CN107948461A - More images hiding in QR codes is realized based on compressed sensing and orthogonal modulation - Google Patents

More images hiding in QR codes is realized based on compressed sensing and orthogonal modulation Download PDF

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Publication number
CN107948461A
CN107948461A CN201711256205.6A CN201711256205A CN107948461A CN 107948461 A CN107948461 A CN 107948461A CN 201711256205 A CN201711256205 A CN 201711256205A CN 107948461 A CN107948461 A CN 107948461A
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image
orthogonal
data
codes
measurement
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周昕
周媛媛
张罗致
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Sichuan University
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Sichuan University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04NPICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/32Circuits or arrangements for control or supervision between transmitter and receiver or between image input and image output device, e.g. between a still-image camera and its memory or between a still-image camera and a printer device
    • H04N1/32101Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title
    • H04N1/32144Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title embedded in the image data, i.e. enclosed or integrated in the image, e.g. watermark, super-imposed logo or stamp
    • H04N1/32149Methods relating to embedding, encoding, decoding, detection or retrieval operations
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04NPICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/32Circuits or arrangements for control or supervision between transmitter and receiver or between image input and image output device, e.g. between a still-image camera and its memory or between a still-image camera and a printer device
    • H04N1/32101Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title
    • H04N1/32144Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title embedded in the image data, i.e. enclosed or integrated in the image, e.g. watermark, super-imposed logo or stamp
    • H04N1/32149Methods relating to embedding, encoding, decoding, detection or retrieval operations
    • H04N1/32267Methods relating to embedding, encoding, decoding, detection or retrieval operations combined with processing of the image
    • H04N1/32272Encryption or ciphering

Abstract

The invention discloses a kind of method for realizing that based on compressed sensing and orthogonal modulation more images hide in QR codes, belong to optical imagery and hide and field of encryption.The present invention mainly utilizes compressed sensing and orthogonal modulation technique, obtains the overall measurement value that multiple image is represented with decimal number, and preserved in the form of QR codes;Decoding when, barcode scanning is carried out to QR codes with photoelectric devices such as mobile phones, regains overall measurement value, then realize as needed entire image piecemeal reconstruction or multiple image in partial reconstitution.From the point of view of optical encryption angle, compressed sensing of the invention and quadrature modulation process can also be considered as two security levels, it is necessary to be correctly only possible to obtain reconstruction image completely in two levels, thus have good encryption performance.

Description

More images hiding in QR codes is realized based on compressed sensing and orthogonal modulation
Technical field
Hidden the invention belongs to optical imagery and field of encryption, specifically a kind of Method of Steganography based on QR codes.
Background technology
With the development of information age, the disposal ability and security of information become more and more important, how to handle sea It is the problem of modern society needs concern to measure data and how to prevent that data from being obtained by unauthorized user, thus various Compress technique and optical encryption technology have obtained extensive concern.QR codes, i.e. quick response matrix code (Quick Response code), it is a kind of matrix two-dimensional barcode that Japanese Denso companies research and develop in September, 1994, extensively The field such as the processing applied to real time data and optical encryption generally.Have benefited from the widely available of smart mobile phone, QR codes are being made Make, sell, logistics, storage, the field such as transport and consumer products gradually have more wide application prospect.But, although it With powerful fault-tolerant and error correcting capability, but still suffer from some limitations and challenge.According to the coding standard of QR codes, it is only Code conversion (i.e. figure pattern, alphanumeric pattern, byte mode and chinese character) can be carried out to the data of four types, And image information is usually not suitable for being converted directly into QR codes since data volume is too big, only those extremely simple, data volumes are very Small image is possible to.Therefore, storage of the image information in QR codes is realized, it is necessary first to reduce the data volume of image.
2006, Donoho proposed theory (the Donoho D L.Compressed sensing [J] of compressed sensing .IEEE Transaction on Information Theory.2006,52(4):1289-1306.), with compressed sensing (or Claim directly to perceive) mode eliminate the information after redundant data, realize the process compressed in collection.By one group with The fractional-sample pixel of machine can reconstruct original image, that is to say, that can be recovered using less significant data original Signal.Up to the present, the most important application of compressive sensing theory is the single pixel camera that rice university of the U.S. works out, profit Line sampling measurement is carried out with digital micromirror array (DMD), measured value vector is obtained, then carries out Accurate Reconstruction.Fig. 1 is The single pixel camera schematic diagram that rice university works out.The imaging system can be divided into three modules:Optical path modulation module, number According to acquisition module, image reconstruction module.The system belongs to passive-type imaging system, having some limitations property, its reconstructed image Resolution ratio is set by calculation matrix, but since pattern of rows and columns of DMD is limited, can only carry out limited resolution The reconstruction of rate image.
