CN104952046B - Compression of images based on statistics perceives low complex degree restoring method - Google Patents
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Abstract
The present invention is directed to compressed sensing based image restoring problem, giving a kind of unified with nature image wavelet indicates the restoring method of lower statistical information and goes back original system, the restoring method includes image high speed restoring method and image high-precision restoring method, can realize that high speed reduction and high-precision are restored according to actual requirement.Wherein, image high speed restoring method includes that one step of column dimension quickly restores, and one step of row dimension quickly restores；Image high-precision restoring method includes that one step of column dimension quickly restores, and one step of row dimension quickly restores, the reduction of row dimension second iteration.The beneficial effects of the present invention are: the present invention makes full use of the statistical information of image, in also proper mass and reduction rate, it improves a lot compared with conventional method, and can choose whether to carry out second iteration according to actual needs, to improve the performance and freedom degree of whole image compression perceptual system.
Description
Technical field
The present invention relates to signal processing and digital image processing fields, more particularly to the compression sense based on image statistics
Know restoring method and system.
Background technique
Compressed sensing (Compressed Sensing) is different from traditional Nyquist sampling thheorem, but points out signal
If showing sparse characteristic in time domain (airspace) or certain transform domain, signal can be projected by calculation matrix another small
Size signal may be implemented much smaller than Nyquist sample rate after transmission, complete from small size signal
Recover original signal.
Compressive sensing theory is widely used in two-dimensional image signal at present, and produces many algorithms on its basis.?
On the basis of the separation perception that Yair Rivenson and Adrian Stern are proposed, YongFang is directed to two dimensional image, proposes
2D-OMP (2D Orthogonal Matching Pursuit, two-dimensional quadrature match tracing) algorithm, obtains preferable reduction effect,
But reduction rate is still excessive.Patent document 1 (China Patent Publication No. CN103400348A): propose one kind with separate perception phase
Corresponding separating reducing algorithm greatly enhances efficiency of algorithm, but calculation amount is still excessively huge, and restore precision compared with
2D-OMP algorithm is declined, therefore reduction effect is still not ideal enough.In recent years, there is scholar using the statistical information of image as first
It tests feature to be dissolved into algorithm, the statistics of one-dimensional signal is realized in the raising, such as Volkan Cevher etc. for realizing reduction precision
Priori is merged with compressed sensing.However be still in infancy using the retrieving algorithm of image statistics, various algorithms are still not
Maturation, particularly with the non-sparse information in signal, loss is serious.
Summary of the invention
In order to solve the problems in existing compressed sensing based image restoring technology, the present invention provides corresponding
Retrieving algorithm and go back original system.
The compressed sensing image restoring method based on image statistics that the present invention provides a kind of includes two kinds of decoding sides
Formula: high speed restoring method: utilizing natural image statistical information, is carried out quickly also to image respectively using two dimensions (column, row)
It is former；High-precision restoring method: using the statistical information of image, image is carried out quickly also respectively using two dimensions (column, row)
On the basis of original, an iteration is carried out to the second dimension reduction result again, sacrifices efficiency and exchange higher reduction precision for.
For the high speed restoring method for the image X that a width size is n × n after projection, obtaining size is m × m's
Projection value Y, i.e. Y=Φ X ΦT=Φ Ψ S ΨTΦT=ASAT, wherein A=Φ Ψ and Φ are random matrix, and Ψ is wavelet transformation
Matrix, S are rarefaction representation of the original image X under wavelet field, i.e. X=Ψ S ΨT, it is restored, in the method step
Include:
(1) one step of column dimension quickly restores: using the weight matrix K of dampening information under characterization image wavelet field, to image
Column dimension carry out a step quickly restore.Enable S1=SAT, Y=Y1Then there is Y1=A × S1, can be obtained column dimension reduction resultWherein, the weight matrix K characterizes natural image statistical information, non-master diagonal
Line element is 0, and the elements in a main diagonal meets under natural image small echo domain representation from top to bottom to a certain extent, is declined from left to right
The characteristics of subtracting；
(2) transposition: by solving resultTransposition,
(3) one step of row dimension quickly restores: using the weight matrix K of dampening information under characterization image wavelet field, to image
Row dimension carry out a step quickly restore.CauseEnable S2=ST, therefore can be converted into formula Y2=A × S2It solves,
Its solving result are as follows:
(4) transposition: to upper step solving resultTransposition,Obtain the wavelet field rarefaction representation of image；
(5) inverse sparse transformation step: being converted to spatial domain picture information for the small echo domain representation for obtaining image,
Restore the original signal of image.
