CN103347189A - Bidimensional compressed sensing image acquisition and reconstruction method based on discrete cosine transformation (DCT) and discrete Fourier transformation (DFT) - Google Patents

Bidimensional compressed sensing image acquisition and reconstruction method based on discrete cosine transformation (DCT) and discrete Fourier transformation (DFT) Download PDF

Info

Publication number
CN103347189A
CN103347189A CN2013103337718A CN201310333771A CN103347189A CN 103347189 A CN103347189 A CN 103347189A CN 2013103337718 A CN2013103337718 A CN 2013103337718A CN 201310333771 A CN201310333771 A CN 201310333771A CN 103347189 A CN103347189 A CN 103347189A
Authority
CN
China
Prior art keywords
matrix
sparse
dct
dft
dimension
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN2013103337718A
Other languages
Chinese (zh)
Other versions
CN103347189B (en
Inventor
程涛
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Guangxi University of Science and Technology
Original Assignee
程涛
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 程涛 filed Critical 程涛
Priority to CN201310333771.8A priority Critical patent/CN103347189B/en
Publication of CN103347189A publication Critical patent/CN103347189A/en
Application granted granted Critical
Publication of CN103347189B publication Critical patent/CN103347189B/en
Expired - Fee Related legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Landscapes

  • Complex Calculations (AREA)
  • Image Processing (AREA)

Abstract

The invention discloses a bidimensional compressed sensing image acquisition and reconstruction method based on discrete cosine transformation (DCT) and discrete Fourier transformation (DFT), belongs to the technical field of designs of measurement matrixes and optimization of reconstruction matrixes in the compressed sensing process and provides a method for firstly determining the measurement matrix and a sparse matrix and then optimizing the reconstruction matrix. In a measurement stage, the 0-1 sparse matrix is adopted; in a reconstruction stage, a Gaussian matrix is adopted; and therefore, an after-optimization method capable of easily implementing hardware and guaranteeing a signal reconstruction effect can be realized. The method comprises the following steps of: performing row vector orthogonal normalization and column vector unitization on the reconstruction matrix obtained by the (i-1)th iteration calculation through ith iteration, optimizing the reconstruction matrix on the basis of maximum values of absolute values of relevant coefficients among row and column vectors, the convergence stability of row vector modules and the number of rows and the number of columns which obey the Gaussian distribution, and finishing the after-optimization on measurement data subjected to one-dimensional and two-dimensional sparse transformation and the measurement matrixes by calculating a transitional matrix and a proximity matrix. The method lays a foundation for the compressed sensing from theoretical research to industrialization.

