CN107170018A - Constitution optimization method based on compressed sensing calculation matrix in image reconstruction - Google Patents
Constitution optimization method based on compressed sensing calculation matrix in image reconstruction Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T9/00—Image coding
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
- H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
- H03M7/3059—Digital compression and data reduction techniques where the original information is represented by a subset or similar information, e.g. lossy compression
- H03M7/3062—Compressive sampling or sensing
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/20—Special algorithmic details
- G06T2207/20048—Transform domain processing
- G06T2207/20064—Wavelet transform [DWT]
Abstract
The present invention is a kind of calculation matrix constitution optimization method based on compressed sensing in image reconstruction.Need to carry out linear measurement observation to image in the image reconstruction of compressed sensing, sampling is not only completed so to primary signal and also completes compression, signal dimension is substantially reduced, and the construction of calculation matrix plays vital effect in linear measurement process.The present invention is that calculation matrix is redesigned on the basis of two-value random measurement matrix, constructs a kind of very sparse diagonal piecemeal calculation matrix, substantially increases the non-correlation of matrix, sensing matrix is preferably met RIP conditions.New calculation matrix is not only easy to hardware realization, accelerates the reconstruction speed of image, and more improve the reconstruction precision of image.When sample rate is 0.1 to 0.5 interval, the Y-PSNR (PSNR) of reconstruction image is improved 1 and arrive 4dB.
Description
Technical field
The present invention relates to it is a kind of based on compressed sensing in image reconstruction calculation matrix constitution optimization method, feature is pair
Signal original signal data goes out the original signal data of higher precision, the pressure applied to signal with lower sample rate restoration and reconstruction
Contracting and recovery, image procossing and computer vision etc., Signal Compression transmission and the restoration and reconstruction belonged in Signal and Information Processing
Field.
Background technology
The core of compression sensing is linear measurement process, if x (n) is primary signal, length is N, and square is measured by premultiplication
Battle array Φ obtains y (m), and length is M (M<N).If x (n) is not sparse signal, orthogonal sparse transformation will be carried out and obtain s (k), remembered
For x=Ψ s, measurement process is re-written as y=Θ s, wherein Θ=Φ Ψ (M × N), referred to as sensing matrix, process such as Fig. 2 institutes
Show.Compressing sensing theory mainly includes three aspects of construction of rarefaction representation, restructing algorithm and calculation matrix of signal.
Image sparse represents to refer to that the larger coefficient set of some numerical value has suffered figure in coefficient of the image on particular transform base
The most of energy and information of picture, and other coefficients are all zero or close to zero, it means that using a small amount of bit number just
The purpose for representing image can be reached.Natural sign in usual time domain is all non-sparse, for example, for a width natural image,
Almost all of pixel value is all non-zero, but when being transformed to wavelet field, the absolute value of most of wavelet coefficients all connects
It is bordering on zero, and limited big coefficient is it can be shown that most information of original image.The openness of signal is that compression is passed
Feel basis and the premise of theory, this paper experiment simulations carry out rarefaction using wavelet transform base to image.
Signal reconstruction algorithm refers to that by M measurement vector y reconstruct length be N (M<N the process of sparse signal x).It is above-mentioned
Unknown number number N exceedes equation number M in equation group, it is impossible to directly recover x (n) from y (m), can be by solving minimum l0
Norm problem (1) is solved.
But minimum l0 norm problems be a NP-hard problem, it is necessary in exhaustion x nonzero value it is allPlanting arrangement can
Can, thus can not solve.Thus solved with the algorithm of near-optimal solution, mainly include minimum l1 norms method, match tracing system
Full calculus of variations of minimum of row algorithm, iteration method and special disposal two dimensional image problem etc., what this paper experiment simulations were used
For orthogonal matching pursuit algorithm (Orthogonal matching pursuit, OMP).