For the high-precision restoring method for the image X that a width size is n × n after projection, acquisition size is m × m
Projection value Y, i.e. Y=Φ X ΦT=Φ Ψ S ΨTΦT=ASAT, wherein A=Φ Ψ and Φ are random matrix, and Ψ is small echo change
Matrix is changed, S is rarefaction representation of the original image X under wavelet field, i.e. X=Ψ S ΨT, it is restored, the method step
In include:
(1) one step of column dimension quickly restores: using the weight matrix K of dampening information under characterization image wavelet field, to image
Column dimension carry out a step quickly restore.Enable S1=SAT, Y=Y1Then there is Y1=A × S1, can be obtained column dimension reduction resultWherein, the weight matrix K characterizes natural image statistical information, non-master diagonal
Line element is 0, and the elements in a main diagonal meets under natural image small echo domain representation from top to bottom to a certain extent, is declined from left to right
The characteristics of subtracting；
(2) transposition: by solving resultTransposition,
(3) one step of row dimension quickly restores: using the weight matrix K of dampening information under characterization image wavelet field, to image
Row dimension carry out a step quickly restore；CauseEnable S2=ST, therefore can be converted into formula Y2=A × S2It solves,
Its solving result are as follows:
(4) row degree second iteration restores: utilizing S in one step rapid solving result of row dimension2Any one columnReconstruction weights matrix K,
Then after second iteration, Y2=A × S2In each column y'=A × z'(wherein y' be Y2Any one column, z' S2With
It is corresponding one column) solving result are as follows:After solving by column, that is, obtain secondary
Reduction result after iteration
(5) transposition: to upper step solving resultTransposition,Obtain the wavelet field rarefaction representation of image；
(6) the small echo domain representation for obtaining image inverse sparse transformation step: is converted into spatial domain picture information.
Restore the original signal of image.
As a further improvement of the present invention, the weight matrix K, using exponential damping, i.e.,
And
The present invention gives a kind of compressed sensing image restoring system based on image statistics, includes two kinds of decodings
Subsystem: atomic system is gone back at a high speed: using natural image statistical information, image being carried out respectively using two dimensions (column, row)
Quickly reduction；High-precision goes back atomic system: using the statistical information of image, using two dimensions (column, row) respectively to image into
Row quickly on the basis of reduction, carries out an iteration to the second dimension reduction result again, sacrifices efficiency and exchanges higher reduction precision for.
The high speed goes back the image X that atomic system is n × n for a width size, and after projection, acquisition size is m × m
Projection value Y, i.e. Y=Φ X ΦT=Φ Ψ S ΨTΦT=ASAT, wherein A=Φ Ψ and Φ are random matrix, and Ψ is small echo change
Matrix is changed, S is rarefaction representation of the original image X under wavelet field, i.e. X=Ψ S ΨT, it is restored, it is described to go back original system
It comprises the following modules:
The quick recovery module of one step of column dimension: using the weight matrix K of dampening information under characterization image wavelet field, to image
Column dimension carry out a step quickly restore；Enable S1=SAT, Y=Y1Then there is Y1=A × S1, can be obtained column dimension reduction resultWherein, the weight matrix K characterizes natural image statistical information, non-master diagonal
Line element is 0, and the elements in a main diagonal meets under natural image small echo domain representation from top to bottom to a certain extent, is declined from left to right
The characteristics of subtracting；
Transposition module: by solving resultTransposition,
The quick recovery module of one step of row dimension: using the weight matrix K of dampening information under characterization image wavelet field, to image
Row dimension carry out a step quickly restore.CauseEnable S2=ST, therefore can be converted into formula Y2=A × S2It solves,
Its solving result are as follows:
Transposition module: to the quick recovery module solving result of one step of row dimensionTransposition,Obtain the small of image
Wave zone rarefaction representation；
Inverse sparse transformation module: being converted to spatial domain picture information for the small echo domain representation for obtaining image,I.e. also
Original goes out the original signal of image.
