CN106612435A - Joint image compression method based on SVD-DWT-DCT - Google Patents
Joint image compression method based on SVD-DWT-DCT Download PDFInfo
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Abstract
The invention puts forward a joint image compression method based on SVD-DWT-DCT. In each stage of image compression, redundant information is removed through low-order approximation in SVD, filtering is carried out in DWT, and association is carried out through DCT. In the first stage, singular value decomposition is carried out, and the singular value of a low-order matrix is discarded from an original image. In the second stage, an approximation band is obtained through discrete wavelet transform. In the final stage, the properties of discrete cosine transform are utilized. Thus, through the hybrid technology, a visual image can be stored, and a good compression ratio can be provided under the condition of low complexity. On the whole, the algorithm provides a creative solution to the problem on how to maintain a high-quality compressed image on the basis of saving the image storage space.
Description
Art
The present invention relates to computer information technology field, more particularly to image compressing transmission field.
Background technology
Compression of images can usually be accompanied by the loss of peculiar picture quality.With multimedia the increasing based on web applications,
Compression of images is particularly important.It can be used to effective network transmission, and moreover Image Compression can be used to beat
Print, data storage, telecommunication industry, facsimile transmission, satellite remotely sense and other digital picture applications.Medically such as MRI, X
Ray, ct fluoroscopy.Image Compression is required storage and analysis for realizing Large Copacity image.
Compression of images is divided into lossy compression method and lossless compress.In lossless compressiong, image and original image phase are compressed
Together, it reduces bit rate without any image fault.Lossless compressiong is used in artificial image, medical science, military field.
Lossy compression is used in save the field of bandwidth and memory space, can sacrifice a part of quality of image.This side
Method is used in transmission and data storage, it is allowed to the partial distortion of image.Method for compressing image constantly develops, including prediction is compiled
Code, transform coding, irregular compression, wavelet transformation, vector quantization etc..
The basic conception of singular value decomposition (Singular Value Decomposition, SVD) is exactly to abandon rudimentary figure
As the singular value of information.One 8 points of discrete cosine transform is orthogonal approximate for meeting low plyability demand, and jpeg image compresses
Realized by discrete cosine transform (Discrete Cosine Transform, DCT).In wavelet transform (Discrete
Wavelet Transform, DWT) in method for compressing image, by estimating DWT coefficients in the value of a determination figure is reduced
The size of picture.Mixed processing technology can be used in black and white and coloured image.The combinatorial theory of 2D-DWT and SVD, is used to subtract
The space requirement of few image storage, keeps scalloping mistake in an acceptable scope.At present, in compression of images field
Technology without SVD-DWT-DCT mixing.
The content of the invention
For above-mentioned weak point, invention introduces the algorithm model of SVD, DWT, DCT mixing, with the pressure of improvement
Shrinkage is ensureing picture quality.Image can be compressed in its each stage transmitted.Hybrid technology includes：Singular value decomposition
(SVD), wavelet transform (DWT), discrete cosine transform (DCT).In the first stage, singular value decomposition, low order matrix it is strange
Different value can be abandoned from original image.Second stage is to obtain approximate band from wavelet transform domain.The last stage is then
Make use of the property of discrete cosine transform.In the algorithm, SVD is used for defining the rudimentary approximation of image.Haar DWT are used for
The rough description of image, and DCT are obtained for the pixel of associated images to realize a suitable compression ratio.
The technical solution adopted in the present invention is：A kind of joint image compression method based on SVD-DWT-DCT.
The implementation procedure of the technical scheme is as follows：
1st, singular value decomposition is carried out to input picture, according to the diagonal matrix that decomposition is obtained, takes the low order singular value of matrix,
Finally give the approximate of image；
2nd, Haar wavelet transformations are carried out to SVD results, after two grades are decomposed approximate image is obtained；
3rd, approximate picture breakdown is converted into the cell of a 8x8 to each unit application 2D-DCT；
4th, by quantifying factor quantification image, then encoded by entropy coder；
5th, decompressed image is fetched, each unit is encoded, quantified, inverse discrete cosine transformation (IDCT)；
6th, last, it is single independent image to change each unit.