Description

Two dimensional compaction perception image collection and reconstructing method based on DCT and DFT
Technical field
The invention belongs to the compressed sensing technical field, a kind of two dimensional compaction perception image collection and reconstructing method based on DCT and DFT specifically is provided.
Background technology
The design of measurement matrix and the optimization of restructuring matrix are the key factors that concerns signal reconstruction in the compressed sensing.Random matrix (Gauss, Bernoulli Jacob's equal matrix) though signal reconstruction ability and universality are preferably arranged, but owing to be difficult to that hardware is realized people then research character is relatively poor, be easy to hard-wired certainty matrix (Teoplitz, circulation, multinomial, 0-1 sparse matrix etc.).The 0-1 sparse matrix not only is easy to hardware and realizes but also the little fast operation of required memory space.But the ranks irrelevance of 0-1 sparse matrix is relatively poor, and adopts sparse matrix can cause each element in the measured value can only comprise a part of information of signal, and each element no longer is in par, the anti-packet loss ability variation.And the ranks irrelevance of the restructuring matrix of 0-1 sparse matrix and sparse transform-based composition is also very poor, a little less than the signal reconstruction ability.
Mostly the optimization of current restructuring matrix be under the fixed situation of sparse transform-based, minimizes or on average turn to the objective optimization restructuring matrix with each row correlation, thereby obtain the measurement matrix that adapts with the restructuring matrix that can improve the signal reconstruction effect.But such measurement matrix design method is not only operated inconvenience, method complexity, and is unfavorable for hardware designs.At the measurement matrix that measuring phases adopts hardware to realize easily, character is relatively poor, adopt in reconstruction stage that hardware is difficult for realizing, character preferably Gauss's matrix be that measurement matrix design and the data that people expect are handled general layout.All to optimize restructuring matrix under the fixed situation also be the design processing scheme that people expect measuring matrix and sparse transform-based.
Summary of the invention
The present invention is low and measure the problem of matrix design in order to solve restructuring matrix signal reconstruction ability, and the spy provides a kind of two dimensional compaction perception image collection and reconstructing method based on DCT and DFT.
The present invention is achieved by following proposal: a kind of two dimensional compaction perception image collection and reconstructing method based on DCT and DFT, and the process of described method is:
Step 1: generate the 0-1 sparse matrix
Figure 285900DEST_PATH_IMAGE001
,
Figure 203041DEST_PATH_IMAGE002
,
Figure 451619DEST_PATH_IMAGE003
Figure 846829DEST_PATH_IMAGE001
Each row vector comprise that to be no less than 2 values be 1 element,
Figure 391029DEST_PATH_IMAGE001
Each column vector comprise that to be no less than 1 value be 1 element.
Figure 151174DEST_PATH_IMAGE004
With
Figure 418208DEST_PATH_IMAGE005
It all is natural number.Generate restructuring matrix
Figure 85949DEST_PATH_IMAGE006
, with optimizing matrix season
Figure 754828DEST_PATH_IMAGE007
, It is sparse transform-based.
Figure 220630DEST_PATH_IMAGE008
Can be DCT matrix (discrete cosine matrix), also can be DFT matrix (discrete fourier matrix);
Step 2: set iterations iInitial value be 0, set iteration error
Figure 426484DEST_PATH_IMAGE009
Step 3: check calculating respectively with Ha Erke-Bei La (Jarque-Bera)
Figure 949869DEST_PATH_IMAGE010
Each row and the real part of each row and the line number (line number of real part Gaussian distributed of imaginary part Gaussian distributed
Figure 848555DEST_PATH_IMAGE011
, the line number of imaginary part Gaussian distributed ) and the columns (columns of real part Gaussian distributed
Figure 834146DEST_PATH_IMAGE013
, the columns of imaginary part Gaussian distributed
Figure 195726DEST_PATH_IMAGE014
), the DFT matrix is that complex matrix possesses real part and imaginary part simultaneously, the DCT matrix is that real number matrix does not have imaginary part; Calculate
Figure 530892DEST_PATH_IMAGE010
Coefficient correlation between each column vector, the maximum of taking out its absolute value
Figure 728655DEST_PATH_IMAGE015
Calculate the coefficient correlation between each row vector, the maximum of taking out its absolute value
Figure 807470DEST_PATH_IMAGE016
Calculate
Figure 774289DEST_PATH_IMAGE010