The high-precision go back atomic system for a width size be n × n image X by projection after, acquisitions size for m ×
The projection value Y of m, i.e. Y=Φ X ΦT=Φ Ψ S ΨTΦT=ASAT, wherein A=Φ Ψ and Φ are random matrix, and Ψ is small echo change
Matrix is changed, S is rarefaction representation of the original image X under wavelet field, i.e. X=Ψ S ΨT, it is restored, it is described to go back original system
It comprises the following modules:
The quick recovery module of one step of column dimension: using the weight matrix K of dampening information under characterization image wavelet field, to image
Column dimension carry out a step quickly restore；Enable S1=SAT, Y=Y1Then there is Y1=A × S1, can be obtained column dimension reduction resultWherein, the weight matrix K characterizes natural image statistical information, non-master diagonal
Line element is 0, and the elements in a main diagonal meets under natural image small echo domain representation from top to bottom to a certain extent, is declined from left to right
The characteristics of subtracting；
Transposition module: by solving resultTransposition,
The quick recovery module of one step of row dimension: using the weight matrix K of dampening information under characterization image wavelet field, to image
Row dimension carry out a step quickly restore；CauseEnable S2=ST, therefore can be converted into formula Y2=A × S2It solves,
Its solving result are as follows:
Row degree second iteration recovery module: S in the quick recovery module solving result of one step of row dimension is utilized2Any one columnReconstruction weights matrix K,
Then after second iteration, Y2=A × S2In it is each column y'=A × z' solving result are as follows:
Wherein y' is Y2Any one column, z' S2After a corresponding column solve by column, i.e., after acquisition second iteration
Reduction result
Transposition module: to row degree second iteration recovery module solving resultTransposition,Obtain the small echo of image
Domain rarefaction representation；
Inverse sparse transformation module: being converted to spatial domain picture information for the small echo domain representation for obtaining image,I.e. also
Original goes out the original signal of image.
The beneficial effects of the present invention are: the present invention makes full use of the statistical information of image, in also proper mass and reduction rate
On, it improves a lot, and high speed retrieving algorithm or high-precision retrieving algorithm can be selected according to actual needs, is promoted compared with conventional method
The performance and freedom degree of whole image compression perceptual system.
Detailed description of the invention
Fig. 1 is the compressed sensing image restoring method schematic of the invention based on image statistics；
Fig. 2 (a) is the schematic diagram of high speed restoring method of the invention, and Fig. 2 (b) is high-precision restoring method of the invention
Schematic diagram；
Fig. 3 (a) is the flow chart at separation perception projection end, and Fig. 3 (b) is the flow chart of high speed restoring method of the invention,
Fig. 3 (c) is the schematic diagram of high-precision restoring method of the invention；
Fig. 4 is wavelet transformation schematic diagram；
Fig. 5 is that image wavelet indicates that ladder form schematic diagram is presented in lower decaying invocation point；
Fig. 6 first step restores standard results decaying fitting schematic diagram；
Fig. 7 (a) is lena image original graph, and Fig. 7 (b) is the lena image after projecting and high speed restores；
Fig. 8 (a) is lena image original graph, and Fig. 8 (b) is the lena image after projecting and high-precision restores；
Fig. 9 is 2D-OMP algorithm, separation algorithm, high speed restoring method of the invention and high-precision restoring method also proper mass
Comparison diagram；
When Figure 10 is that 2D-OMP algorithm, separation algorithm, high speed retrieving algorithm of the invention and high-precision retrieving algorithm restore
Between comparison diagram；
Figure 11 is reduction quality diagram of the 3 width natural images under differential declines coefficient.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
As shown in Fig. 1, the compressed sensing image restoring method based on image statistics that the present invention provides a kind of, packet
Containing two kinds of decoding processes (wherein, for second decoding process of dotted line is peculiar in attached drawing 1): high speed retrieving algorithm: utilizing nature
Image statistics respectively quickly restore image using two dimensions (column, row), as shown in attached drawing 2 (a)；In high precision
Retrieving algorithm: using the statistical information of image, the basis that image is quickly restored respectively using two dimensions (column, row)
On, an iteration is carried out to the second dimension reduction result again, efficiency is sacrificed and exchanges higher reduction precision for, as shown in attached drawing 2 (a).