In order to increase the flexibility of image reconstruction resolution ratio, and the needs of active imaging system are adapted to, can adopted The random measurement picture of generation is projected to the mode on object with liquid crystal projection apparatus, to replace the function of above-mentioned DMD, is realized The single pixel imaging of dynamic lighting.A series of pictures that will be generated at random according to certain probability distribution, are thrown successively by projecting apparatus Penetrate on testee, then carry out data receiver and sampling with single pixel photodetector, here it is single image is carried out Compress the process of collection.
The content of the invention
The present invention is directed to multiple image, carries out orthogonal modulation respectively by the sampled value to multiple image, is then added To total measurement Value Data, the method for being converted to QR codes is re-encoded, realizes multiple image hiding in QR codes.The present invention exists The compressed sensing of single image, collection have following innovation on the basis of rebuilding:First, although the data capacity of QR codes does not increase Add, but due to the application of compressed sensing, QR codes is concealed more information with same capacity, that is, add and be stored in QR Information content in code, condition is created to convert the image into QR codes;Secondly, which can meet wanting for active imaging system Ask, by setting the size of random measurement matrix, can easily change the resolution ratio of reconstructed image, so as to fulfill more points The reconstruct of resolution image;Further, since the application of orthogonal modulation principle, it can be achieved that in the multiple image of record only reconstruction portion Partial image, or required partial information is only extracted in huge image, the flexibility of data reconstruction is increased, and drop The low operand rebuild;Finally, which also has preferable data security, because from the point of view of angle is encrypted, the present invention Compressed sensing and quadrature modulation process, two security levels can be considered to be, it is necessary to correctly just may be used completely in two levels Reconstruction image can be obtained;The potentiality of the invention that are widely used in life, such as unit or personal much information centralized management Deng.
Fig. 2 is the structure principle chart of the present invention, its target is to realize to carry out larger entire image piecemeal storage and again Build or the restoration and reconstruction wherein piece image from the multiple image of storage.By taking the reconstruction of entire image piecemeal as an example, its basic work It is that original image is subjected to uniform piecemeal first as flow, and measures processing respectively, equivalent to the compression sense to multiple image Primary data gathers;Then orthogonal basic matrix is multiplied by the sampled value of each block image respectively, and be added and obtain by positive intermodulation Overall measurement value after system;It is again QR codes by overall measurement value code conversion with QR codes compiler.When needing to rebuild certain blocking information When, barcode scanning is carried out to QR codes with common Quick Response Code optoelectronic scanning device (such as mobile phone) and retrieves overall measurement value, multiplied by with The transposition of the orthogonal basic matrix of partial response to be restored, can extract the view data for needing to recover.
It is of the present invention based on compressed sensing and orthogonal modulation realize more images in QR codes hide method, including with Lower step:
1) by the pending uniform piecemeal of entire image and be sequentially placed in the first lens rear, by by calculation matrix generate with Machine picture is cast out after being sent into liquid crystal projection apparatus, and projection light field is converged on block image through the first lens;From block image The light transmitted is collected by the second lens again, and is focused on silicon optical detector;The electric signal of explorer response is adopted through data Storage obtains data, is then converted into digital quantity and preserves in a computer.Projecting apparatus often exports a width projection image, data Collector records an electric signal amount corresponding with transmission total light intensity, can after projecting M times for each block image The size for obtaining measured value y, M that M × 1 is tieed up is determined by the sample rate set;Adopted as long as a block image completes measurement Sample, another block image then repeat the process, until all block images complete measurement gatherer process;
2) orthogonal modulation is carried out respectively to these measurement results, by orthogonal basic matrix with each block diagram as corresponding measurement result It is multiplied, you can obtain the corresponding measurement data after orthogonal modulation;Then each block image measurement data is summed to obtain total Measurement Value Data;It is finally QR codes by overall measurement Value Data code conversion, realizes more images hiding in Quick Response Code;
3) if it is desired to rebuilding the parts of images information in entire image, then retrieved always with photoelectric device barcode scanning decoding QR codes Measurement Value Data, the measured value y collected is then multiplied by with the transposition of orthogonal basic matrix corresponding with the part, you can carry The corresponding data of the parts of images are taken out, the parts of images is then recovered from the data extracted with algorithm for reconstructing again.