The invention has the beneficial effects as follows：The mixed processing technology not only can stored visualisation image, moreover it is possible to relatively low multiple
One good compression ratio is provided under conditions of miscellaneous degree and obtains high-quality compression image.And the invention can solve how to save
On the basis of image storage space, high-quality compression image demand is maintained.
Description of the drawings
Fig. 1：Represent the detail flowchart of the present invention
Fig. 2：Represent the exemplary plot of wavelet transformation
Fig. 3：Zig-Zag scan mode exemplary plots are represented, the coefficient of 8x8 is changed into into one-dimensional sequence
Fig. 4：Represent DCT coefficient frequency distribution exemplary plot
Specific embodiment
The mixing compress technique of the present invention, by SVD singular value decomposition, DWT wavelet transforms, DCT discrete cosine transforms
Three kinds of algorithms are combined, and substantially increase the quality of algorithm performance and compression of images.
The mixing compress technique flow process of the present invention as shown in figure 1, first to image carry out singular value decomposition first, then small echo
Conversion finally carries out discrete cosine transform.Key step is expressed as follows with reference to Fig. 1-Fig. 4：
Step one, singular value decomposition is carried out to input picture, according to the diagonal matrix that decomposition is obtained, the low order for taking matrix is strange
Different value, finally gives the approximate of image；
Step 2, Haar wavelet transformations are carried out to SVD results, after two grades are decomposed approximate image is obtained；
Step 3, by approximate picture breakdown into a 8x8 cell, to the conversion of each unit application 2D-DCT；
Step 4, by quantify factor quantification image, then by entropy coder encode；
Step 5, decompressed image is fetched, each unit is encoded, quantified, inverse discrete cosine transformation (IDCT)；
Step 6, last, it is single independent image to change each unit.
Each step is described in detail below.
First, singular value decomposition (SVD) is carried out to input picture
Singular value decomposition is a kind of linear matrix disassembling method, and it is made to solve many mathematical problems such as image pressure
Contracting.Piece image is resolved into two orthogonal matrixes and a diagonal matrix by SVD.If L is a figure matrix, then SVD by its
Resolve into three matrixes：One orthogonal matrix U, a diagonal matrix S, the transposition V of an orthogonal matrix, formula is as follows：
Singular value is arranged in diagonal matrix with the order of descending, i.e. S11>S22>…>Snn, thus can be special
Little singular value is ignored, and removes the approximate matrix value of some low orders to reduce the size of image.A grade point k is selected, is based on
This relatively low approximation k is compressing image.
Singular value decomposition is a critically important linear algebra instrument, is had very in terms of compression of images and field of signal processing
Important application.If from from the perspective of linear algebra, a width digital picture can be regarded as and is made up of many non-negative scalars
Matrix, therefore, the technology of various matrix disposals can be applied to image procossing, realize the fast of image large-scale data
Speed is processed.
Digitized image file is stored in the matrix form in computer.Each element representation of matrix image
The value of middle corresponding coordinate pixel.From from the point of view of linear algebra, a secondary gray level image can be seen as a nonnegative matrix, matrix
Middle element type is all 8 unsigned ints, can represent the different color of 0-255 kinds.But, to store a width triple channel
RGB color image then need three with picture size identical matrix, each Color Channel in image with a matrix come
Represent.Therefore, process of the computer to digital picture is exactly a series of computings to nonnegative matrix.Property based on singular value decomposition
Matter, the main theory applied in Digital Image Processing is according to being:First, the stability of image singular value is very good, that is, work as figure
As the singular value of image when being applied in little disturbance will not be varied widely.Second, what singular value was showed is the interior of image
Accumulate characteristic rather than visual characteristic, reflection is relation between image matrix element.Because singular value has transposition invariance, rotation
Turn the critical natures such as invariance, shift invariant and mirror transformation invariance so that singular value features have more when image is described
Stability.