For the high speed retrieving algorithm for the image X that a width size is n × n after projection, obtaining size is m × m's
Projection value Y, i.e. Y=Φ X ΦT=Φ Ψ S ΨTΦT=ASAT, such as attached drawing 3 (a), wherein A=Φ Ψ and Φ are random matrix, Ψ
For wavelet transform matrix, S is rarefaction representation of the original image X under wavelet field, i.e. X=Ψ S ΨT, feature are as follows: image is small
Under the expression of wave system matrix number, low frequency component concentrates on the upper left corner, and high fdrequency component concentrates on the lower right corner, and the spy of piecemeal is presented
Point is denoted as S such as attached drawing 4.It sums line by line to S, it may be assumed that
Wherein, si,jFor the element of S, the size of S is n × n, the S known to S block characteristic and attenuation characteristicsumElement is presented
Stairstepping attenuation characteristic.Statistics is summed up by taking lena image as an example, such as attached drawing 5, wherein blue solid lines are 512 × 512 images
The average value of each row under Wavelet representation for transient, can find out from statistical result, and stepped decaying is from top to bottom presented in each row average value.?
Here, according to the ladder attenuation characteristic feature by SsumIt is divided into multiple energy levels, enabling minimum energy level length is 8,8,16 are followed successively by,
32 ..., then each energy level is corresponding in SsumLength and each energy level include the corresponding average value of pixel absolute value, such as table 1.
It can be seen that from the case where each energy level, significantly attenuation trend be presented, can be decayed with exponential function and it is fitted,
Such as attached drawing 6, fitting result are as follows:
F (x)=aebx
Wherein, a=597.5, b=-1.208.It is tested by the multiple investigation to other different natural image Wavelet representation for transient,
It knows to show similar attenuation law from top to bottom line by line, i.e., significantly rapid exponential grade decays.This shows different natures
Image have the characteristics that in wavelet field distribution it is more similar, and by this model foundation are as follows:
F (n)=aebn
Wherein, n is energy level where certain point, and a, b are parameter.According to the multiple statistics to multiple image, substantially conform to refer to
Number attenuation law, referred herein to parameter b are attenuation coefficient, and fitting result shows that b is basically stable between -0.7 to -1.3.And it is different
Image, as long as attenuation trend is sufficiently large, can guarantee more excellent reduction effect for decay coefficient b and insensitive.