And in terms of the construction of calculation matrix, it need to meet the equidistant condition of constraint with the sensing matrix Θ that sparse base is constituted
(RIP conditions, 2 formulas), it is possible to which primary signal is recovered by above restructing algorithm.
Wherein, δkMinimum value be referred to as RIP constants, be a standard for weighing RIP properties quality.
RIP conditions are to ensure the adequate condition that signal can be reconstructed, but to verify whether sensing matrix meets this condition
The problem of being one extremely complex, it is therefore desirable to have a kind of easy, RIP condition alternatives for being easily achieved.It is theoretical and real
If trampling proof can guarantee that calculation matrix Φ and orthogonal basis Ψ are uncorrelated, Θ meets RIP properties on very big probability.Due to
Ψ is fixed, to cause Θ=Φ Ψ to meet the equidistant condition of constraint, can be solved by designing calculation matrix Φ.Pass through mathematics
It is theoretical and substantial amounts of practice have shown that, be commonly used to calculation matrix have shellfish make great efforts calculation matrix (two-value random measurement matrix), with
Machine Gauss measurement matrix, Fourier random measurement matrix, Hadamard calculation matrix, these matrixes all meet RIP with high probability
Condition.It is exactly that redesign optimization is carried out to calculation matrix on the basis of two-value random measurement matrix herein, has constructed one
Plant very sparse two-value random measurement matrix.
The content of the invention
The invention solves the problems that technical problem is：Existing two-value random measurement matrix can not in being rebuild for compression transducing signal
The problem of precision is not high after the RIP properties and reconstruction signal that meet well, has constructed a kind of very sparse diagonal point
Block 0,1 two-value random measurement matrix, make sensing matrix better meet RIP conditions.In reconstruction bar of the equal sample rate as
Under part, this method can improve the precision and signal to noise ratio of reconstruction signal to a certain extent.
The present invention solve the technical scheme that uses of above-mentioned technical problem for：One kind is surveyed based on compressed sensing in image reconstruction
The constitution optimization method of moment matrix, this method is based on two-value random measurement matrix, constructs a kind of very sparse diagonal piecemeal two
It is worth random measurement matrix, the sensing matrix that the calculation matrix after improvement is constituted with sparse base is better met RIP conditions, so that
The reconstruct to sparse signal is more favorable for, primary signal is finally gone out by sparse signal reconfiguring again.
It is described it is a kind of based on compressed sensing in image reconstruction calculation matrix constitution optimization method, RIP conditions are to protect
The adequate condition that can reconstruct of card signal, but to verify whether sensing matrix meets this condition and be one and extremely complex ask
Topic, is proved, calculation matrix and sparse base non-correlation are lower by theory and practice, then sensing matrix is full on very big probability
Sufficient RIP properties.
It is described it is a kind of based on compressed sensing in image reconstruction calculation matrix constitution optimization method, the bar of sensing matrix
The RIP attributes of number of packages and sensing matrix have it is substantial contact, the conditional number of sensing matrix is maximum unusual for sensing matrix
The ratio or the size of singular value interval of value and minimum singular value, are also a related important parameter of RIP constants, reduce
The interval of sensing matrix singular value, can make the sensing matrix newly obtained have more preferable RIP constants.
It is described it is a kind of based on compressed sensing in image reconstruction calculation matrix constitution optimization method, sensing matrix condition
Number is smaller, and calculation matrix Φ and sparse orthogonal basis Ψ non-correlation are better, and obtained sensing matrix will have more preferable RIP normal
Number；The conditional number of sensing matrix is smaller simultaneously, the more non-morbid state of matrix, the more solution beneficial to restructing algorithm, therefore sensing matrix
Conditional number is to weigh a good and bad important indicator of calculation matrix performance.
