CN106600657A - Adaptive contourlet transformation-based image compression method - Google Patents
Adaptive contourlet transformation-based image compression method Download PDFInfo
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Abstract
The present invention relates to an adaptive contourlet transformation-based image compression method and belongs to the signal processing technical field. The objective of the invention is to improve sparseness of image representation. According to the method of the invention, adaptive contourlet transformation is put forward based on the pseudo-polar Fourier transformation theory; according to the adaptive contourlet transformation, different directional decomposition schemes can be developed according to different input images, so that optimal sparse representation can be performed for the images, and therefore, a compression and reconstruction effect can be improved; and the schemes do not involve the design of conventional directional filter banks, and therefore, design complexity is lower. The adaptive contourlet transformation proposed by the invention can match the non-uniform directional distribution features of the images and is of general significance in practical application. When the adaptive contourlet transformation is adopted to perform image compression, a poor image reconstruction effect caused by a fixed directional decomposition scheme can be avoided.
Description
Technical field
The invention belongs to signal processing technology field, specially a kind of image pressure based on self adaptation contourlet transformation
Compression method.
Background technology
In information acquired in the mankind, about 60% is visual information, and about 20% is auditory information, and passes through other approach and obtain
Information summation less than the mankind obtain informational capacity 20%.Image with its it is directly perceived, concrete, lively the features such as become people identification
With the important channel for obtaining signal.But with developing rapidly for information technology, the image data amount increased with geometry speed is much
The speed of hard disk dilatation is exceeded.Therefore the research with regard to method for compressing image is always focus of concern.
Wavelet transformation has obtained widely should in compression of images field with its time-frequency localization properties and multiple dimensioned characteristic
With.It can effectively portray the point singularity characteristics of one-dimensional signal, realize representing the optimum of one-dimensional signal.But with application
Extending application gos deep into, and people have also discovered some shortcomings of wavelet transformation presence, because its limited directivity, by one-dimensional little
The separable waveletses of ripple can not " best approximation " with the unusual function in line or face, so wavelet transformation is to X-Y scheme
The key character of picture or dimensional images can not realize " most sparse " expression, and compressive sensing theory shows：Graphical representation is diluter
Dredge, the effect after compression reconfiguration is better.
The above-mentioned deficiency of exactly wavelet analysises promotes people to look for a kind of more effective method for expressing, through researchers
Effort for many years, multi-scale geometric analysis (MGA) are suggested and are developed rapidly.Wherein, Do et al. is proposed
Contourlet transformation is the two-dimensional image representation method of a kind of " real ".It provides support Interval length and width with dimensional variation
Basic function, can describe the intrinsic geometric properties of image in the way of being close to optimum, more more compact than the graphical representation of small echo sparse.Become
Change owner will be made up of two parts：" point " in first by laplacian-pyramid filter group (LP) capture images is unusual, is used for
Realize multi-resolution decomposition；Then the singular point that will be distributed in same direction by anisotropic filter group (DFB) synthesizes a coefficient,
Realize multi-direction decomposition.Contourlet transformation can represent the geometric properties such as the edge and texture of image in the way of more sparse,
There is more preferable set direction than wavelet transformation in HFS, this is highly beneficial to compression of images.But DFB in converting
Tree structure is limited to, direction splitting scheme and directional subband number are all fixed.And the direction point of most of natural image
Cloth is all the effectiveness that arbitrary, fixed Directional Decomposition will affect that image sparse is represented.In this context, set forth herein one
Plant the self adaptation contourlet transformation that can decompose according to the directional spreding feature self adaptation travel direction of input picture.It is based on
This conversion, proposes the method for compressing image based on self adaptation contourlet transformation.