Specific steps such as attached drawing 3 (b), including:
(1) one step of column dimension quickly restores: using the weight matrix K of dampening information under characterization image wavelet field, to image
Column dimension carry out a step quickly restore.Enable S1=SAT, Y=Y1Then there is Y1=A × S1, wherein Y1Size is m × m, S1Size
For n × m
According to prior information has been obtained, attenuation law is presented in natural image small echo domain representation are as follows:
F (n)=aebn
Then according to each energy level point size distribution feature, f (n)=aebn, construct weight matrix K
Wherein, first 8 are worth for the first energy level i.e.: k1:8=a × eb.9 to 16 are worth for the second energy level i.e.: k9:16=a × en ×b.And so on obtain:
Therefore, the core of retrieving algorithm is in the countless solutions of the underdetermined system of equations, to find one group of solution, be best suitable for above-mentioned decaying
Rule.Wherein, the elements in a main diagonal meets natural image under Wavelet representation for transient from top to bottom, and attenuation law from left to right is more
As long as kind of fit approach attenuation degree is enough big, retrieving algorithm can be achieved, herein kiIt can simplify are as follows:
Herein if will if formula Y1=A × S1Regard the m underdetermined system of equations as, enables wherein any one group are as follows: y=A × z, wherein y
It is any one column vector of matrix Y, z is corresponding S1A column vector, and enable z=(z1,z2,…,zn)TThen basis
Desired Energy distribution,Then have:
It can get, m group underdetermined system of equations Y1=A × S1In, the solving result of any one group of underdetermined system of equations y=A × z are as follows: therefore can analogize, first step reduction result may be expressed as:
(2) transposition: by solving resultTransposition,
(3) one step of row dimension quickly restores: using the weight matrix K of dampening information under characterization image wavelet field, to image
Row dimension carry out a step quickly restore.CauseEnable S2=ST, therefore can be converted into formula Y2=A × S2It solves.
Y2Size is n × m, S2Size is n × n, constructs weight matrix
Wherein, the elements in a main diagonal meets natural image under Wavelet representation for transient from top to bottom, attenuation law from left to right,
As long as a variety of fit approach attenuation degrees are enough big, retrieving algorithm can be achieved, use exponential damping herein, i.e.,
The attenuation law, which has been subjected to image wavelet, indicates the fitting of lower result, can generally represent natural image in small wave table
Attenuation law under showing.
Herein if will if formula Y2=A × S2Regard the n underdetermined system of equations as, enables wherein any one group are as follows: y'=A × z',
In, y' is matrix Y2Any one column vector, z' be corresponding S2A column vector, and enable z'=(z'1,z
'2,…,z'n)TThen as expected Energy distribution,Then have:
It can get, n group underdetermined system of equations Y2=A × S2In, the solving result of any one group of underdetermined system of equations y'=A × z'
Are as follows: therefore can analogize, first step reduction result may be expressed as:
(4) transposition: to upper step solving resultTransposition,Obtain the wavelet field rarefaction representation of image
(5) the small echo domain representation for obtaining image inverse sparse transformation: is converted into spatial domain picture information.I.e. also
Original goes out the original signal of image.
For the high-precision retrieving algorithm for the image X that a width size is n × n after projection, acquisition size is m × m
Projection value Y, i.e. Y=Φ X ΦT=Φ Ψ S ΨTΦT=ASAT, such as Fig. 3 (a), wherein A=Φ Ψ and Φ are random matrix, Ψ
For wavelet transform matrix, S is rarefaction representation of the original image X under wavelet field, i.e. X=Ψ S ΨT, it is restored, step
Such as Fig. 3 (c), including:
(1) one step of column dimension quickly restores: using the weight matrix K of dampening information under characterization image wavelet field, to image
Column dimension carry out a step quickly restore.Enable S1=SAT, Y=Y1Then there is Y1=A × S1, can be obtained column dimension reduction result
Wherein,And
(2) transposition: by solving resultTransposition,
(3) one step of row dimension quickly restores: using the weight matrix K of dampening information under characterization image wavelet field, to image
Row dimension carry out a step quickly restore.CauseEnable S2=ST, therefore can be converted into formula Y2=A × S2It solves,
Its solving result are as follows:
Wherein,And
(4) row dimension second iteration restores: due to the limitation to signal energy distribution of energy weight matrix K, a step is fast
Speed reduction has been closer to original signal standard value, such as schemes, if attempting to sacrifice a part of recovery time carrys out lift portion reduction
Effect can do second iteration to the second dimension reduction result.According to modified result energy weight matrix after an iteration:
The element that its elements in a main diagonal meets for a rapid solving result, that is,
So that
The result solved similar to a rapid solving, second iteration are as follows:
After restoring line by line to it, second step reduction result S is obtained2,
(5) transposition: to upper step solving resultTransposition,Obtain the wavelet field rarefaction representation of image；
(6) the small echo domain representation for obtaining image inverse sparse transformation step: is converted into spatial domain picture information.
