transmission speed is improved, and encryption to a certain degree is realized. Furthermore, a Chen chaotic system is adopted to generate two chaotic sequences to encrypt the medical image, one chaotic sequence is used for spatial scrambling, and the other chaotic sequence is used for digital hiding. Specifically, as shown in fig. 1 and 3, the method includes the following steps S101 to S104:
step S101: acquiring an original medical image, and performing sparse representation on the medical image to obtain a corresponding sparse matrix.
Step S102: the method comprises the steps of generating a first chaotic matrix based on a first initial parameter and a second chaotic matrix based on a second initial parameter by adopting a logistic chaotic system, calculating tensor products of the first chaotic matrix and the second chaotic matrix, sampling and compressing a sparse matrix of the medical image according to the tensor products to obtain an observation matrix, and normalizing the observation matrix.
Step S103: generating a first chaotic sequence based on a third initial parameter and a second chaotic sequence based on a fourth initial parameter by adopting a chaotic system, carrying out spatial scrambling on the observation matrix after the normalization processing by adopting the first chaotic sequence, and carrying out digital hidden encryption on the observation matrix after the spatial scrambling by adopting the second chaotic sequence to obtain an encrypted image;
step S104: and sending the first initial parameter, the second initial parameter, the third initial parameter, the fourth initial parameter, the standard parameter in the normalization processing and the encrypted image to a receiving end. The standard parameters are the maximum value, the minimum value and/or the average value in the observation matrix, the receiving end regenerates a first chaotic matrix based on a first initial parameter by adopting a logistic chaotic system and regenerates a second chaotic matrix based on a second initial parameter, regenerates a first chaos sequence based on a third initial parameter by adopting a chaotic system and regenerates a second chaos sequence based on a fourth initial parameter, performs digital hidden inverse operation on the encrypted image by adopting the second chaos sequence, performs inverse operation of spatial scrambling on the obtained image according to the first chaos sequence and performs inverse normalization operation by adopting the standard parameters to obtain the observation matrix, and reconstructs the observation matrix by utilizing a preset reconstruction algorithm based on the first chaotic matrix and the second chaotic matrix to obtain a reconstructed image.
In step S101, based on the compressed sensing principle, if a signal is sparse, the signal can be reconstructed and recovered by sampling points far lower than the requirement of the sampling theorem. Therefore, compressed sensing (CS model) requires sparsity of the signal in a certain domain. In particular, for medical images, the sparse domain of the medical image is found by the discrete wavelet transform. In other embodiments, a sparse domain of the image may be found for a particular image using discrete cosine transform or fourier transform.
Illustratively, assume the medical image matrix is X ∈ Rq×qAssuming that the orthogonal basis of the discrete wavelet is psi ∈ Rq×qConverting a medical image to a sparse domain may be represented as X ═ Ψ S, S being a corresponding sparse matrix
In step S102, a logistic chaotic system is used to generate a first chaotic matrix and a second chaotic matrix based on the first initial parameter and the second initial parameter to form two low-dimensional measurement matrices, and a tensor product of the first chaotic matrix and the second chaotic matrix is further calculated to form a high-dimensional measurement matrix. In the prior art, the complexity of constructing a high-dimensional measurement matrix is higher than that of constructing the high-dimensional measurement matrixIn this embodiment, a high-dimensional measurement matrix is generated by using two low-dimensional measurement matrices based on a tensor product technology, so that the calculation power can be greatly saved, and the construction time of the measurement matrix can be reduced. On the other hand, the compressed sensing technology has the characteristic that the image is compressed and simultaneously has the encryption property, so that the measurement matrix can be regarded as a key for image decryption, and the image can be restored by the correct key. Based on a tensor product technology, the two Chaotic matrices can be regarded as encryption, the adopted Chaotic matrices are generated by a Chaotic system, and the system is characterized in that the output is greatly changed due to slight change of input parameters, so that the tensor product of the two Chaotic matrices is much larger than the key space of one measurement matrix, and the safety in the image transmission process is greatly improved. Suppose a key space of a Chaotic matrix is S1The key space of the measurement matrix generated by the two Chaotic matrices in the tensor compressed sensing mode is S1×S1Key space S far larger than Chaotic matrix in traditional compressed sensing mode1。
Specifically, the first initial parameter includes three parameters of a first control value, a first initial value and a first sampling distance, the second initial parameter includes three parameters of a second control value, a second initial value and a second sampling distance, the value ranges of the first control value and the second control value are (3.5699457, 4), the value ranges of the first initial value and the second initial value are (0, 1), and the value ranges of the first sampling distance and the second sampling distance are [15, + ∞ ].