The mould of each row vector takes out its maximum And minimum value
Figure 965416DEST_PATH_IMAGE018
Step 4: quadrature standardization
Figure 566030DEST_PATH_IMAGE010
Each row vector, each column vector of unitization makes then i= i+ 1, matrix just can be optimized
Figure 918514DEST_PATH_IMAGE019
Calculate transition matrix simultaneously
Figure 329904DEST_PATH_IMAGE020
, approximate matrix
Figure 767838DEST_PATH_IMAGE021
, and order
Step 5: judgement optimization matrix
Figure 129867DEST_PATH_IMAGE023
With
Figure 712158DEST_PATH_IMAGE024
With
Figure 637388DEST_PATH_IMAGE025
With
Figure 579805DEST_PATH_IMAGE026
With
Figure 641302DEST_PATH_IMAGE027
With With ((
Figure 807021DEST_PATH_IMAGE029
With
Figure 303862DEST_PATH_IMAGE030
) or (
Figure 485444DEST_PATH_IMAGE031
With
Figure 143959DEST_PATH_IMAGE032
)), if execution in step six, otherwise return execution in step three;
Step 6: obtain the optimization matrix
Figure 43782DEST_PATH_IMAGE033
, transition matrix
Figure 328001DEST_PATH_IMAGE034
And approximate matrix
Step 7: gather by row with the method shown in the following formula by sparse matrix
Figure 459086DEST_PATH_IMAGE036
Measurement data
Figure 315046DEST_PATH_IMAGE037
,
Figure 684848DEST_PATH_IMAGE038
(for the sparse conversion of one dimension Or ),
Figure 168284DEST_PATH_IMAGE040
:
Figure 341777DEST_PATH_IMAGE041
Step 8: divide the sparse conversion of one dimension and two kinds of situations of two-dimentional sparse conversion to optimize measurement data with transition matrix to the measurement data that collects:
The sparse conversion of one dimension:
Figure 821300DEST_PATH_IMAGE042
The sparse conversion of two dimension:
Step 9: divide the sparse conversion of one dimension and two kinds of situations of two-dimentional sparse conversion to find the solution by following formula to the measurement data of optimizing With
Figure 65833DEST_PATH_IMAGE045
, wherein
Figure 399863DEST_PATH_IMAGE046
Be
Figure 256829DEST_PATH_IMAGE044
Column vector,
Figure 840257DEST_PATH_IMAGE047
Be Column vector,
Figure 544088DEST_PATH_IMAGE048
,
Figure 322688DEST_PATH_IMAGE049
:
The sparse conversion of one dimension:
Figure 862254DEST_PATH_IMAGE050
The sparse conversion of two dimension:
Figure 915661DEST_PATH_IMAGE051
Step 10: divide the sparse conversion of one dimension and two kinds of situations of two-dimentional sparse conversion to pass through respectively
Figure 473550DEST_PATH_IMAGE052
With
Figure 954210DEST_PATH_IMAGE053
Restoring signal
Figure 715492DEST_PATH_IMAGE036
The present invention is with right
Figure 41431DEST_PATH_IMAGE054
The iterative cycles computing of the quadrature standardization of each row vector and the unitization of each column vector has realized the optimization of restructuring matrix.The measurement data that collects by transition matrix near-optimal conventional method then
Figure 204560DEST_PATH_IMAGE037
And restructuring matrix
Figure 856121DEST_PATH_IMAGE054
Optimize matrix and approximate matrix and both had the universality of Gauss's matrix, improved the signal reconstruction ability again.Method of the present invention has not only been simplified hardware designs and the realization of measuring matrix, and improved the signal reconstruction effect, have a wide range of applications in fields such as the image processing of compressed sensing, video analysis, radar remote sensing, communication code, digital audio.
Description of drawings
Fig. 1 is that embodiment one is described a kind of based on the two dimensional compaction perception image collection of DCT and DFT and the flow chart of reconstructing method; Fig. 2 uses embodiment 128 * 256 restructuring matrix is handled optimization matrix and the capable module maximum of approximate matrix and the graph of a relation of iterations that obtains; Fig. 3 uses embodiment 128 * 256 restructuring matrix is handled optimization matrix and the ranks coefficient correlation of approximate matrix and the graph of a relation of iterations that obtains; Fig. 4 uses embodiment optimization 128 * 256 restructuring matrix to be handled optimization matrix and the ranks number that meets Ha Erke-Bei La (Jarque-Bera) check of approximate matrix and the graph of a relation of iterations that obtains; Fig. 5 uses embodiment 128 * 256 restructuring matrix is handled the reconstruct probability of the optimization matrix, approximate matrix and the restructuring matrix that obtain and the graph of a relation of degree of rarefication; Fig. 6 uses embodiment is handled the optimization matrix, approximate matrix and the restructuring matrix that obtain to 128 * 256 restructuring matrix the reconstruct effect contrast figure to lena figure; Fig. 7 uses embodiment 128 * 256 restructuring matrix to be handled the optimization matrix, approximate matrix and the restructuring matrix that obtain to the signal to noise ratio of lena figure reconstruction result.