Restore the original signal of image.
The present invention gives a kind of compressed sensing image restoring system based on image statistics, includes two kinds of decodings
Subsystem: atomic system is gone back at a high speed: using natural image statistical information, image being carried out respectively using two dimensions (column, row)
Quickly reduction, shown in principle such as attached drawing 2 (a)；High-precision goes back atomic system: using the statistical information of image, using two dimensions
(column, row) respectively carries out on the basis of quickly restoring image, carries out an iteration again to the second dimension reduction result, sacrifices effect
Rate exchanges higher reduction precision for, shown in principle such as attached drawing 2 (b).
In order to verify effectiveness of the invention, carried out on dominant frequency 3.30GHz, 64 bit manipulation systems using Matlab software
Emulation experiment, and obtain simulation result.
Simulation parameter and result:
(1) attached drawing 7 (a) lena image original size: 512 × 512, size after attached drawing 7 (b) compression: 256 × 256, data
Compression ratio: 0.25, image is restored in decay coefficient b=- 1.2 and original image compares: PSNR=29.0912
(2) attached drawing 8 (a) lena image original size: 512 × 512, size after attached drawing 8 (b) compression: 256 × 256, data
Compression ratio: image is restored in 0.25 decay coefficient b=- 1.2 and original image compares: PSNR=29.4311
(3) compared with simulation result has method with part:
Simulation parameter: lena image, data compression ratio are all made of are as follows: (m/n)2=(3/4)2=0.5625.Specific method and
Details is as shown in table 2.But since 2D-OMP method is excessively complicated, there is no it in picture size is 512 × 512 or more
Image simulation data.
In reduction precision aspect, attached drawing 9 gives PSNR (Peak of various sizes of image when using four kinds of methods
Signal to Noise Ratio) comparison.
In terms of the computation complexity, attached drawing 10 has gone out various sizes of image when using four kinds of methods, about also original image
As the comparison of time used, in order to intuitive, this comparison diagram uses logarithmic coordinates.
(4) to prove that different images for decay coefficient b and insensitive, enable three width different images under differential declines coefficient
Compression reduction is carried out, result is as shown in Fig. 11.
The beneficial effects of the present invention are: the present invention is different from the reduction that traditional restoring method is confined to sparse partial information
Method makes full use of the statistical information of image, in also proper mass and reduction rate, improves a lot compared with conventional method, and can
High speed retrieving algorithm or high-precision retrieving algorithm are selected according to actual needs, improve the performance of whole image compression perceptual system
And freedom degree.
The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be said that
Specific implementation of the invention is only limited to these instructions.For those of ordinary skill in the art to which the present invention belongs, exist
Under the premise of not departing from present inventive concept, a number of simple deductions or replacements can also be made, all shall be regarded as belonging to of the invention
Protection scope.