Illustratively, the first initial parameter is (Φ)_u，Φ_x0，Φ_d) Generating a phi matrix based on a logistic chaotic systemm×n(representing a matrix Φ with m rows and n columns); the second initial parameter is (P)_u，P_x0，P_d) Generating a P matrix as P based on the logistic chaotic systems×t(ii) a Of the first initial parameter and the second initial parameter, the first parameter is a control value u e (3.5699457, 4), the second parameter is an initial value x0 e (0, 1), and the third parameter is a sampling distance d e [15, + ∞ ]. The tensor product operation of the two matrices can be expressed as
Wherein the content of the first and second substances,
then
The calculation result is as follows:
wherein the content of the first and second substances,
therefore, the first and second electrodes are formed on the substrate,
that is, we can obtain a matrix of (m · s) rows and (n · t) columns by performing tensor product operation on a matrix of m rows and n columns and a matrix of s rows and t columns.
Furthermore, taking a tensor product of the first chaotic matrix and the second chaotic matrix as a measurement matrix to perform sampling compression on a coefficient matrix of the original medical image to obtain an observation matrix.
Assuming that the observation matrix is Y ∈ R(mq/n)×qThen we normalize the elements in the Y matrix to a certain value range [0, 2 ]α-1]The process can be expressed as:
wherein Y is an observation matrix, YmaxTo observe the maximum value in the matrix Y, YminIs the minimum value in the observation matrix Y, alpha is a positive integer, and N is the observation matrix after normalization processing. Since the medical image is a gray scale image, each pixel can have 256 gray scale values, so the value of α is 8.
In step S103, spatial scrambling and digital concealment are also performed on the observation matrix after the normalization processing to realize encryption. Firstly, a first chaotic sequence and a second chaotic sequence are generated by adopting a chaotic system based on a third initial parameter and a fourth initial parameter.
In some embodiments, the third initial parameter and the fourth initial parameter each include 4 randomly generated chaotic system initial values and 1 chaotic system sampling distance, the value range of the chaotic system initial values is (0, 1), and the value range of the chaotic system sampling distance is [1, + ∞ ]. Specifically, let the parameter of the chaotic system be (Ci)_X0，Ci_y0，Ci_H0，Ci_Z0，Ci_d) I is 1 or 2, wherein Ci_X0、Ci_y0、Ci_H0And Ci_Z0The value ranges are the same as (0, 1), Ci_dThe value range of [1, + ∞). Inputting the third initial parameter and the fourth initial parameter into a chaotic system to obtain a chaotic sequence
i is 1 or 2, and further converted into a first chaotic sequence and a second chaotic sequence which are marked as SicI is 1 or 2, calculated as:
wherein A isi(: 1) represents a matrix AiA column vector of the first column ofi(: 2) represents a matrix AiThe column vector of the second column of (1), and so on.
In some embodiments, in step S103, spatially scrambling the normalized observation matrix by using the first chaotic sequence includes steps S1031 to S1033:
step S1031: and expanding the observation matrix after the normalization processing into a row vector, and marking a first sequence number for each element in the row vector according to the sequence from left to right.
Step S1032: and marking a second sequence number for each element in the first chaotic sequence according to the sequence from left to right, rearranging the elements in the first chaotic sequence according to the sequence from small to large, and forming an index sequence by the second sequence numbers corresponding to the elements after rearrangement.
Step S1033: and rearranging and splicing the elements in the row vector according to the one-to-one correspondence relationship between the first sequence number and the index sequence to obtain the observation matrix after spatial scrambling.
In particular, with S1cThe observation matrix after normalization processing is encrypted in the first step, and S is obtained1cAnd converting into a row vector, using C1 to represent that the elements in C1 are numbered, and rearranging the elements in C1 in the order from small to large to obtain a sorted sequence C1_ SORT. The sequence numbers of the elements in the observation matrix obtained after the normalization processing in step S102, i.e., the image matrix N in equation (2), are rearranged according to the index of C1_ SORT in C1, and spatial scrambling is completed to obtain an N1 matrix.