Embodiment
Embodiment one: specify present embodiment according to Figure of description 1.A kind of two dimensional compaction perception image collection and reconstructing method based on DCT and DFT, the process of described method is:
Step 1: generate the 0-1 sparse matrix
Figure 619546DEST_PATH_IMAGE001
,
Figure 483597DEST_PATH_IMAGE002
,
Figure 32390DEST_PATH_IMAGE003
Figure 589273DEST_PATH_IMAGE001
Each row vector comprise that to be no less than 2 values be 1 element,
Figure 856307DEST_PATH_IMAGE001
Each column vector comprise that to be no less than 1 value be 1 element.
Figure 524048DEST_PATH_IMAGE004
With
Figure 645457DEST_PATH_IMAGE005
It all is natural number.Generate restructuring matrix
Figure 904400DEST_PATH_IMAGE006
, with optimizing matrix season
Figure 127571DEST_PATH_IMAGE007
,
Figure 864583DEST_PATH_IMAGE008
It is sparse transform-based.
Figure 856810DEST_PATH_IMAGE008
Can be DCT matrix (discrete cosine matrix), also can be DFT matrix (discrete fourier matrix);
Step 2: set iterations iInitial value be 0, set iteration error
Figure 755495DEST_PATH_IMAGE009
Step 3: check calculating respectively with Ha Erke-Bei La (Jarque-Bera)
Figure 731542DEST_PATH_IMAGE010
Each row and the real part of each row and the line number (line number of real part Gaussian distributed of imaginary part Gaussian distributed
Figure 990354DEST_PATH_IMAGE011
, the line number of imaginary part Gaussian distributed
Figure 102666DEST_PATH_IMAGE012
) and the columns (columns of real part Gaussian distributed
Figure 906674DEST_PATH_IMAGE013
, the columns of imaginary part Gaussian distributed ), the DFT matrix is that complex matrix possesses real part and imaginary part simultaneously, the DCT matrix is that real number matrix does not have imaginary part; Calculate
Figure 901361DEST_PATH_IMAGE010
Coefficient correlation between each column vector, the maximum of taking out its absolute value
Figure 399338DEST_PATH_IMAGE015
Calculate the coefficient correlation between each row vector, the maximum of taking out its absolute value
Figure 374247DEST_PATH_IMAGE016
Calculate
Figure 590465DEST_PATH_IMAGE010
The mould of each row vector takes out its maximum
Figure 941812DEST_PATH_IMAGE017
And minimum value
Step 4: quadrature standardization
Figure 705686DEST_PATH_IMAGE010
Each row vector, each column vector of unitization makes then i= i+ 1, matrix just can be optimized
Figure 861729DEST_PATH_IMAGE019
Calculate transition matrix simultaneously
Figure 751188DEST_PATH_IMAGE020
, approximate matrix
Figure 692599DEST_PATH_IMAGE021
, and order
Figure 540470DEST_PATH_IMAGE022
Step 5: judgement optimization matrix
Figure 934542DEST_PATH_IMAGE023
With
Figure 158850DEST_PATH_IMAGE024
With
Figure 204035DEST_PATH_IMAGE025
With
Figure 957227DEST_PATH_IMAGE026
With
Figure 838596DEST_PATH_IMAGE027
With
Figure 601015DEST_PATH_IMAGE028
With ((
Figure 251440DEST_PATH_IMAGE029
With
Figure 424801DEST_PATH_IMAGE030
) or (
Figure 324624DEST_PATH_IMAGE031
With
Figure 359576DEST_PATH_IMAGE032
)), if execution in step six, otherwise return execution in step three;
Step 6: obtain the optimization matrix
Figure 395665DEST_PATH_IMAGE033
, transition matrix
Figure 490660DEST_PATH_IMAGE034
And approximate matrix
Step 7: gather by row with the method shown in the following formula by sparse matrix
Figure 180670DEST_PATH_IMAGE036
Measurement data
Figure 805687DEST_PATH_IMAGE037
,
Figure 602742DEST_PATH_IMAGE038
(for the sparse conversion of one dimension Or
Figure 853911DEST_PATH_IMAGE039
),
Figure 333434DEST_PATH_IMAGE040
:
Figure 301390DEST_PATH_IMAGE041
Step 8: divide the sparse conversion of one dimension and two kinds of situations of two-dimentional sparse conversion to optimize measurement data with transition matrix to the measurement data that collects:
The sparse conversion of one dimension:
The sparse conversion of two dimension:
Figure 30498DEST_PATH_IMAGE043
Step 9: divide the sparse conversion of one dimension and two kinds of situations of two-dimentional sparse conversion to find the solution by following formula to the measurement data of optimizing
Figure 630106DEST_PATH_IMAGE044
With
Figure 768964DEST_PATH_IMAGE045
, wherein
Figure 821233DEST_PATH_IMAGE046
Be
Figure 70949DEST_PATH_IMAGE044
Column vector,
Figure 774332DEST_PATH_IMAGE047
Be
Figure 84090DEST_PATH_IMAGE045
Column vector,
Figure 623656DEST_PATH_IMAGE048
,
Figure 677063DEST_PATH_IMAGE049
:
The sparse conversion of one dimension:
Figure 985684DEST_PATH_IMAGE050
The sparse conversion of two dimension:
Figure 935186DEST_PATH_IMAGE051