Wherein, above-mentioned steps 1) the specific implementation process is as follows:
Uniform piecemeal 1a) is carried out to entire image as required, if multiple image, then all picture sizes are pressed into the maximum It is extended to by way of mending zero value pixels consistent.As illustrated in fig. 2, it is assumed that entire image is uniformly divided into m blocks (X1,X2,..., Xm), they are also considered as the different independent image of m width, are sequentially placed in order after the first lens and carry out each measurement step Suddenly.If necessary to recover to the parts of images of reconstruction according to the resolution ratio of N=n × n, then the sampling of each block image Number is (i.e. the quantity of measured value y) M=N × sample rate %.According to compressed sensing principle, the measured value of each block image It is represented by y=ΦM×NXN×1, wherein Φ is calculation matrix generate at random, that size is M × N, and image X also need to through The sparse matrix progress for crossing proper transformation is sparse.Understood according to limited isometry (RIP) property and accurate reconstruction principle (ERP), Useful information can be extracted from compression sampling, it is necessary to meet calculation matrix and the uncorrelated condition of sparse matrix.
1b) since entire image has been uniformly divided into m blocks, the random measurement that corresponding m size of generation is M × N is also required to Matrix (Φ12,...,Φm) (1), a block image is corresponded to respectively.Generated with every a line of each random measurement matrix One width random pictures, are so generated after one group of random pictures is sent into liquid crystal projection apparatus (2) by m calculation matrix and cast out, thrown Light field is penetrated to converge on block image (4) through the first lens (3);The light transmitted from block image (4) is again by the second lens (5) collect and focus on silicon optical detector (6);The electric signal of explorer response is through data collector (7) gathered data, so After be converted to digital quantity and preserve in a computer.Projecting apparatus often exports a width projection image, data collector record one with Transmit the corresponding electric signal amount of total light intensity.For each block image, the measurement that M × 1 is tieed up is can obtain after projecting M times Value y.1c) when a block image completes measurement sampling, another block image replaces it and repeats above procedure, until institute There is block image to complete measurement sampling.It is not difficult to know, after all be measured, we can obtain one group of measurement result (y1,y2,...,ym) (8), each measured value is the column vector for including M element.
The step 2) is implemented as follows:
Each block image measured value result 2a) obtained to the gatherer process Jing Guo compressed sensing carries out orthogonal modulation respectively, The orthogonal basic matrix used in the present invention by Hadamard orthogonal matrixes Column vector groups into.Hadamard orthogonal matrixes are one A square formation, its column vector are orthogonal.If the Hadamard orthogonal matrixes that one size of generation is mM × mM, and by it per M Row propose one new orthogonal basic matrix of composition, then can generate and corresponding m orthogonal basic matrixs of m group measured values (O1,O2,...,Om)(9).The orthogonal basic matrix O of mM × M element is so included by eachiWith each block image Corresponding measurement result yiIt is multiplied, you can obtain the corresponding measurement data D after orthogonal modulationi, its mathematic(al) representation is:
Di=Oiyi=OiΦiXi,i∈[1,m]. (1)
2b) measurement Value Data of each block image after orthogonal modulation is summed, obtains total measurement Value Data D (10):
2c) total measurement Value Data D contains the information of all block images.By more image informations in the present invention through overcompression Perception and orthogonal modulation, obtain one group of metric measurement Value Data, then with QR code compilers, are advised according to the coding of QR codes Then it is encoded to QR codes.
The step 3) is implemented as follows:
3a) according to step 2a) structure orthogonal basic matrix (O1,O2,...,Om) (9), it is by the row of Hadamard orthogonal matrixes Vector forms, and is mutually orthogonal between each column vector, so meeting:
Wherein, OTIt is the transposition of orthogonal basic matrix O, E is a unit matrix, and c is a constant (mould of column vector).