It is described it is a kind of based on compressed sensing in image reconstruction calculation matrix constitution optimization method, based on compressed sensing
The Performance Evaluating Indexes of calculation matrix enter on the basis of original two-value random measurement matrix to calculation matrix in image reconstruction
Go improvement, reconfigure out a kind of very sparse diagonal piecemeal two-value random measurement matrix, the calculation matrix after improvement
There is smaller conditional number with the sensing matrix that sparse base is constituted, RIP conditions are preferably met, so as to be more conducive to last to original
The reconstruction of signal.
The principle of the present invention is：A kind of calculation matrix constitution optimization method based on compressed sensing in image reconstruction,
A kind of very sparse diagonal piecemeal 0,1 two-value random measurement matrix have been constructed, sensing matrix is better met RIP bars
Part.The measured value that the calculation matrix after optimizing is obtained again reconstructs sparse signal by restructing algorithm, is finally passed through by sparse signal
Cross wavelet inverse transformation and reconstruct primary signal.
Theory and practice shows, conditional number (maximum singular value of sensing matrix and the ratio of minimum singular value of sensing matrix
The size of value or singular value interval) with the RIP attributes of sensing matrix have it is substantial contact, be also that RIP constants are related
An important parameter, reduce the interval of sensing matrix singular value, can have the sensing matrix that newly obtains more preferable
RIP constants.Sensing matrix conditional number is smaller, and calculation matrix Φ and sparse orthogonal basis Ψ non-correlation are better, obtained sensing
Matrix Θ will have more preferable RIP constants.The conditional number of sensing matrix is smaller simultaneously, the more non-morbid state of matrix, is more calculated beneficial to reconstruct
The solution of method, therefore the conditional number of sensing matrix is to weigh a good and bad important indicator of calculation matrix performance.
It is right on the basis of original two-value random measurement matrix according to the above-mentioned analysis to calculation matrix Performance Evaluating Indexes
Calculation matrix redesign and improved, and has constructed a kind of very sparse diagonal piecemeal 0,1 two-value random measurement matrix,
As shown in Figure 3.
As shown in figure 3, calculation matrix size is M × N, the wherein matrix in block form on diagonal is that size isIt is one-dimensional
Two-value random matrix, remaining element is 0.The two-value random measurement matrix of this diagonal piecemeal is two very sparse Distribution values,
It is convenient to calculate and hardware realization, while also accelerating the calculating speed of image reconstruction.Each point on calculation matrix diagonal
Block minor matrix is arranged to identical 0,1 random distribution, is so to ensure constituted sensing matrix singular value point as far as possible
The stability of cloth, reduces singular value distributed area, reduces sensing matrix conditional number.Taken at random relative to each piecemeal minor matrix
0,1 distribution situation, experiment proves to have last reconstruction image using the piecemeal minor matrix of identical 0,1 distribution more preferable
Effect.
Design it is a kind of can preferably meet the calculation matrix of RIP conditions, so as to higher precision reconstruct it is original
Signal, the technical solution adopted in the present invention is：
Analyzed from background technology, sparse transformation base Ψ is it has been determined that be wavelet transform base.Due to sensing matrix
Conditional number determine the RIP properties that it is met, after diagonal piecemeal two-value random matrix is constructed, in order to verify that it is met
RIP properties, in the case where sample rate (M/N) is respectively 0.0625,0.125,0.25 and 0.5, respectively before and after computed improved
Calculation matrix be multiplied with wavelet transformation base obtained by sensing matrix Θ conditional number, and compare both sizes.Due to measurement
Matrix is random generation, in order to avoid contingency, takes five experimental results to do average, obtains the result of calculation shown in table one.
It was found from table one, under four kinds of different sample rates, gained sensing matrix singular value distributed area and condition after improvement
Number is greatly reduced, and with the raising of sample rate, and the conditional number reduction magnification of sensing matrix also more and more higher, shows after improvement
Calculation matrix after improvement better meets RIP conditions.