2nd, wavelet transform (DWT) is carried out after SVD
DWT can be described as follows with reference to Fig. 2 exemplary plots：It is a kind of conversion method, capture frequency and positional information, small echo
By discrete sampling, property specific to Haar wavelet transformations becomes the effective ways of compression of images.It divides piece image
Into 4 subbands：Approximate band LL, horizontal stripes HL, belt LH, diagonal band HH.The approximate rough description letter that image is contained with LL
Breath, belt LH contains the vertical information of image, corresponding to horizontal belt edge.Horizontal stripes HL illustrate the water in vertical edge
Flat detailed information, diagonal band HH then contains diagonal detail information.LL subbands are the copies of original image, in the feelings without distortion
Under condition, by obtaining the approximation of image the storage size shared by image is reduced.
Used as a kind of mathematical tool, wavelet transformation is to widely known Fourier transformation and window Fourier transform
Individual important breakthrough, is that the research field of signal analysis, image procossing, quantum physics and other nonlinear sciences brings revolutionary
Affect.The Wavelet Analysis Theory grown up by multiscale analysis, time frequency analysis, pyramid algorith etc. has become data pressure
Contract, process and analyze most useful instrument.Fourier transformation is using all unlimited sine wave for stretching in the two directions as just
Basic function is handed over, it is applied to the analysis of stationary signal.To Non-stationary Signal Analysis, simple pure time-domain analyses or pure frequency domain divide
Analysis is inapplicable, and for the simultaneously accurate time-domain information and frequency domain information for obtaining signal, Time-Frequency Analysis Method is developed.
Wavelet Analysis Theory provides an adjustable time frequency window, and when high-frequency signal is observed, time window narrows and works as automatically
During research low frequency signal, time window broadens automatically, that is, the characteristics of with zoom.Wavelet function possesses two important spies
Property：Concussion property and Decay Rate.Due to the two characteristics so that wavelet transformation has Time-Frequency Localization characteristic.In addition, wavelet decomposition
Carry out according to level, the scale parameter in every layer of wavelet decomposition is all change, so in different scale during wavelet decomposition
On carry out, referred to as multiresolution analysis.From in the angle of multiresolution analysis, wavelet decomposition is equivalent to a high-pass filtering
The combination of device and a low pass filter, decomposes always original signal is decomposed in two time frequency spaces every time.
Show that it has good direction in space selectivity based on the image Multiresolution Decomposition feature of wavelet transformation, with
Human vision property is very identical.Approximate part LL concentrated most energy of original image, and referred to as original image is forced
Nearly subgraph.Sub-band images HL, LH and HH maintain respectively horizontal edge details, vertical edge details and the focusing side of original image
Edge details, they feature the details characteristic of image, referred to as details subgraph.Ll channel has stronger opposing alien influence
Ability, stability is preferable；Edge details subgraph is easily affected by attacks such as extraneous noise, image procossings, less stable.
3rd, discrete cosine transform (DCT)
DCT is changed to the process of frequency domain by signal from transform of spatial domain.State such as with reference to Fig. 4 DCT coefficient frequency distribution exemplary plot
Under：DCT visualization important informations of image with several DCT coefficient concentrated expressions, coefficient provides splendid relating attribute.This
Sample, DCT presents the reduction of Image entropy.
It is found that if the value of u and N increases from 1D-DCT formula, being given increases the waveform of frequency.NXN is input into sequence
The 2D-DCT formula of row are：
P (x, y) is input picture, and x, y are the coordinates of matrix element, and i, j are the coordinates of coefficient.
Piece image divide into the basic function of this 8x8 the pixel value block of several associations, so cut after quantization
Associated pixel value, HFS is gone to be ignored.