For example, assume that the observation matrix N obtained after the normalization process is:
the method is expanded into a row vector form according to rows (2824123561919933), the chaotic sequence C1 is (0.0030.0010.0020.0070.1120.1370.0040.0890.006), the elements in the C1 are rearranged from small to large, the rearranged sequence C1_ SORT is (0.0010.0020.0030.0040.0060.0070.00890.1120.137), and the indexes of the elements in the C1_ SORT in the C1 are (231794856) in sequence. The first sequence number corresponding to each element in the line vector (2824123561919933) is (123456789), the first sequence numbers corresponding to the elements in the line vector (2824123561919933) are rearranged according to the index sequence (231794856) to be subjected to spatial scrambling to obtain (2412281333995619), and the obtained encrypted image is:
in some embodiments, in step S103, performing digital concealment encryption on the spatially scrambled observation matrix by using a second chaotic sequence to obtain an encrypted image, including steps S1034 to S1035:
step S1034: amplifying 10 elements in the second chaotic sequencei5Multiplying the integer part and then taking 2αAnd adjusting the dimensionality according to the row number and the column number of the observation matrix to obtain an encryption sequence, wherein alpha is a positive integer.
Step S1035: and encrypting the observation matrix after spatial scrambling by adopting an encryption sequence, wherein the calculation formula is as follows:
N2m＝β·N1+(1-β)·C2m (4)
where N1 is the spatially scrambled observation matrix, C2mFor encrypting the sequence, N2mTo encrypt an image, β ∈ (0, 1).
Further, in step S1034, a second chaotic sequence S is adopted2cThe N1 sequence obtained by the first encryption is encrypted in the second encryption step to obtain S2cDigital amplification in sequence 1015Multiple down-integers and then 2αSince the bit depth of the grayscale image is 8, α is 8 in this embodiment. Specifically, the calculation formula is as shown in formula 5:
C2＝floor(S2c×1015)mod 2α (5)
dimension adjustment is carried out on the C2 according to the column number and the row number of the observation matrix Y to ensure that the dimensions are consistent, and the encryption sequence C is obtained2m. Further, the final encrypted image N is obtained by encrypting the image using the above equation 42m。
In step S104, the decrypted image is transmitted to the receiving end. In the process of decryption and image reconstruction at the receiving end, a first chat matrix, a second chat matrix, a first chaotic sequence and a second chaotic sequence are also needed, so that in order to further reduce the size of transmission data, a first initial parameter, a second initial parameter, a third initial parameter and a fourth initial parameter can be sent to the receiving end together with the encrypted image, and the first chat matrix, the second chat matrix, the first chaotic sequence and the second chaotic sequence are regenerated by adopting a logistic chaotic system and a chaotic system. In other embodiments, the first chaotic matrix, the second chaotic matrix, the first chaotic sequence, the second chaotic sequence, and the encrypted image may also be transmitted to the receiving end.
Further, after receiving the first initial parameter, the second initial parameter, the third initial parameter, the fourth initial parameter and the encrypted image, the receiving end performs decryption and reconstruction based on the inverse operation of steps S101 to S103. Specifically, the present invention further provides a medical image security receiving method, which is used for receiving, decrypting and reconstructing a medical image transmitted in an encrypted manner at a receiving end, and as shown in fig. 4, the method includes steps S201 to S205:
step S201: receiving a first initial parameter, a second initial parameter, a third initial parameter, a fourth initial parameter, a standard parameter and an encrypted image, wherein the encrypted image is obtained by encrypting and compressing the medical image security sending method; the standard parameters are the maximum value, the minimum value and/or the average value of the observation matrix in the medical image security transmission method.
Step S202: and regenerating a first chaotic matrix based on the first initial parameters and regenerating a second chaotic matrix based on the second initial parameters by adopting a logistic chaotic system.
Step S203: and regenerating the first chaotic sequence based on the third initial parameter and the second chaotic sequence based on the fourth initial parameter by adopting a chaotic system.
Step S204: and performing digital hidden inverse operation on the encrypted image by adopting the second chaotic sequence, performing inverse operation of spatial scrambling on the image obtained by decryption according to the first chaotic sequence, and performing inverse normalization operation according to standard parameters to obtain an observation matrix.