3b) Fig. 3 is the schematic diagram that part block image is rebuild from the QR codes for store multiple image information.Utilize the light such as mobile phone Electrical part carries out barcode scanning to QR codes, can decode and regain total measurement Value Data.Such as need to rebuild wherein any one width piecemeal Image, then with the transposition of corresponding orthogonal basic matrixCorresponding jth width block image is extracted from overall measurement Value Data D Measurement Value Data yj
Therefore, can select to rebuild any one block image as needed, without first rebuilding entire image, this is just significantly Reduce the calculation amount of redundancy.(4) formula is the measurement Value Data corresponding to the block image that the needs extracted are rebuild, then profit With 3c) in algorithm for reconstructing realize image reconstruction recover.The partial information for only extracting needs is thereby realized, without Algorithm reconstruction is carried out to all data.
3c) restructuring procedure of signal needs the conventional image reconstruction algorithm using compressive sensing theory, mainly there is greedy tracing algorithm (OMP), convex this three classes of relaxed algorithm and combinational algorithm.And OMP algorithms are main flow algorithm, it is to utilize iteration thought, each In iterative process select a locally optimal solution come progressively approach original signal:First with the principle of correlation, select With the most matched atom of iteration surplus, the atom is then subjected to Gram-Schmidt orthogonalization process, then signal is projected to By these orthogonalization atomic buildings spatially, so that obtaining signal has selected component and iteration surplus on atom at these, Then repeat the decomposition that the process carries out surplus.
Advantages of the present invention can be summarized as follows:
1) present invention is projected the random measurement picture of generation on object with liquid crystal projection apparatus, is suitable for active dynamic and is shone Bright single pixel imaging, it is possible to achieve the reconstruction of a variety of image in different resolution, equipment are simple;
2) present invention can reduce the treating capacity of data based on compressive sensing theory, offer convenience for post-processing so that in QR Storage multiple image information becomes possible in code;
3) for the larger image of single width, the piecemeal for realizing image using quadrature modulation method is rebuild, and can not only be reduced superfluous Remaining calculation amount, and total calculation amount also significantly reduces, in a particular application, can only recover required parts of images and nothing Whole huge image need to be rebuild;
4) this scheme as optical encryption in application, there is two security levels of compressed sensing and orthogonal modulation, only when measurement square Battle array and orthogonal basic matrix could correctly be rebuild when all correctly matching needed for image, thus encryption is good;Need to rebuild certain width figure During picture, it is only necessary to carry out corresponding extraction, be independent of each other between each view data, efficiency greatly improves;
5) processing method of the invention can be divided into two parts:Rebuild on line under collection and line., can be into one according to this principle Step develops the system that medical treatment and aviation etc. need to transmit mass data that can be applied to, and mitigates the pressure of data transfer.
Brief description of the drawings
Attached drawing 1 is the single pixel camera schematic diagram that rice university works out;
Attached drawing 2 is the method for the present invention coding stage systematic schematic diagram;
Attached drawing 3 is the method for the present invention decoding stage systematic schematic diagram;
Attached drawing 4 is the square objects that four pierced patterns are included in present example;
Attached drawing 5 has been illustrated the process that projector projects random pictures are transmitted through object and is equivalent to random pictures and is weighed Build the product between image;
Attached drawing 6 is the QR codes for including four width hollow out image sampling values in present example;
Attached drawing 7 is the reconstruction experimental result picture of each block image in present example;
Attached drawing 8 is original image to be reconstructed in present example;
Attached drawing 9 is to rebuild some point using the orthogonal basic matrix of mistake or the calculation matrix of mistake respectively in present example The design sketch of block diagram picture;
Shown by reference numeral in above-mentioned attached drawing is:
The random measurement picture of 1 calculation matrix generation, 2 liquid crystal projection apparatus, 3 first lens, 4 represent the object of block image, and 5 the Two lens, 6 photodetectors, 7 data collectors, 8 measured values, 9 orthogonal basic matrixs, 10 overall measurement values, 11 orthogonal basic matrixs Transposition.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings, and the specific embodiment of the present invention is described.
The liquid crystal projection apparatus model EPSON CB-S03 used in the present embodiment, data collector model 7IDA3, light For electric explorer using silicon photocell as probe, preposition amplification, active filter circuit are that the software such as self-control, system control is used Python is worked out.Block image as shown in Figure 4 includes the square objects of four pierced patterns, and photodetector is positioned over On the back focal plane of mirror, four pieces are carried out to the object, and collection and recovery, each block image carry out weight with the resolution ratio of 64*64 respectively Build.