Discrete cosine transform, is one of linear transformation the most frequently used in Digital Signal Processing, and discrete Fourier transform one
Sample, discrete cosine transform there is also fast algorithm.Discrete cosine transform is, based on the orthogonal transformation of real number, to avoid Fourier
Complex operation in conversion, therefore calculating speed obtained significantly being lifted, and with good energy compression ability and go
GL, therefore be widely used in the field such as compressing digital audio and compression of images.Particularly, digital picture
Compression standard be just built upon on the basis of discrete cosine transform.Meanwhile, energy is concentrated after discrete cosine transform conversion,
Algorithm complex is moderate, is relatively easy to quickly be realized in digital signal processor.
Two-dimension discrete cosine transform is not only able to the main information of natural image be focused on minimum low frequency coefficient, and
And the image blocking effect minimum for causing, the information that can realize concentrates the good compromise of ability and computation complexity, therefore is compressing
It is widely used in coding, such as JPEG compression standard.JPEG is a kind of dct transform based on piecemeal, and this is to compare at present
A kind of more common dct transform.
JPEG compression carries out two-dimensional dct transform firstly the need of the sub-block for dividing the image into 8x8 to all sub-blocks, obtains 8x8
DCT coefficient, then DCT coefficient is quantified, first to all of DCT coefficient divided by one group of quantized value during quantization, and take most
Close integer.As shown in table 1
| Coordinate | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 0 | 16 | 11 | 10 | 16 | 24 | 40 | 51 | 61 |
| 1 | 12 | 12 | 14 | 19 | 26 | 58 | 60 | 55 |
| 2 | 14 | 13 | 16 | 24 | 40 | 57 | 69 | 56 |
| 3 | 14 | 17 | 22 | 29 | 51 | 87 | 80 | 62 |
| 4 | 18 | 22 | 37 | 56 | 68 | 109 | 103 | 77 |
| 5 | 24 | 35 | 55 | 64 | 81 | 104 | 113 | 92 |
| 6 | 49 | 64 | 78 | 87 | 103 | 121 | 120 | 101 |
| 7 | 72 | 92 | 95 | 98 | 112 | 100 | 103 | 99 |
Table 1
Combined shown in Fig. 3 exemplary plots using Zig-Zag scan modes in compression, the coefficient of 8x8 is changed into into one-dimensional sequence, this
Plant the frequency content that scan mode show also image：First is DC coefficient, and left is divided into low frequency coefficient, the lower right corner
Part is high frequency coefficient, and zone line is intermediate frequency coefficient.The absolute value of low frequency coefficient is larger, becomes slowly between representative image pixel
Change, and the absolute value of high frequency coefficient is less, represents the fast change between pixel.Therefore, low frequency part contains the big portion of image
Divide energy, it may also be said that, the most important message part of vision to people all concentrates on the middle low frequency part of image.General pattern
Compression and process, in order to keep the visuality of image, all remain the middle low frequency part of image, the change of low frequency part has can
The large variation of image can be caused.
The result of implementation of the algorithm is as follows：Mean square error (MSE) and Y-PSNR (PSNR) are used for describing compression image
Quality, compression ratio (CR) be used for compression of images degree is described.As can be seen that input picture size from test result
42.6KB, output image size 13.4KB, mixed image compression algorithm invention can have in the case where ensureing that distortion is less
Effect ground compression image size.
Table 2
Mean square error (MSE) is the cumulative errors square between original image and compression image, and MSE values are lower, then miss
Difference is less.It is the difference between desired response and reality output square meansigma methodss.Mean square error is defined as follows： Wherein L (x, y) expression original images, the image of F (x, y) expression reconstruct, m,
N represents the size of image.
Y-PSNR (PSNR) is the ratio of original image and reconstructed image error, is defined as follows：
Compression ratio (CR) is an important parameter of compression of images performance, and it has measured the compression degree of data, definition
It is as follows：
Although embodiments of the invention have been shown and described above, it is to be understood that above-described embodiment is example
Property, it is impossible to limitation of the present invention is interpreted as, one of ordinary skill in the art within the scope of the invention can be to above-mentioned
Embodiment is changed, changes, replacing and modification.Therefore, protection scope of the present invention should be by appending claims
Content determines.