Step S205: and reconstructing the observation matrix by using an IRLS (iterative weighed Least square) algorithm based on the first and second chat matrixes to obtain a reconstructed image.
In steps S201 to S203, after receiving the first initial parameter, the second initial parameter, the third initial parameter, the fourth initial parameter, and the encrypted image, the first chaotic matrix, the second chaotic matrix, the first chaotic sequence, and the second chaotic sequence are regenerated with reference to the steps in step S102 and step S103.
In step S204, the encrypted image is subjected to the inverse operation of digital concealment using the second chaotic sequence. In some embodiments, based on the digital hiding method in steps S1034 to S1035, the second chaotic sequence may be calculated according to the method in step S1034 to obtain an encrypted sequence, and the inverse operation is further performed on step S1035, where the specific decryption formula of formula 4 is:
wherein N is2m_rFor the encrypted image received by the receiving end, N in equation 42mThe same; c2mFor the encrypted sequence, β ∈ (0, 1), β being the same as the value in equation 4;
n1_ d is the image obtained by the inverse operation of digital concealment, and corresponds to the observation matrix after spatial scrambling in step S103, and the decryption process for the second-step encryption is also completed.
Further, referring to the methods in steps S1031 to S1033, the image obtained after the first decryption is subjected to the inverse operation of spatial scrambling, that is, the decryption process of the first encryption in step S103 is completed, and the observation matrix obtained after the normalization processing in step S102 is obtained and is denoted as N _ d.
Further, referring to the normalization method in step S102, the matrix N _ d is denormalized by using the standard parameter sent by the sending end. In some embodiments, when the sender performs the normalization calculation according to equation 2, the calculation formula of the matrix N _ d for inverse normalization is:
wherein, YmaxTo observe the maximum value in the matrix Y, YminIs the minimum value in the observation matrix Y, YrAnd alpha is a positive integer and is the same as the value in the formula 2, wherein alpha is an observation matrix obtained by the reverse normalization operation. Alpha can be determined by means of advance appointment at the transmitting end and the receiving end, and can also be transmitted to the receiving end by the transmitting end under a specific scene. Y ismaxAnd YminSending the standard parameters to a receiving end by a sending end; the content of the standard parameters is adaptively adjusted according to different normalization calculation modes, for example, when the Z-score normalization processing is adopted, the standard parameters are the mean value and the standard deviation of elements in the observation matrix.
In step S205, the observation matrix is reconstructed by using an IRLS algorithm, and in other embodiments, other image reconstruction algorithms, such as an OMP (Orthogonal Matching Pursuit) algorithm, may also be used.
In some embodiments, the IRLS algorithm employs lρUpdating the weight of norm, rho is 0.8, and defines epsilonnIn order to iterate the weights,
for iterating the ith column of the matrix at the nth time, xi (n)For the ith column of the reconstruction matrix at the nth iteration, ε is initialized0＝1，
The reconstruction process comprises the following steps:
for each column vector yi in the observation matrix y, when ε > 10-9Then, the following operations are performed:
updating
Order to
Updating
Updating epsilonn+1＝min(εn，[r(x(n+1))k+1]/q) (11)
At the end of the iteration, output x ═ x(n+1)。
Wherein, r (x)(n+1) k+1The method comprises the steps that the absolute value of a (k + 1) th component is arranged in a descending order in a signal x of q rows and 1 columns, k is the sparsity of the signal x, n is the iteration number, i is the serial number of a column in a matrix, x' is a reconstructed column vector, y is an observation matrix, phi is a low-dimensional measurement matrix, namely a first chaotic matrix, P is an expanded-dimensional matrix, namely a second chaotic matrix, and T is a transposed matrix.
In another aspect, the present invention further provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and when the processor executes the computer program, the steps of the method are implemented.
The invention is illustrated below with reference to a specific example:
the medical image security sending method is adopted to carry out encryption compression and transmission on a medical image, and the medical image matrix is X epsilon Rq×qAssuming that the orthogonal basis of the discrete wavelet is psi ∈ Rq×qThen, the conversion of the medical image into the sparse domain may be represented as X ═ Ψ S, and S is a sparse matrix obtained by performing sparse representation on the medical image matrix.