Step 10: divide the sparse conversion of one dimension and two kinds of situations of two-dimentional sparse conversion to pass through respectively
Figure 945736DEST_PATH_IMAGE052
With
Figure 802834DEST_PATH_IMAGE053
Restoring signal
Figure 965962DEST_PATH_IMAGE036
Embodiment two: this embodiment is described a kind of based on the two dimensional compaction perception image collection of DCT and DFT and further specifying of reconstructing method to embodiment one, sets iteration error in the step 2 Err1 is
Figure 617523DEST_PATH_IMAGE055
, Err2 are
Figure 131681DEST_PATH_IMAGE055
, Err3 are
Figure 526890DEST_PATH_IMAGE055
Embodiment three: this embodiment is described a kind of based on the two dimensional compaction perception image collection of DCT and DFT and further specifying of reconstructing method to embodiment one, the described quadrature standardization of step 4
Figure 544525DEST_PATH_IMAGE010
Each row vector, the detailed process of each column vector of unitization is then: at first right The vectorial orthogonalization of each row, each row vector, each column vector of unitization at last of unitization then.
Embodiment four: specify present embodiment below in conjunction with Fig. 2-Fig. 7.Present embodiment is to adopt gaussian signal and the 0-1 signal of different degree of rarefications to be applied to optimize matrix, approximate matrix and restructuring matrix respectively, relatively the reconstruct probability after each the 500 times experiments.And adopt lena figure to verify the reconstruct effect of optimizing matrix, approximate matrix and restructuring matrix respectively with 1D-DCT, 2D-DCT, 1D-DFT and 2D-DFT.Band among Fig. 2 "
Figure 617709DEST_PATH_IMAGE056
" mark be the maximum curve; Band " " mark be the minimum value curve; Band "
Figure 688750DEST_PATH_IMAGE058
" mark be reference line.Band among Fig. 3-Fig. 4 " " mark be the row curves; Band " " mark be the row curve.(a) represents the optimization matrix that sparse matrix is the DFT matrix among Fig. 2-Fig. 3; (b) represent the approximate matrix that sparse matrix is the DFT matrix; (c) represent the optimization matrix that sparse matrix is the DCT matrix; (d) represent the approximate matrix that sparse matrix is the DCT matrix.(a) represents the real part that sparse matrix is the optimization matrix of DFT matrix among Fig. 4; (b) represent the real part that sparse matrix is the approximate matrix of DFT matrix; (c) represent the imaginary part that sparse matrix is the optimization matrix of DCT matrix; (d) represent the imaginary part that sparse matrix is the approximate matrix of DCT matrix; (e) represent the optimization matrix that sparse matrix is the DFT matrix; (f) represent the approximate matrix that sparse matrix is the DFT matrix.Band among Fig. 5 "
Figure 376717DEST_PATH_IMAGE059
,
Figure 900103DEST_PATH_IMAGE060
,
Figure 782477DEST_PATH_IMAGE061
" curve of mark is respectively to adopt the reconstruct probability curve of optimizing matrix, approximate matrix and restructuring matrix.Among Fig. 5 (a) to represent sparse matrix be the DFT matrix, signal is Gauss's sparse signal; (b) representing sparse matrix is the DFT matrix, and signal is the 0-1 sparse signal; (c) representing sparse matrix is the DCT matrix, and signal is Gauss's sparse signal; (d) representing sparse matrix is the DCT matrix, and signal is the 0-1 sparse signal.Being respectively the Lena figure of 1D-DCT, 2D-DCT, 1D-DFT and 2D-DFT from top to bottom among Fig. 6, is respectively restructuring matrix, the reconstruct image of optimizing matrix and approximate matrix from left to right, and rightmost is original Lena figure.Fig. 7 is signal to noise ratio (snr) and the Y-PSNR (PSNR) of each figure among Fig. 6.
Experimental result such as Fig. 2-shown in Figure 7.As seen from Figure 2, restructuring matrix is optimized optimization matrix and the extreme difference of the corresponding vectorial mould of each row of the approximate matrix convergence that constantly diminishes with it in the iterative process; As seen from Figure 3, the maximum of optimizing matrix and each ranks coefficient correlation absolute value of the approximate matrix convergence that constantly diminishes; As seen from Figure 4, restructuring matrix optimize optimize in the iterative process matrix and with it the ranks number of corresponding each ranks Gaussian distributed of approximate matrix become many rapidly in the iteration later stage, Gaussian distributed nearly all; As seen from Figure 5, optimize the reconstruct probability curve of matrix and approximate matrix very near similar, be positioned at the right side of the curve of restructuring matrix fully; As seen from Figure 7, signal to noise ratio and the Y-PSNR of optimization matrix and approximate matrix are very approaching.