The content of the invention
Present invention aims to the deficiencies in the prior art, propose a kind of new MGA instruments --- self adaptation
Contourlet transformation, it Adaptive matching input picture directional spreding can carry out the rarefaction representation of non-homogeneous Directional Decomposition
Algorithm.And this algorithm is based on, propose a kind of compression of images based on self adaptation contourlet transformation.The method is primarily based on puppet
A kind of adaptive anisotropic filter group (ADFB) of pole Fourier transformation Design Theory, and be allowed to combine with LP, composition one
Plant new multiple dimensioned multi-direction decomposition texture.New departure carries out Scale Decomposition, then centering high frequency subgraph first to input picture
Adaptively Directional Decomposition is carried out, so as to improve the degree of rarefication of graphical representation, so as to improve the effect of reconstructed image.
In new algorithm, adaptive direction splitting scheme can more accurately describe direction specific to different natural images
Feature, and farthest retain intrinsic geometry feature (profile and edge) in image.Its simple design is complicated
Degree also substantially increases the practicality of algorithm.The algorithm contributes to the degree of rarefication after lifting picture breakdown, and its principle is：
Traditional DFB in contourlet transformation is limited to tree structure, and in expression directional spreding uneven image, degree of rarefication is big
Give a discount.Therefore for the different input picture of more accurate description, design self adaptation anisotropic filter group heterogeneous is very
It is necessary.The present invention formulates matching direction division side according to the distribution characteristicss of image using the method for threshold determination
Case.Energy point of the image that the present invention is detected by pseudo- pole Fourier transformation in each directions of rays (by frequency plane origin)
Cloth travel direction decomposition, maximum advantage are that two-dimensional directional filter heterogeneous is realized in one-dimensional design complexities
Ripple, and improve image sparse and represent effectiveness.Low frequency component to avoid image is leak in several directivity subbands, promotes many
The combination of resolution decomposition module LP and invented direction decomposing module ADFB, obtains self adaptation contourlet transformation.Obviously,
Self adaptation contourlet transformation also has the advantages that the non-homogeneous Directional Decomposition of self adaptation.In sum, the present invention is answered actual
It is significant with.
Description of the drawings
The pseudo- polar net lattice of Fig. 1 present invention；
BV the and BH parts based on cartesian grid of Fig. 2 present invention；
Pseudo- pole Fourier transformation result X after the adjustment of Fig. 3 present inventionPPFFT(k1,k2) grid；
The flow chart based on self adaptation contourlet transformation compressed sensing of Fig. 4 present invention；
The directions of rays energy grade figure with regard to Barbara of Fig. 5 present invention；
The frequency allocation plan adaptive heterogeneous with regard to Barbara of Fig. 6 present invention；
Reconstructed image PSNR comparison diagram under the different sample rates with regard to Barbara of Fig. 7 present invention；
Specific embodiment
Pseudo- pole Fourier transformation is to carry out Fourier transformation on pseudo- polar net lattice to image, and image is converted to one uniformly
Polar coordinate or log-polar on Fourier Representations.Pseudo- pole grid is made up of the point being spacedly distributed along ray, this
A little different rays are spacedly distributed along slope direction, comprising substantially vertical (BV) partly with two class of basic horizontal (BH) part
Sample, as shown in Figure 1 (solid dot represents BV, and hollow dots represent BH).For a width N × N imagesIts
Two-dimensional Fourier transform is：
To the ω in above formulax、ωyCarry out following substitution of variable respectively successively,
BV and BH parts can be accordingly obtained, as shown in Fig. 2
Wherein, in XBVIn (m, l), m represents slope direction ωx/ωy, in XBHIn (m, l), m represents slope direction ωy/ωx；l
Represent radial direction.It has and quick calculating Fourier Transform Algorithm identical computation complexity O under cartesian coordinate
(N2logN).Meanwhile, also demonstrate the fast algorithm be it is stable, reversible, and only need to it is one-dimensional operation can just realize
The inverse transformation of pseudo- pole Fourier transformation.