Based on a keystream (phi)_u，Φ_x0，Φ_d) And (P)_u，P_x0，P_d) Generation of phi using a logistic chaotic systemm×nMatrix sum Ps×tA matrix, the first parameter being a control value u e (3.5699457, 4), the second parameter being an initial value x0 e (0, 1), the third parameter being a sampling distance d e [15, + ∞), and calculating the tensor product of the two matrices
Taking the tensor product as a measurement matrix, sampling and compressing the sparse matrix, wherein the sampling and compressing process can be expressed as:
and Y is a compressed image obtained by sampling and compressing, and is called an observation matrix. Let Y be E.R(mq/n)×qNormalizing the elements in the Y matrix to a certain value range [0, 2 ]α-1]The process can be expressed as:
wherein Y is an observation matrix, YmaxTo observe the maximum value in the matrix Y, YminIs the minimum value in the observation matrix Y, alpha is a positive integer, and N is the observation matrix after normalization processing. Since the medical image is a gray scale image, each pixel can have 256 gray scale values, so that the value of alpha is 8, and the value of alpha can be jointly appointed by a transmitting terminal and a receiving terminal without transmission.
The matrix N belongs to R(mq/n)×qAnd further generating two chaotic sequences by means of a chen chaotic system for encrypting the N matrix. In particular, based on the parameter (Ci)_X0，Ci_y0，Ci_H0，Ci_Z0，Ci_d) I is 1 or 2, wherein Ci_X0、Ci_y0、Ci_H0And Ci_Z0The value ranges are the same as (0, 1), Ci_dHas a value range of [1, + ∞ ]), and utilizes the chaotic system to generate a chaotic sequence
And converted into Sic(i ═ 1, 2), the process can be represented as:
wherein A isi(: 1) represents a matrix AiA column vector of the first column ofi(: 2) represents a matrix AiThe column vector of the second column of (1), and so on. Will be provided withS1cConverting into a row vector, using C1 to indicate, and sorting the elements in C1 according to the method in step S1032 to obtain an index sequence C1 SORT.
Carrying out the first step of encryption, and expanding the image matrix N into an array form according to rows, namely SicAnd (4) converting the obtained row vector into a row vector, rearranging and splicing the elements in the row vector according to the one-to-one correspondence relationship between the first sequence number and the index sequence to obtain the observation matrix N1 after spatial scrambling, and specifically referring to step S1033.
Performing a second encryption to obtain a chaotic sequence S2cPerforming the following operation of2cMagnification of element (10)15Multiplying the integer part and then taking 2αAnd adjusting the dimensionality according to the row number and the column number of the observation matrix to obtain an encryption sequence, wherein alpha is a positive integer, and the calculation formula is as follows:
C2＝floor(S2c×1015)mod 2α (5)
dimension adjustment is carried out on the C2 according to the column number and the row number of the observation matrix Y to ensure that the dimensions are consistent, and the encryption sequence C is obtained2m. And encrypting the observation matrix after spatial scrambling by adopting an encryption sequence, wherein the calculation formula is as follows:
N2m＝β·N1+(1-β)·C2m (4)
where N1 is the spatially scrambled observation matrix, C2mFor encrypting the sequence, N2mFor encrypting the image, the value of beta belongs to (0, 1), and the value of beta can be jointly appointed by the transmitting terminal and the receiving terminal without transmission.
After the encryption is finished, the sending end encrypts the image and the (phi)_u，Φ_x0，Φ_d)、(P_u，P_x0，P_d) Parameter (Ci)_X0，Ci_y0，Ci_H0，Ci_Z0，Ci_d) (i-1 or 2), YmaxAnd YminAnd sending the data to a receiving end. In other embodiments, the encrypted image, Φ, may also be directly usedm×nMatrix, Ps×tMatrix, S1cMatrix, S2cMatrix YmaxAnd YminAnd sending the data to a receiving end.
The receiving end firstly decrypts the encryption process of the second step, and the decryption formula is as follows:
wherein N is2m_rFor the encrypted image received by the receiving end, N in equation 42mThe same; c2mFor the encrypted sequence, β ∈ (0, 1), β being the same as the value in equation 4;
n1_ d is an image obtained by the inverse digital concealment operation, and corresponds to the observation matrix after spatial scrambling in step S103.