Claims (8)

1. two dimensional compaction perception image collection and reconstructing method based on DCT and a DFT, it is characterized in that: the process of described method is:
Step 1: generate the 0-1 sparse matrix ,
Figure 934434DEST_PATH_IMAGE002
,
Figure 781167DEST_PATH_IMAGE003
,
Figure 850754DEST_PATH_IMAGE001
Each row vector comprise that to be no less than 2 values be 1 element,
Figure 314097DEST_PATH_IMAGE001
Each column vector comprise that to be no less than 1 value be 1 element, With
Figure 343419DEST_PATH_IMAGE005
All be natural number, generate restructuring matrix , with optimizing matrix season
Figure 534545DEST_PATH_IMAGE007
,
Figure 885892DEST_PATH_IMAGE008
Be sparse transform-based,
Figure 707218DEST_PATH_IMAGE008
Can be DCT matrix (discrete cosine matrix), also can be DFT matrix (discrete fourier matrix);
Step 2: set iterations iInitial value be 0, set iteration error
Step 3: check calculating respectively with Ha Erke-Bei La (Jarque-Bera)
Figure 540231DEST_PATH_IMAGE010
Each row and the real part of each row and the line number (line number of real part Gaussian distributed of imaginary part Gaussian distributed
Figure 226427DEST_PATH_IMAGE011
, the line number of imaginary part Gaussian distributed
Figure 902259DEST_PATH_IMAGE012
) and the columns (columns of real part Gaussian distributed
Figure 15708DEST_PATH_IMAGE013
, the columns of imaginary part Gaussian distributed ), the DFT matrix is that complex matrix possesses real part and imaginary part simultaneously, the DCT matrix is that real number matrix does not have imaginary part; Calculate
Figure 102930DEST_PATH_IMAGE010
Coefficient correlation between each column vector, the maximum of taking out its absolute value
Figure 430006DEST_PATH_IMAGE015
Calculate the coefficient correlation between each row vector, the maximum of taking out its absolute value Calculate
Figure 579414DEST_PATH_IMAGE010
The mould of each row vector takes out its maximum And minimum value
Figure 726678DEST_PATH_IMAGE018
Step 4: quadrature standardization
Figure 181930DEST_PATH_IMAGE010
Each row vector, each column vector of unitization makes then i= i+ 1, matrix just can be optimized
Figure 550595DEST_PATH_IMAGE019
, calculate transition matrix simultaneously , approximate matrix
Figure 870904DEST_PATH_IMAGE021
, and order
Figure 965899DEST_PATH_IMAGE022
Step 5: judgement optimization matrix
Figure 87438DEST_PATH_IMAGE023
With
Figure 926081DEST_PATH_IMAGE024
With
Figure 551098DEST_PATH_IMAGE025
With
Figure 348153DEST_PATH_IMAGE026
With With
Figure 989535DEST_PATH_IMAGE028
With ((
Figure 718326DEST_PATH_IMAGE029
With ) or (
Figure 720097DEST_PATH_IMAGE031
With
Figure 900542DEST_PATH_IMAGE032
)), if execution in step six, otherwise return execution in step three;
Step 6: obtain the optimization matrix
Figure 761137DEST_PATH_IMAGE033
, transition matrix And approximate matrix
Step 7: gather by row with the method shown in the following formula by sparse matrix
Figure 670822DEST_PATH_IMAGE036
Measurement data
Figure 124937DEST_PATH_IMAGE037
,
Figure 434695DEST_PATH_IMAGE038
(for the sparse conversion of one dimension
Figure 957949DEST_PATH_IMAGE038
Or
Figure 11356DEST_PATH_IMAGE039
), :
Figure 269479DEST_PATH_IMAGE041
Step 8: divide the sparse conversion of one dimension and two kinds of situations of two-dimentional sparse conversion to optimize measurement data with transition matrix to the measurement data that collects:
The sparse conversion of one dimension:
Figure 296341DEST_PATH_IMAGE042
The sparse conversion of two dimension:
Figure 887859DEST_PATH_IMAGE043
Step 9: divide the sparse conversion of one dimension and two kinds of situations of two-dimentional sparse conversion to find the solution by following formula to the measurement data of optimizing
Figure 565834DEST_PATH_IMAGE044
With
Figure 686237DEST_PATH_IMAGE045
, wherein Be Column vector,
Figure 613239DEST_PATH_IMAGE047
Be
Figure 153810DEST_PATH_IMAGE045
Column vector,
Figure 889685DEST_PATH_IMAGE048
,
Figure 88585DEST_PATH_IMAGE049
:
The sparse conversion of one dimension:
The sparse conversion of two dimension:
Figure 688511DEST_PATH_IMAGE051
Step 10: divide the sparse conversion of one dimension and two kinds of situations of two-dimentional sparse conversion to pass through respectively With
Figure 163541DEST_PATH_IMAGE053
Restoring signal
2. a kind of two dimensional compaction perception image collection and reconstructing method based on DCT and DFT according to claim 1 is characterized in that step 1 is described
Figure 320032DEST_PATH_IMAGE001
Each row vector comprise that to be no less than 2 values be 1 element,
Figure 30500DEST_PATH_IMAGE001
Each column vector comprise that to be no less than 1 value be 1 element.
3. a kind of two dimensional compaction perception image collection and reconstructing method based on DCT and DFT according to claim 1 is characterized in that the computing formula of transition matrix and approximate matrix in the described iterative process of step 4 With
Figure 417936DEST_PATH_IMAGE021
4. a kind of two dimensional compaction perception image collection and reconstructing method based on DCT and DFT according to claim 1 is characterized in that the described Rule of judgment of step 5 ,
Figure 668974DEST_PATH_IMAGE024
, ,
Figure 714608DEST_PATH_IMAGE027
, , (( With
Figure 506349DEST_PATH_IMAGE030
) or ( With
Figure 739064DEST_PATH_IMAGE032
)).
5. a kind of two dimensional compaction perception image collection and reconstructing method based on DCT and DFT according to claim 1 is characterized in that the computing formula of the described final transition matrix of step 6 and approximate matrix
Figure 176999DEST_PATH_IMAGE034
With
Figure 332037DEST_PATH_IMAGE035
6. a kind of two dimensional compaction perception image collection and reconstructing method based on DCT and DFT according to claim 1 is characterized in that the computing formula that the described measurement data that conventional method is collected of step 8 is optimized with transition matrix
Figure 257136DEST_PATH_IMAGE042
(the sparse conversion of one dimension) and
Figure 370586DEST_PATH_IMAGE043
(two-dimentional sparse conversion).
7. a kind of two dimensional compaction perception image collection and reconstructing method based on DCT and DFT according to claim 1, it is characterized in that step 9 described with
Figure 764658DEST_PATH_IMAGE054
With
Figure 457808DEST_PATH_IMAGE055
Reconstruction model for core (the sparse conversion of one dimension) and
Figure 272497DEST_PATH_IMAGE051
(two-dimentional sparse conversion).
8. a kind of two dimensional compaction perception image collection and reconstructing method based on DCT and DFT according to claim 1 is characterized in that the described signal of step 10 recovers model
Figure 685024DEST_PATH_IMAGE052
(the sparse conversion of one dimension) and
Figure 431132DEST_PATH_IMAGE053
(two-dimentional sparse conversion).
CN201310333771.8A 2013-08-03 2013-08-03 Based on two dimensional compaction perception image collection and the reconstructing method of DCT and DFT Expired - Fee Related CN103347189B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201310333771.8A CN103347189B (en) 2013-08-03 2013-08-03 Based on two dimensional compaction perception image collection and the reconstructing method of DCT and DFT