Due to the revolving property of pseudo- pole Fourier transformation, a rectangular support region respective frequencies plane on pseudo- pole grid
On a wedge area, i.e., pseudo- pole Fourier transformation and wedge shape anisotropic filter group have similar geometric properties.Based on
Upper principle, we can be suitably adjusted and be extracted to pseudo- pole Fourier transformation result, so as to realize wedge shape side heterogeneous
To decomposition.Because BH and BV parts are to be obtained by different substitution of variable successively, it is to simplify design and ensure slope direction
Flatness, we merge them by following steps：
1. XBH(m, l) is along m to left N/2；
2. XBH(m, l) is inverted on m axles；
3. the X after reversionBH(m, l) is along m to right translation N/2.
Pseudo- pole Fourier transformation result X after being adjustedPPFT(k1,k2), as shown in figure 3,
Wherein, k1Represent directions of rays, the adjusted rear interval with continuously smooth；k2Represent radial direction.
To realize adaptivity, need to quantify support Intervals different in non-homogeneous splitting scheme, and quantify institute
The data of foundation are Energy distribution of the input picture in frequency domain.Obviously, the amplitude for too considering each stepped-frequency signal is
It is unpractiaca, therefore we take a half-way house：The energy grade of each wedge shape subband is calculated, then does threshold value and sentenced
Not.Comprise the following steps that：
(1) to input picture x (n1,n2) adjust after pseudo- pole Fourier transformation, obtain XPPFT(k1,k2)；
(2) calculate XPPFT(k1,k2) in each column element sum, obtain S1(k1)。S1In element representation frequency plane [-
π,π)2The energy grade of a upper directions of rays composition；
(3) being divided into 2i(i∈N+) equal portions, calculate per a sum, obtain S2(k3)。S2In element representation frequency plane
[-π,π)2The energy grade of a upper wedge shape directional subband；
(4) given threshold,I.e. 2iIndividual wedge shape sub-belt energy minima
'sTimes；
(5) S2Middle element is compared with th,
Wherein, ak={ 1,1 } represent two by S2(2k-1) and S2(2k) directional subband of labelling, ak={ 2 } represent one
By subband S2(2k-1) and S2(2k) merge the double directional subband of the support Interval for obtaining.There are two kinds there are different Support
Between directional subband constitute splitting scheme heterogeneousIn a, element number M=length (a) is represented
The number of subband, in interval [2i-1,2i] in.Although number M sizes are indefinite, always haveSet up.
According to decomposing scheme derived above, Directional Decomposition is realized by multiplication operation in frequency domain.One group is designed first by 0
With matrix (and the X of 1 compositionPPFT(k1,k2) be of the same size), they are corresponding with above-mentioned decomposing scheme.Again this
Group matrix is multiplied successively with the Fourier transformation result after adjustment, you can accurately capture desired frequency content.OrderRepresent from XPPFT(k1,k2) the middle directional subband for extracting, and assume a [0]=0, then have
To subband XpDo pseudo- pole Fourier transformation inverse transformation, you can obtain the space shape of the directional subband of wedge shape frequency support
Formula.
To eliminate the data redundancy produced in above-mentioned steps, need to add sampling element in Directional Decomposition stage rear end.Root
According to multidimensional sampling thheorem, it is that guarantee is output as rectangle, sampling matrix must be diagonal form.Because heterogeneous stroke in this programme
It is intrinsic, sampling matrix S needed for the directional subband with different frequency support IntervalpSample rate also differ, its selection side
Formula is as follows：
Wherein,WithBV parts and BH parts are corresponded to respectively.Can by above-mentioned analysis
Know there is 2M-2iBy 1 labelling, the sample rate of its sampling matrix is 1/2 to individual directional subbandi；Have 2i- M directional subbands by 2 labellings,
The sample rate of its sampling matrix is 1/2i-1.Then the data volume after decomposition is
That is to after decomposition, data total amount does not change, and is highly suitable for compression of images for image classical prescription.In sum,
Image can adaptively obtain one group of break-even directional subband heterogeneous by ADFB.The present invention is not related to tradition side
To the design process of wave filter group, but two-dimensional directional filtering is realized in a kind of easier method.