And performing inverse operation on the spatial scrambling in the first-step encryption process to obtain a matrix N _ d.
Further, performing an inverse normalization operation, wherein the calculation formula is as follows:
wherein, YmaxTo observe the maximum value in the matrix Y, YminIs the minimum value in the observation matrix Y, YrAnd alpha is a positive integer and is the same as the value in the formula 2, wherein alpha is an observation matrix obtained by the reverse normalization operation.
Finally, the observation matrix Y is subjected to IRLS algorithm based on the first and second visual matrixesrAnd reconstructing to obtain a reconstructed image. Wherein the IRLS algorithm adopts lρUpdating the weight of norm, rho is 0.8, and defines epsilonnIn order to iterate the weights,
for iterating the ith column of the matrix at the nth time, xi (n)For the ith column of the reconstruction matrix at the nth iteration, ε is initialized0＝1，
The reconstruction process comprises the following steps:
for each column vector y in the observation matrix yiWhen ε > 10-9Then, the following operations are performed:
updating
Order to
Updating
Updating epsilonn+1＝min(εn，[r(x(n+1))k+1]/q) (11)
At the end of the iteration, output x ═ x(n+1)。
Wherein, r (x)(n+1) k+1The method comprises the steps that the absolute value of a (k + 1) th component is arranged in a descending order in a signal x of q rows and 1 columns, k is the sparsity of the signal x, n is the iteration number, i is the serial number of a column in a matrix, x' is a reconstructed column vector, y is an observation matrix, phi is a low-dimensional measurement matrix, namely a first chaotic matrix, P is an expanded-dimensional matrix, namely a second chaotic matrix, and T is a transposed matrix.
The beneficial effects of the present invention are explained below with reference to experimental data:
the method for constructing the measurement matrix by the P tensor product compressed sensing is to construct a low-dimensional measurement matrix and obtain a high-dimensional measurement matrix by using the tensor product, and the performance of the low-dimensional measurement matrix directly influences the performance of the high-dimensional measurement matrix. Specifically, the image is Xq×qThe low-dimensional measurement matrix is phim×nThen the P matrix for size enlargement is
The dimension expansion multiple is q/n.
1. According to the method, a tensor product compressed sensing method is used for constructing the measurement matrix, with the increase of the dimension expansion multiple q/n, the length exponential level of a chaos sequence required to be generated for constructing the Chaotic matrix is reduced, meanwhile, the speed exponential level for generating the Chaotic matrix is accelerated, and the required time exponential level is reduced, as shown in tables 1 and 2.
2. The method for constructing the measurement matrix by using the tensor product compressed sensing method can reduce the occupation of the measurement matrix on the storage space, as shown in table 3, wherein the traditional CS is a traditional compressed sensing model, and the size of the P matrix in the compressed sensing of the CS-8 representing P tensor product is P8×8In the compressed sensing of CS-4 representing P tensor product, the P matrix size is P4×4。
3. Based on the encryption transmission method, under the same condition, the effect of the reduction and reconstruction of the IRLS algorithm is more stable than that of the Orthogonal Matching Pursuit (OMP) algorithm, meanwhile, the reduction and reconstruction effect of the IRLS algorithm has a peak signal-to-noise ratio which is higher, and the accuracy of the restored image is higher, as shown in Table 4.
In particular, the key space of the cryptographic system amounts to 10200. Enough to resist brute force. The sensitivity of the key of the simultaneous encryption reaches 10-16And the information entropy of the encrypted image can reach about 7.
In summary, the method and the device for safely transmitting and receiving the medical image generate two chaotic matrixes based on the logistic chaotic system and calculate the tensor product as the measurement matrix in the transmission process, and compared with a method for constructing the measurement matrix, the method and the device can greatly reduce the calculation complexity and reduce the construction time of the measurement matrix. In the compressed sensing technology, the same measurement matrix and user encryption sequence are required for the steps of image compression and image restoration, and in the transmission process, except for the encrypted images, only the initial parameters for generating the first chat matrix, the second chat matrix, the first chaotic sequence and the second chaotic sequence are transmitted, so that the data volume is greatly reduced, and the transmission speed is improved.