Table 1 compares for the sensing matrix conditional number (singular value interval) before and after being improved in the case of different sample rates
| Sample rate | Before improvement | After improvement |
| 6.25% | 13.61/[4.66,63.41] | 1.18/[2.01,2.38] |
| 12.5% | 23.61/[3.79,89.47] | 1.27/[1.24,1.57] |
| 25% | 47.93/[2.64,126.53] | 1.61/[0.33,0.53] |
| 50% | 145.21/[1.23,178.61] | 2.55/[0.11,0.28] |
The advantage of the present invention compared with prior art is：
(1) present invention have devised a kind of very sparse diagonal point on the basis of existing two-value random measurement matrix
Block two-value random matrix.Due to being 0,1 two Distribution values entirely, it is easy to hardware to realize, it is such diagonal dilute relative to former calculation matrix
Thin matrix accelerates the desin speed of calculation matrix and simplifies calculating, improves the reconstruction efficiency of image, and can be easily
Put into application to engineering practice, more practical significance.
(2) in general compressed sensing image reconstruction is all poor for the image reconstruction effect of high grain details class, this hair
Improved method used in bright allows the reconstruction precision of this high texture image of fingerprint to have a certain degree of lifting, makes the thin of image
Section reconstruction ability has certain enhancing, therefore compensate for a certain extent in existing compression sensing technology to high frequency texture class
The problem of image reconstruction accuracy is not high.
(3) present invention is designed using the simple diagonal building method being easily achieved to calculation matrix, is allowed to efficient
RIP conditions are met to rate, the conditional number and Degree of Ill Condition of sensing matrix is greatly reduced, is more favorable for Algorithm for Solving.In phase
In the case of same sample rate, relative to original calculation matrix, the Y-PSNR of the calculation matrix reconstruction image after improvement is improved
About 1 arrives 4dB, substantially increases reconstruction precision, improvement is obvious.
Brief description of the drawings
Fig. 1 is that the inventive method is used for the implementation process figure that compressed sensing data-signal is rebuild；
Fig. 2 is the general principle block diagram of compressed sensing linear measurement process in the present invention；
The very sparse diagonal piecemeal two-value random matrix that Fig. 3 is constructed for the present invention；
Fig. 4 is that Peppers, Lena and Fingerprint image rebuild effect pair when sample rate is 0.25 before and after improving
Than；
Fig. 5 (a), (b), (c) are respectively the peak value letter of Peppers, Lena and Fingerprint reconstruction image before and after improving
Make an uproar than the relation between sample rate.
Embodiment
Opinion embodiment further illustrates the present invention below in conjunction with the accompanying drawings.
The theory diagram in Fig. 2, the diagonal piecemeal two-value random matrix constructed with figure three as calculation matrix Φ,
New calculation matrix reduces sensing matrix Θ (Θ=Φ Ψ) conditional number, sensing matrix is better met RIP conditions, from
And it is more favorable for reconstruction of the compressed sensing to image.
Image is done to the gray-scale map that Peppers, Lena and Fingerprint size are 512*512 respectively with matlab
The emulation experiment of reconstruction, in order to avoid the row and column effect formed after reconstruction image, respectively to length for 512 image line and
Row are rebuild, and finally do averagely obtaining reconstruction image.When sample rate is 0.25, obtain improving front and rear image reconstruction effect pair
Than as shown in Figure 4.
As shown in Figure 4, calculation matrix is carried out after diagonal piecemeal improvement, image reconstruction quality and precision have been obtained significantly
Raising, image is more smooth, and noise is smaller.It is the brightest for the more image lifting effect of this low-frequency components of Peppers
It is aobvious, when sample rate is 0.25, PSNR liftings about 4dB.Secondly for the Lena image weights containing high and low frequency composition simultaneously
Build quality and also have and significantly lifted, the reconstruction due to compression sensing to high frequency texture class image has significant limitation,
Fingerprint is high frequency texture detail pictures, therefore lifting effect is limited but a certain degree of relative to there has also been before improvement
Lifting, PSNR improves about 1dB after improvement.