Claims (3)
1. a kind of joint image compression method based on SVD-DWT-DCT, the invention by singular value decomposition, wavelet transform,
Three kinds of technologies of discrete cosine transform combine, and it is characterized in that：The implementation procedure of the invention is as follows：
Step one, singular value decomposition is carried out to input picture, according to the diagonal matrix that decomposition is obtained, the low order for taking matrix is unusual
Value, finally gives the approximate of image；
Step 2, Haar wavelet transformations are carried out to SVD results, after two grades are decomposed approximate image is obtained；
Step 3, by approximate picture breakdown into a 8x8 cell, to the conversion of each unit application 2D-DCT；
Step 4, by quantify factor quantification image, then by entropy coder encode；
Step 5, decompressed image is fetched, each unit is encoded, quantified, inverse discrete cosine transformation（IDCT）；
Step 6, last, it is single independent image to change each unit.
2. a kind of joint image compression method based on SVD-DWT-DCT according to claim 1, is characterized in that：This
Bright singular value decomposition（SVD) piece image is resolved into into two orthogonal matrixes and a diagonal matrix, if L is a figure square
Battle array, then SVD is broken down into three matrixes：One orthogonal matrix U, a diagonal matrix S, the transposition V of an orthogonal matrix,
Formula is as follows：=
Singular value is arranged in diagonal matrix with the order of descending, i.e. S11>S22>>Snn, thus can be especially little strange
Different value is ignored, and removes the approximate matrix value of some low orders to reduce the size of image, and the present invention selects a grade point k, is based on
This relatively low approximation k is compressing image.
3. a kind of joint image compression method based on SVD-DWT-DCT according to claim 1, is characterized in that：
The detailed process of step 3 is：DCT visualization important informations of image with several DCT coefficient concentrated expressions, coefficient is carried
Splendid relating attribute is supplied, so, DCT presents the reduction of Image entropy, and 1D-DCT formula are as follows：
f(x) =
It is found that if the value of u and N increases from 1D-DCT formula, being given increases the waveform of frequency, NXN list entries
2D-DCT formula are：
Y(i,j) = C(i)C(j)
Wherein P (x, y) is input picture, and x, y are the coordinates of matrix element, and i, j are the coordinates of coefficient
C(u) =
Piece image divide into the basic function of this 8x8 the pixel value block of several associations, and pass is so cut after quantization
Connection pixel value, HFS is ignored.
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| CN108093259A (en) * | 2017-12-14 | 2018-05-29 | 希诺麦田技术（深圳）有限公司 | Picture motion estimating method, device and computer readable storage medium |
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| CN112912922A (en) * | 2018-10-29 | 2021-06-04 | 京瓷株式会社 | Image processing device, camera, moving object, and image processing method |
| CN110516100A (en) * | 2019-08-29 | 2019-11-29 | 武汉纺织大学 | A kind of calculation method of image similarity, system, storage medium and electronic equipment |
| CN112070211A (en) * | 2020-08-21 | 2020-12-11 | 北京科技大学 | Image identification method based on calculation unloading mechanism |
| CN112070211B (en) * | 2020-08-21 | 2024-04-05 | 北京科技大学 | Image recognition method based on computing unloading mechanism |
| CN114648674A (en) * | 2022-03-03 | 2022-06-21 | 北京国腾创新科技有限公司 | Filtering method and device for resisting sample image, electronic equipment and medium |
| CN116781870A (en) * | 2023-08-23 | 2023-09-19 | 北京大业桥科技股份有限公司 | Remote microwave monitoring method and system |
| CN116781870B (en) * | 2023-08-23 | 2024-05-31 | 北京大业桥科技股份有限公司 | Remote microwave monitoring method and system |
| CN116828126A (en) * | 2023-08-25 | 2023-09-29 | 北京大业桥科技股份有限公司 | Remote microwave transmission method and system |
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