Furthermore, the compressed sensing technology has the characteristic that the image is compressed and simultaneously has the encryption property, the measurement matrix can be regarded as a key for image decryption, the image can be restored by the correct key, two Chaotic matrices can be regarded as encryption based on the tensor product technology, the adopted Chaotic matrices are generated by a Chaotic system, and the system has the characteristic that the output is greatly changed due to the tiny change of input parameters, so the tensor products of the two Chaotic matrices are much larger than the key space of one measurement matrix, and the safety in the image transmission process is greatly improved.
Those of ordinary skill in the art will appreciate that the various illustrative components, systems, and methods described in connection with the embodiments disclosed herein may be implemented as hardware, software, or combinations of both. Whether this is done in hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention. When implemented in hardware, it may be, for example, an electronic circuit, an Application Specific Integrated Circuit (ASIC), suitable firmware, plug-in, function card, or the like. When implemented in software, the elements of the invention are the programs or code segments used to perform the required tasks. The program or code segments may be stored in a machine-readable medium or transmitted by a data signal carried in a carrier wave over a transmission medium or a communication link. A "machine-readable medium" may include any medium that can store or transfer information. Examples of a machine-readable medium include electronic circuits, semiconductor memory devices, ROM, flash memory, Erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, fiber optic media, Radio Frequency (RF) links, and so forth. The code segments may be downloaded via computer networks such as the internet, intranet, etc.
It should also be noted that the exemplary embodiments mentioned in this patent describe some methods or systems based on a series of steps or devices. However, the present invention is not limited to the order of the above-described steps, that is, the steps may be performed in the order mentioned in the embodiments, may be performed in an order different from the order in the embodiments, or may be performed simultaneously.
Features that are described and/or illustrated with respect to one embodiment may be used in the same way or in a similar way in one or more other embodiments and/or in combination with or instead of the features of the other embodiments in the present invention.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made to the embodiment of the present invention by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. A medical image security transmission method is characterized by comprising the following steps:
acquiring an original medical image, and performing sparse representation on the medical image to obtain a corresponding sparse matrix;
generating a first chaotic matrix based on a first initial parameter and a second chaotic matrix based on a second initial parameter by adopting a logistic chaotic system, calculating a tensor product of the first chaotic matrix and the second chaotic matrix, sampling and compressing a sparse matrix of the medical image according to the tensor product to obtain an observation matrix, and normalizing the observation matrix;
generating a first chaotic sequence based on a third initial parameter and a second chaotic sequence based on a fourth initial parameter by adopting a chaotic system, carrying out spatial scrambling on the observation matrix after the normalization processing by adopting the first chaotic sequence, and carrying out digital hidden encryption on the observation matrix after the spatial scrambling by adopting the second chaotic sequence to obtain an encrypted image;
sending the first initial parameter, the second initial parameter, the third initial parameter, the fourth initial parameter, the standard parameter in the normalization process and the encrypted image to a receiving end; wherein the standard parameter is a maximum value, a minimum value and/or an average value in the observation matrix, the receiving end regenerates the first chaotic matrix based on the first initial parameter and the second chaotic matrix based on the second initial parameter by adopting a logistic chaotic system, regenerates the first chaotic sequence based on the third initial parameter and the second chaotic sequence based on the fourth initial parameter by adopting a chaotic system, performs digital hidden inverse operation on the encrypted image by adopting the second chaotic sequence, performs spatial scrambling inverse operation on the obtained image according to the first chaotic sequence and performs inverse normalization operation by adopting the standard parameter to obtain the observation matrix, and reconstructs the observation matrix by utilizing a preset reconstruction algorithm based on the first chaotic matrix and the second chaotic matrix to obtain a reconstructed image.
2. The medical image security transmission method according to claim 1, wherein the obtaining of the corresponding sparse matrix after the medical image is sparsely represented comprises: and performing discrete wavelet transformation on the medical image to obtain a sparse matrix.
3. The method according to claim 1, wherein the first initial parameter includes three parameters of a first randomly generated control value, a first initial value and a first sampling distance, the second initial parameter includes three parameters of a second randomly generated control value, a second initial value and a second sampling distance, the value ranges of the first control value and the second control value are (3.5699457, 4), the value ranges of the first initial value and the second initial value are (0, 1), and the value ranges of the first sampling distance and the second sampling distance are [15, + ∞ ]; the third initial parameter and the fourth initial parameter both comprise 4 randomly generated chaotic system initial values and 1 chaotic system sampling distance, the value range of the chaotic system initial values is (0, 1), and the value range of the chaotic system sampling distance is [1, + ∞ ].