The overall measurement value of 4 width block images is obtained by compressed sensing and orthogonal modulation.The object of four hollow out patterns, quilt After being placed sequentially in the first lens.The random pictures generated by calculation matrix are projected to the every of hollow out object by liquid crystal projection apparatus On a block.Often project M times, recorded one group of measured value of one of block diagram picture, next block diagram picture repeats the process.Fig. 5 The process that projector projects random pictures are transmitted through object has been illustrated to be equivalent between random pictures and reconstructed image Product.Therefore, each output voltage of photodiode amplifier circuit is random measurement picture and treats between reconstructed image The expression of inner product.The hits M of each block image is by by wanting the resolution ratio of reconstruction image and sample rate to determine.In this example In, it is that the original is divided into 4 pieces to be acquired and recover respectively, is rebuild per block diagram picture with resolution ratio 64*64, and with 30% sample rate is sampled, i.e., needs to carry out M=1024 accidental projection for each block diagram picture, that is to say, that, it is necessary to The measured value that the Hadamard orthogonal matrixes O of one 4096 × 4096 obtains each block diagram picture after compressed sensing carries out Orthogonal modulation, every 1024 row form a new orthogonal basic matrix, so as to generate and four block measured values corresponding four A orthogonal basic matrix (O1,O2,O3,O4).Sum after being multiplied by the measured value of each image respectively using each orthogonal basic matrix, you can One group of total measurement Value Data is obtained, is represented by:
Realize multiple image information hiding in QR codes.The electric signal of explorer response, first passes through amplifier and filtering Device processing, is then fed into data collector and carries out A/D conversions, become digital signal and preserved, what is so finally obtained is total Measured value is one group of decimal number, can be easily QR codes with QR code compiler code conversions, realize the hidden of multiple image Hide.Fig. 6 is the QR codes for including four width hollow out image sampling values.
The restoration and reconstruction of each block image are realized in decoding.Barcode scanning decoding QR codes can retrieve total measurement Value Data, so Orthogonal modulation principle is based on afterwards, uses the figure needed for the transposition from total measured value extracting data of corresponding orthogonal basic matrix As data.If for example, recovering the first block diagram picture, useCorresponding first width block diagram is extracted from overall measurement Value Data D The measurement Value Data y of picture1
Then the image is reconstructed using orthogonal matching pursuit algorithm (OMP).The recovery of other each block images similarly, each piecemeal The reconstruction experimental result of image is as shown in fig. 7, only could be accurate under the conditions of calculation matrix and orthogonal basic matrix are matched at the same time Rebuild, illustrate that encryption is good.Certainly, the image of reconstruction also includes certain noise, this is inevitable for compressed sensing , but can be improved to a certain extent by increasing the number of measurement or improving reconstruction resolution ratio.
Rebuild respectively with resolution ratio 32*32 as shown in figure 8, the image is divided into four pieces, Fig. 9 is illustrated with mistake Orthogonal basic matrix extraction data or the design sketch that testee is rebuild with the calculation matrix of mistake.Wherein, Fig. 9 (a)-(d) is use The image that the orthogonal basic matrix of mistake and correct calculation matrix are rebuild, Fig. 9 (e)-(h) is with the calculation matrix of mistake and just The image that true orthogonal basic matrix is rebuild.As can be seen that from the perspective of encryption, the present invention has good encryption, only Could accurate reconstruction image under the conditions of calculation matrix and orthogonal basic matrix are matched at the same time.

Claims (2)

1. a kind of realize multiple image method hiding in QR codes based on compressed sensing and orthogonal modulation technique, its feature exists In:One group of decimal number is collected by multiple image is measured, and is converted to the preservation of QR codes form;In decoding, use The photoelectric devices such as mobile phone carry out barcode scanning to QR codes, so that it may the overall measurement value of multiple image is reacquired, then can be right as needed Which part image is individually rebuild;Without carrying out computing reconstruction to all data, operand greatly reduces;From optical encryption From the point of view of angle, the compressed sensing and quadrature modulation process of this method can be considered to be two security levels, only when measurement square Battle array and orthogonal basic matrix could correctly be rebuild when all correctly matching needed for image, thus have good encryption performance.