1 image sparse of table indicates each energy level length and gray scale absolute value average value
Each method detailed description is compared in the emulation of table 2
Claims (4)
1. a kind of compressed sensing image restoring method based on image statistics, it is characterised in that: the restoring method uses
Two dimensions respectively carry out on the basis of quickly restoring image, carry out an iteration again to the second dimension reduction result, sacrifice
Efficiency exchanges higher reduction precision for, and specially for the image X that a width size is n × n after projection, acquisition size is m × m
Projection value Y, i.e. Y=Φ X ΦT=Φ Ψ S ΨTΦT=ASAT, wherein A=Φ Ψ and Φ are random matrix, and Ψ is small echo change
Matrix is changed, S is rarefaction representation of the original image X under wavelet field, i.e. X=Ψ S ΨT, it is restored, the restoring method
The following steps are included:
(1) one step of column dimension quickly restores: using the weight matrix K of dampening information under characterization image wavelet field, to the column of image
Dimension carries out a step and quickly restores；Enable S1=SAT, Y=Y1Then there is Y1=A × S1, can be obtained column dimension reduction resultWherein, the weight matrix K characterizes natural image statistical information, non-master diagonal
Line element is 0, and the elements in a main diagonal meets under natural image small echo domain representation from top to bottom to a certain extent, is declined from left to right
The characteristics of subtracting；
(2) transposition: by solving resultTransposition,
(3) one step of row dimension quickly restores: using the weight matrix K of dampening information under characterization image wavelet field, to the row of image
Dimension carries out a step and quickly restores；CauseEnable S2=ST, therefore can be converted into formula Y2=A × S2It solves, asks
Solve result are as follows:
(4) row dimension second iteration restores: using in one step rapid solving result of row dimensionAny one columnReconstruction weights matrix K2:
Then after second iteration, Y2=A × S2In it is each column y'=A × z' solving result are as follows:
Wherein, y is any one column vector of matrix Y, y' Y2Any one column, z' S2A corresponding column, are asked by column
Xie Hou, i.e. reduction result after acquisition second iteration
(5) transposition: to upper step solving resultTransposition,Obtain the wavelet field rarefaction representation of image；
(6) inverse sparse transformation step: being converted to spatial domain picture information for the small echo domain representation for obtaining image,I.e. also
Original goes out the original signal of image.
2. the compressed sensing image restoring method according to claim 1 based on image statistics, it is characterised in that: institute
State weight matrix K using exponential damping, i.e.,
And
Wherein, b is attenuation coefficient.
3. a kind of compressed sensing image restoring system based on image statistics, it is characterised in that: described to go back original system use
Two dimensions respectively carry out on the basis of quickly restoring image, carry out an iteration again to the second dimension reduction result, sacrifice
Efficiency exchanges higher reduction precision for, and specially for the image X that a width size is n × n after projection, acquisition size is m × m
Projection value Y, i.e. Y=Φ X ΦT=Φ Ψ S ΨTΦT=ASAT, wherein A=Φ Ψ and Φ are random matrix, and Ψ is small echo change
Matrix is changed, S is rarefaction representation of the original image X under wavelet field, i.e. X=Ψ S ΨT, it is restored, it is described to go back original system
It comprises the following modules:
The quick recovery module of one step of column dimension: using the weight matrix K of dampening information under characterization image wavelet field, to the column of image
Dimension carries out a step and quickly restores；Enable S1=SAT, Y=Y1Then there is Y1=A × S1, can be obtained column dimension reduction resultWherein, the weight matrix K characterizes natural image statistical information, non-master diagonal
Line element is 0, and the elements in a main diagonal meets under natural image small echo domain representation from top to bottom to a certain extent, is declined from left to right
The characteristics of subtracting；
Transposition module: by solving resultTransposition,
The quick recovery module of one step of row dimension: using the weight matrix K of dampening information under characterization image wavelet field, to the row of image
Dimension carries out a step and quickly restores；CauseEnable S2=ST, therefore can be converted into formula Y2=A × S2It solves, asks
Solve result are as follows:
Row dimension second iteration recovery module: using in the quick recovery module solving result of one step of row dimensionAny one columnReconstruction weights matrix K,
Then after second iteration, Y2=A × S2In it is each column y'=A × z' solving result are as follows:
Wherein, y is any one column vector of matrix Y, y' Y2Any one column, z' S2A corresponding column are asked by column
Xie Hou, i.e. reduction result after acquisition second iteration
Transposition module: to row dimension second iteration recovery module solving resultTransposition,Obtain the wavelet field of image
Rarefaction representation；
Inverse sparse transformation module: being converted to spatial domain picture information for the small echo domain representation for obtaining image,Restore
The original signal of image.
4. the compressed sensing image restoring system according to claim 3 based on image statistics, it is characterised in that: institute
State weight matrix K using exponential damping, i.e.,
And
Wherein, b is attenuation coefficient.
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