4. The medical image security transmission method according to claim 1, wherein the calculation formula for performing normalization processing on the observation matrix is:
wherein Y is an observation matrix, YmaxTo observe the maximum value in the matrix Y, YminIs the minimum value in the observation matrix Y, alpha is a positive integer, and N is the observation matrix after normalization processing.
5. The method according to claim 4, wherein α is 8.
6. The medical image security transmission method according to claim 1, wherein spatially scrambling the normalized observation matrix using the first chaotic sequence includes:
expanding the observation matrix after the normalization processing into a row vector, and marking a first sequence number for each element in the row vector according to the sequence from left to right;
marking a second sequence number for each element in the first chaotic sequence according to the sequence from left to right, rearranging the elements in the first chaotic sequence according to the sequence from small to large, and forming an index sequence by the second sequence numbers corresponding to the elements after rearrangement;
and rearranging and splicing the elements in the row vector according to the one-to-one correspondence relationship between the first sequence number and the index sequence to obtain the observation matrix after spatial scrambling.
7. The medical image security transmission method according to claim 1, wherein the step of performing digital hidden encryption on the spatially scrambled observation matrix by using the second chaotic sequence to obtain an encrypted image comprises:
amplifying 10 elements in the second chaotic sequence15Multiplying the integer part and then taking 2αAdjusting the dimensionality according to the row number and the column number of the observation matrix to obtain an encryption sequence, wherein alpha is a positive integer;
and encrypting the observation matrix after spatial scrambling by adopting the encryption sequence, wherein the calculation formula is as follows:
N2m＝β·N1+(1-β)·C2m；
where N1 is the spatially scrambled observation matrix, C2mFor encrypting the sequence, N2mTo encrypt an image, β ∈ (0, 1).
8. A method for receiving medical image security, comprising:
receiving a first initial parameter, a second initial parameter, a third initial parameter, a fourth initial parameter, a standard parameter and an encrypted image, wherein the encrypted image is obtained by encrypting and compressing the medical image security transmission method according to any one of claims 1 to 7, and the standard parameter is a maximum value, a minimum value and/or an average value of an observation matrix in the medical image security transmission method according to any one of claims 1 to 7;
regenerating the first visual matrix based on the first initial parameters and the second visual matrix based on the second initial parameters by adopting a logistic chaotic system;
regenerating the first chaotic sequence based on the third initial parameter and regenerating the second chaotic sequence based on the fourth initial parameter by adopting a chaotic system;
performing digital hidden inverse operation on the encrypted image by adopting the second chaotic sequence, performing inverse operation of spatial scrambling on the decrypted image according to the first chaotic sequence, and performing inverse normalization operation according to the standard parameter to obtain the observation matrix;
and reconstructing the observation matrix by utilizing an IRLS algorithm based on the first and second visual matrixes to obtain a reconstructed image.
9. The medical image security receiving method according to claim 8, wherein reconstructing the observation matrix based on the first and second chaotic matrices by using an IRLS algorithm to obtain a reconstructed image comprises:
definition of εnIn order to iterate the weights,
for iterating the ith column of the matrix at the nth time, xi (n)For the ith column of the reconstruction matrix at the nth iteration, ε is initialized0＝1，
The IRLS algorithm employs lρUpdating the weight of the norm, wherein rho is 0.8, and the reconstruction process comprises the following steps:
for each column vector y in the observation matrix yiWhen ε > 10-9Then, the following operations are performed:
updating
Order to
Updating
Updating epsilonn+1＝min(εn，[r(x(n+1))k+1]/q)；
At the end of the iteration, output x ═ x(n+1)。
Wherein, r (x)(n+1))k+1The absolute value of the (k + 1) th component arranged in descending order in the signal x of q rows and 1 columns is defined as k, the sparsity of the signal x is defined as k, the iteration number is defined as n, i is the serial number of the column in the matrix, x' is the reconstructed column vector, y is the observation matrix, phi is the first chaotic matrix, P is the second chaotic matrix, and T is the transposed matrix.
10. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the steps of the method according to any of claims 1 to 8 are implemented when the processor executes the program.
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