As traditional DFB, to avoid low frequency leakage, ADFB from image sparse can not being provided separately and represents.Therefore we
It is combined with LP, a kind of new multiple dimensioned multi-direction analytical tool --- self adaptation contourlet transformation is formed.It is each
Layer LP decomposition obtains a low-pass pictures (it is generally acknowledged that being non-sparse) and a band logical image, and the latter can be by ADFB certainly
Adaptively it is decomposed into one group of directional subband heterogeneous to match the directional spreding feature of image.The selection of sampling matrix also ensures
Subband after sampling being capable of Perfect Reconstruction.Corresponding inverse transformation is carried out to each subimage, image can be reconstructed.Based on certainly
The implementing procedure for adapting to the compression of images of contourlet transformation is as shown in Figure 4.To illustrate the effectiveness of the invention, we are input into
Barbara images are emulated, and take i=4, and the energy grade of its directions of rays is distributed as shown in figure 5, what is generated is non-homogeneous
Splitting scheme it is as shown in Figure 6.Finally, with 4 layers of DFB contourlet transformation, the figure of the contourlet transformation of 3 layers of DFB
Picture compression reconfiguration Contrast on effect is as shown in Figure 7.Wherein, experiment has been respectively adopted random observation method and orthogonal matching pursuit algorithm
(OMP) realize compression and reconstruct, performance indications selected by quality reconstruction are Y-PSNR (PSNR).
Claims (3)
1. a kind of method for compressing image based on self adaptation contourlet transformation, its step is that first input picture is entered
Row Scale Decomposition, obtains a low-pass pictures and a band logical image, and then the pseudo- pole Fourier after being adjusted to the latter becomes
Change.Then the Directional Decomposition scheme for matching is generated according to transformation results, this is by each wedge shape directional subband of image
Energy grade carries out threshold value and differentiates what is obtained.Decomposed according to scheme, and carried out two-dimentional sampling.As frequency spectrum splitting scheme is
It is uneven, therefore the sample rate of sampling matrix also accordingly changes.Finally, to the subimage random observation after sampling, and adopt
OMP algorithms complete reconstruct, observe quality reconstruction.
2. a kind of method for compressing image based on self adaptation contourlet transformation according to claim 1, its feature exist
In the band logical image to being input into carries out adaptive Directional Decomposition to match its directional spreding feature, proposes a kind of adaptive
Anisotropic filter group, its specific catabolic process comprise the steps：
(1) to input picture x (n1,n2) adjust after pseudo- pole Fourier transformation, obtain XPPFT(k1,k2)；
(2) calculate XPPFT(k1,k2) in each column element sum, obtain S1(k1), S1In element representation frequency plane [- π, π)2
The energy grade of a upper directions of rays composition；
(3) being divided into 2i(i∈N+) equal portions, calculate per a sum, obtain S2(k3), S2In element representation frequency plane [- π,
π)2The energy grade of a upper wedge shape directional subband；
(4) given threshold,I.e. 2iIndividual wedge shape sub-belt energy minima
Times；
(5) S2Middle element is compared with th,
MergeSplitting scheme a is obtained, and travel direction decomposes on this basis.
3. a kind of method for compressing image based on self adaptation contourlet transformation according to claim 1, it is characterised in that
The sampling matrix of the different sample rates of sampling realizes irredundant Directional Decomposition, and the formula of its foundation is as follows：
According to above-mentioned sampling plan, it becomes possible to the data redundancy of image direction decomposition is completely eliminated.
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| CN112837220A (en) * | 2021-01-21 | 2021-05-25 | 华北电力大学（保定） | Method for improving resolution of infrared image and application thereof |
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Application publication date: 20170426 |