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201310333771.8A CN103347189B (en) 2013-08-03 2013-08-03 Based on two dimensional compaction perception image collection and the reconstructing method of DCT and DFT

Publications (2)

Publication Number Publication Date
CN103347189A true CN103347189A (en) 2013-10-09
CN103347189B CN103347189B (en) 2016-02-17

Family

ID=49281960

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201310333771.8A Expired - Fee Related CN103347189B (en) 2013-08-03 2013-08-03 Based on two dimensional compaction perception image collection and the reconstructing method of DCT and DFT

Country Status (1)

Country Link
CN (1) CN103347189B (en)

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109347482A (en) * 2018-08-03 2019-02-15 西安电子科技大学 Frequency Hopping Signal compressed sensing reconstructing method based on parameter Estimation
CN110542855A (en) * 2019-09-08 2019-12-06 广东石油化工学院 Load switch event detection method and system based on discrete cosine transform
CN111028136A (en) * 2019-12-24 2020-04-17 上海寒武纪信息科技有限公司 Method and equipment for processing two-dimensional complex matrix by artificial intelligence processor
CN111651879A (en) * 2020-05-28 2020-09-11 南京工业大学 Geological survey scheme optimization method based on compressed sensing
US10785496B2 (en) 2015-12-23 2020-09-22 Sony Corporation Video encoding and decoding apparatus, system and method

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5168375A (en) * 1991-09-18 1992-12-01 Polaroid Corporation Image reconstruction by use of discrete cosine and related transforms
CN102158701A (en) * 2011-04-19 2011-08-17 湖南大学 Compressed sensing theory-based classification quantification image coding method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5168375A (en) * 1991-09-18 1992-12-01 Polaroid Corporation Image reconstruction by use of discrete cosine and related transforms
CN102158701A (en) * 2011-04-19 2011-08-17 湖南大学 Compressed sensing theory-based classification quantification image coding method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
潘榕: "基于局部DCT系数的图像压缩感知编码与重构", 《自动化学报》 *
陈涛: "基于0-1稀疏循环矩阵的测量矩阵分离研究", 《光学学报》 *

Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US10785496B2 (en) 2015-12-23 2020-09-22 Sony Corporation Video encoding and decoding apparatus, system and method
CN109347482A (en) * 2018-08-03 2019-02-15 西安电子科技大学 Frequency Hopping Signal compressed sensing reconstructing method based on parameter Estimation
CN109347482B (en) * 2018-08-03 2021-04-06 西安电子科技大学 Frequency hopping signal compressed sensing reconstruction method based on parameter estimation
CN110542855A (en) * 2019-09-08 2019-12-06 广东石油化工学院 Load switch event detection method and system based on discrete cosine transform
CN110542855B (en) * 2019-09-08 2021-09-21 广东石油化工学院 Load switch event detection method and system based on discrete cosine transform
CN111028136A (en) * 2019-12-24 2020-04-17 上海寒武纪信息科技有限公司 Method and equipment for processing two-dimensional complex matrix by artificial intelligence processor
CN111028136B (en) * 2019-12-24 2023-04-07 上海寒武纪信息科技有限公司 Method and equipment for processing two-dimensional complex matrix by artificial intelligence processor
CN111651879A (en) * 2020-05-28 2020-09-11 南京工业大学 Geological survey scheme optimization method based on compressed sensing
CN111651879B (en) * 2020-05-28 2024-04-05 南京工业大学 Compressed sensing-based geological exploration scheme optimization method

Also Published As

Publication number Publication date
CN103347189B (en) 2016-02-17

Similar Documents

Publication Publication Date Title
CN103347189A (en) Bidimensional compressed sensing image acquisition and reconstruction method based on discrete cosine transformation (DCT) and discrete Fourier transformation (DFT)
Liu et al. Robust recovery of subspace structures by low-rank representation
Chen et al. Coordinate-independent sparse sufficient dimension reduction and variable selection
CN102801428A (en) Approximation optimization and signal acquisition reconstruction method for 0-1 sparse cyclic matrix
CN106980106A (en) Sparse DOA estimation method under array element mutual coupling
CN107016656B (en) Wavelet sparse basis optimization method in image reconstruction based on compressed sensing
CN113034414B (en) Image reconstruction method, system, device and storage medium
WO2021068496A1 (en) Co-prime array two-dimensional direction of arrival estimation method based on structured virtual domain tensor signal processing
CN110174658B (en) Direction-of-arrival estimation method based on rank-dimension reduction model and matrix completion
CN102622331B (en) A kind of Gaussian matrix optimization method based on compressed sensing
CN103558498B (en) Based on the insulator pollution flashover leakage current signal sparse representation method of wavelet analysis
CN104598971A (en) Radial basis function neural network based unit impulse response function extraction method
Yao et al. Research of incoherence rotated chaotic measurement matrix in compressed sensing
Wang et al. Efficient dimension reduction for high-dimensional matrix-valued data
Fan et al. Compressed sensing based remote sensing image reconstruction via employing similarities of reference images
CN113708771B (en) Half tensor product compressed sensing method based on Style algorithm
CN103606189A (en) Track base selection method facing non-rigid body three-dimensional reconstruction
CN104881846A (en) Structured image compressive sensing restoration method based on double-density dual-tree complex wavelet
CN110174657B (en) Direction-of-arrival estimation method based on rank-one dimension reduction model and block matrix recovery
Liu et al. Mixture of manifolds clustering via low rank embedding
CN103942805A (en) Rapid image sparse decomposition method based on partial polyatomic matching pursuit
Jie et al. A new construction of compressed sensing matrices for signal processing via vector spaces over finite fields
CN107092006A (en) For the DOA array signal processing methods estimated and system
CN103489207B (en) Gradual model regularization self-adaptive matching tracking method
Cao et al. Direct application of excitation matrix as sparse transform for analysis of wide angle EM scattering problems by compressive sensing

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
C14 Grant of patent or utility model
GR01 Patent grant
TR01 Transfer of patent right
TR01 Transfer of patent right

Effective date of registration: 20170613

Address after: Guangxi University of science and Technology Faculty P.O. Box 268, the Guangxi Zhuang Autonomous Region city 545006 District of Liuzhou City, East Ring Road No. 30

Co-patentee after: Cheng Tao

Patentee after: Guangxi University of Science and Technology

Address before: Guangxi University of science and Technology Faculty P.O. Box 268, the Guangxi Zhuang Autonomous Region city 545006 District of Liuzhou City, East Ring Road No. 30

Patentee before: Cheng Tao

CF01 Termination of patent right due to non-payment of annual fee
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20160217

Termination date: 20170803