2. one kind according to claim 1 realizes that multiple image is hidden in QR codes based on compressed sensing and orthogonal modulation technique The method of Tibetan, it is characterised in that comprising data below acquisition phase, QR coding preservation stages and data extraction phase of regeneration three Step:
1) data acquisition phase:
Uniform piecemeal 1a) is carried out to entire image as required, if multiple image, then all picture sizes are pressed into the maximum It is extended to by way of mending zero value pixels consistent;Assuming that entire image is uniformly divided into m blocks (X1,X2,...,Xm), they It can be considered as the different independent image of m width, be sequentially placed in order after the first lens and carry out each measuring process;If desired The parts of images of reconstruction is recovered according to the resolution ratio of N=n × n, then the sampling number of each block diagram picture is (i.e. measured value The quantity of y) M=N × sample rate %;According to compressed sensing principle, the measured value of each block diagram picture is represented by y=Φ NXN×1, wherein Φ is calculation matrix generate at random, that size is M × N, and image X is also needed to by the sparse of proper transformation Matrix carries out sparse;
M blocks 1b) have been uniformly divided into according to entire image, it is corresponding to generate the random measurement matrix (Φ that m size is M × N1, Φ2,...,Φm) (1), a block image is corresponded to respectively;A width random pictures are generated with every a line of each calculation matrix, this M calculation matrix of sample is generated after one group of random pictures is sent into liquid crystal projection apparatus (2) and cast out, and projection light field is through the first lens (3) converge on block image (4);The light transmitted from block image (4) is collected by the second lens (5) again, and is focused on On silicon optical detector (6);The electric signal of explorer response is then converted into digital quantity simultaneously through data collector (7) gathered data Preserve in a computer;Projecting apparatus often exports a width projection image, and data collector record one is corresponding with transmission total light intensity Electric signal amount, for each block image, can obtain the measured value y that M × 1 is tieed up after projecting M times;
After 1c) block image completes measurement sampling, another block image replaces it and then repeats above step, until institute There is block image to complete measurement gatherer process;After all be measured, one group of measurement result (y is obtained1,y2,...,ym) (8), Each measured value is the column vector for including M element;
2) QR encodes the preservation stage:
Each block image measured value result 2a) obtained to the gatherer process Jing Guo compressed sensing carries out orthogonal modulation respectively; The orthogonal basic matrix used in the present invention is the Column vector groups by Hadamard orthogonal matrixes into Hadamard orthogonal matrixes are one A square formation, its column vector are orthogonal;If the Hadamard orthogonal matrixes that one size of generation is mM × mM, and by it per M Row propose one new orthogonal basic matrix of composition, then can generate and corresponding m orthogonal basic matrix (O of m group measured values1, O2,...,Om)(9);The orthogonal basic matrix O of mM × M element is so included by eachiIt is corresponding with each block image Measurement result yiIt is multiplied, you can obtain the corresponding measurement data D after orthogonal modulationi, its mathematic(al) representation is:
Di=Oiyi=OiΦiXi,i∈[1,m]. (1)
2b) measurement Value Data of each block image after orthogonal modulation is summed, obtains total measurement Value Data D (10):
2c) total measurement Value Data D contains the information of all block images;These overall measurement values are one group of decimal numbers, so QR code compilers are utilized afterwards, and QR codes are encoded to according to QR coding rules;
3) data extraction phase of regeneration:
3a) according to step 2a) structure orthogonal basic matrix (O1,O2,...,Om) (9), be from Hadamard orthogonal matrixes row to Amount forms, and is mutually orthogonal between its each column vector, so meeting:
Wherein, OTIt is the transposition of orthogonal basic matrix O, E is a unit matrix, and c is a constant (mould of column vector);
3b) to storing the QR codes of multiple image information, barcode scanning decoding can be carried out by photoelectric devices such as mobile phones, regained Total measurement Value Data D;Such as need to rebuild wherein any one width block image, then with the transposition of corresponding orthogonal basic matrixFrom The measurement Value Data y of corresponding jth width block image is extracted in overall measurement Value Data Dj
Then compressed sensing reconstruction algorithm is used again from measurement Value Data yjIn recover the parts of images.
CN201711256205.6A 2017-12-04 2017-12-04 More images hiding in QR codes is realized based on compressed sensing and orthogonal modulation Pending CN107948461A (en)

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