According to appeal method, reconstruction image before and after being improved when sample rate is 1/32,1/16,1/8,1/4,1/2 is calculated respectively
Y-PSNR.For the purposes of avoiding the contingency of experiment, equally take five result of calculations to do average, draw out sample rate and exist
PSNR change curve before and after calculation matrix is improved within 0.5, shown in such as Fig. 5 (a) (b) (c).
As can be seen from Figure 5, in addition to the sample rate except 1/32, calculation matrix is more equal than improving preceding reconstruction image precision after improving
Have and largely lifted, lift the effect most preferably more image of Peppers low-frequency components, next to that Lena images, and
The effect improved worst still high texture images of Fingerprint, but when sample rate is 0.5, Fingerprint image reconstructions
Precision, which has, to be substantially improved, and improves about 3dB.On the whole, after redesign improvement is carried out to calculation matrix, figure is rebuild
The quality and precision improvement of picture are obvious.
Non-elaborated part of the present invention belongs to the known technology of those skilled in the art.
Those of ordinary skill in the art it should be appreciated that the embodiment of the above be intended merely to explanation the present invention,
And be not used as limitation of the invention, if in the spirit of the present invention, to embodiment described above change,
Modification will all fall in the range of claims of the present invention.
Claims (5)
1. it is a kind of based on compressed sensing in image reconstruction calculation matrix constitution optimization method, it is characterized in that：This method is based on
Two-value random measurement matrix, constructs a kind of very sparse diagonal piecemeal two-value random measurement matrix, makes the measurement square after improvement
The sensing matrix that battle array is constituted with sparse base better meets RIP conditions, so as to be more favorable for the reconstruct to sparse signal, again finally
Primary signal is gone out by sparse signal reconfiguring.
2. it is according to claim 1 it is a kind of based on compressed sensing in image reconstruction calculation matrix constitution optimization method,
It is characterized in that：RIP conditions are to ensure the adequate condition that signal can be reconstructed, but to verify whether sensing matrix meets this condition
The problem of being one extremely complex, proved by theory and practice, calculation matrix and sparse base non-correlation are lower, then sense square
Battle array meets RIP properties on very big probability.
3. it is according to claim 1 it is a kind of based on compressed sensing in image reconstruction calculation matrix constitution optimization method,
It is characterized in that：The conditional number of sensing matrix and the RIP attributes of sensing matrix have it is substantial contact, the conditional number of sensing matrix
The ratio of maximum singular value and minimum singular value for sensing matrix or the size of singular value interval, are also RIP constant phases
The important parameter closed, reduces the interval of sensing matrix singular value, can have the sensing matrix newly obtained more preferable
RIP constants.
4. a kind of constitution optimization side based on compressed sensing calculation matrix in image reconstruction according to Claims 2 or 3
Method, it is characterized in that：Sensing matrix conditional number is smaller, and calculation matrix Φ and sparse orthogonal basis Ψ non-correlation are better, obtain
Sensing matrix will have more preferable RIP constants；The conditional number of sensing matrix is smaller simultaneously, the more non-morbid state of matrix, more beneficial to reconstruct
The solution of algorithm, therefore the conditional number of sensing matrix is to weigh a good and bad important indicator of calculation matrix performance.
5. a kind of constitution optimization side based on compressed sensing calculation matrix in image reconstruction according to Claims 2 or 3
Method, it is characterized in that：Performance Evaluating Indexes based on compressed sensing calculation matrix in image reconstruction are in original two-value random measurement
Calculation matrix is improved on the basis of matrix, a kind of very sparse diagonal piecemeal two-value has been reconfigured out and has surveyed at random
Moment matrix, the calculation matrix after improvement has smaller conditional number with the sensing matrix that sparse base is constituted, and preferably meets RIP bars
Part, so as to be more conducive to the last reconstruction to primary signal.
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Application publication date: 20170915 |