CN104820969B - A kind of realtime graphic blind restoration method - Google Patents

Abstract

The invention provides a kind of realtime graphic blind restoration method, including：Fourier transformation is carried out to degraded image, then the normalized spatial spectrum of degraded image is obtained, spectrum distribution rule according to natural image, frequency spectrum to the original image of degraded image is rebuild, estimate the normalized spatial spectrum of original image, normalized spatial spectrum and reconstructed spectrum to degraded image are compared, ask for the optical transfer function of system, and then ask for the point spread function of degraded image, according to the point spread function for being obtained, Wiener filtering recovery is carried out to degraded image, so as to obtain preferable image.This method is not comprising time-consuming iteration, and method is simple, it is easy to accomplish, so as to reduce algorithm complex, while obtain accurate point spread function estimating, achieve good image restoration effect.

Description

A kind of realtime graphic blind restoration method

Technical field

The invention belongs to technical field of image processing, it is related to adaptive optical image to restore theoretical and method, and in particular to A kind of real-time blindly restoring image algorithm in adaptive optics.

Background technology

Image restoration is based on the reason for image degradation, to utilize observed degraded image to recover clearly true field Scape.Image restoration technology is had been widely used in astronomical observation, remote sensing, many fields such as security monitoring and medical imaging.Most feelings Under condition, the point spread function PSF (Point Spread Function) of image degradation is unknown, therefore for degraded image Carry out restoration disposal and generally use blind restoration algorithm.Current blind restoration algorithm is substantially mostly iteration, due to degraded image The problem of some pathosis of data, local convergence or Divergent Phenomenon are often occurred in the blind recuperation of iteration；Even if repeatedly For process stabilization, iteration is also up to thousands of times or even thousands of times, takes very much, it is difficult to meet the requirement of realtime graphic recovery.

It is being extremely difficult without PSF in the case of any priori, is estimated, until today, how exactly Estimate that PSF is still the topic for being active in this field.It is therefore proposed that one kind fast and effectively realtime graphic blind restoration method turns into Current this area important technological problems urgently to be resolved hurrily.And the image degradation problem that G class point spread functions cause is a kind of normal The reason for image degradation seen because G classes point spread function image degradation system occupy very big ratio, such as some days Literary observation, satellite sounding, aerospace detection, Electron micrographs and MRI system etc..

APEX algorithms go out the PSF of system according to the feature assessment of the spectrum information of degraded image, then using SECB (Slow Evolution of Continuation Boundary, the slow evolution of continuum boundary) restored method restores to degraded image. APEX algorithm principles are simple, do not have iteration link, some degraded images can be restored with the short time, restored in realtime graphic There is the conventional iterative unexistent advantage of blind restoration algorithm in treatment.But, APEX algorithms are still present some problems：First, APEX algorithms replace the spectrum signature of target image with a default constant value, in the physical sense and unreasonable, therefore estimate Meter error is larger；Secondly, some parameters of APEX algorithms need artificial determination, and these parameters must be selected rule of thumb Select, it usually needs trial repeatedly could obtain suitable value；Again, APEX methods are rebuild using SECB methods to image, The method is easily affected by noise.APEX algorithms when the frequency spectrum to true picture is estimated, using simple constant Substituted, this does not meet the spectral nature of true picture, caused larger evaluated error, influenceed recovery effects.Although later People have carried out some improvement, but do not tackle the problem at its root.In addition, for astronomical degraded image and micro- Degenerate Graphs During as (because the target and background contrast of these images is very big, and background is simple), APEX algorithms can effectively carry out image Restore；But when ground image is processed, due to the complexity of background, restoration result is generally difficult to satisfactory.To true picture Frequency when being estimated, these methods are substituted using simple constant, and this does not meet the frequency spectrum of true picture Matter.

The content of the invention

The technical problem to be solved in the present invention is：To overcome iteration blind restoration method real-time in image restoration technology application Difference, non-iterative blind restoration method estimates point spread function inaccurate shortcoming, and the present invention is proposed based on image spectrum and frequency The method for blindly restoring image of rate double-log relation.The general principle that this method is based on APEX methods is improved, to degraded image The normalized spatial spectrum of original image estimated that the point spread function to being tried to achieve is averaged on four straight lines, improve The accuracy estimated, this method restores that speed is fast, and point spread function estimates accurate, achieves good recovery effect.

To achieve these goals, the present invention is realized by following technical proposals：

A kind of realtime graphic blind restoration method, comprises the following steps：

1) Fourier transformation is carried out to degraded image, then obtains the normalized spatial spectrum of degraded image；

2) the spectrum distribution rule according to natural image, the frequency spectrum to the original image of degraded image is rebuild, and estimates Go out the normalized spatial spectrum of original image；

3) normalized spatial spectrum and reconstruction original image normalized spatial spectrum to degraded image is compared, and asks for degeneration system Optical transfer function, and then ask for the point spread function of degraded image；

4) according to the point spread function for being obtained, image reconstruction is carried out using Wiener filtering to degraded image.

Further, the step 1) in, degraded image g (x) is carried out Fourier transformation obtain G (μ, v), to G (μ, v) It is normalized, obtains：G^*(μ, v)=G (μ, v)/σ (1)

Wherein, G^*(μ, v) is the normalized spatial spectrum of degraded image, and (μ, is v) degraded image to G, and σ is normaliztion constant, takes σ =G (0,0), i.e. value of the Fourier transformation of degraded image in origin.

Further, the step 2) in, by taking μ=0 as an example, the reconstruction formula of original image normalized frequency is：

Wherein, k is the slope of the picture rich in detail estimated, G^*(μ v) is the normalized spatial spectrum of degraded image, F^*(μ v) attaches most importance to The original image normalized spatial spectrum built, g₁And g₂It is ln | G^*(μ, v) |The value at place, * is convolution symbol, μ and v It is the coordinate of domain space, N is image size.

G (x) is carried out into Fourier transformation to obtain G (μ, v), (μ, v) is normalized, and obtains G to G^*(μ v) is degraded image Normalized frequency.

Further, the g₁, g₂Take ln | G^*(0, n) |, ln | G^*(0 ,-n) | in ln | G^*(0, v) | on weighted average Value.

Further, the step 3) in, the point spread function to degraded image is estimated, by following process reality It is existing：

1) when the point spread function of system is G class point spread functions, the frequency domain table of G class point spread functions is：,

H (μ, v)=exp [- α (μ²+v²)^β],α>0,0<β≤1 (3)

In formula, α and β is the parameter in G class point spread functions, and μ and v is the coordinate of domain space；

Image degradation system can be expressed as

G (μ, v)=F (μ, v) H (μ, v)+N (μ, v)=exp [- α (μ²+v²)^β]F(μ,v)+N(μ,v) (4)

In formula, (μ, v) is the optical transfer function of system to H, and (μ v) is the noise of system to N；

To being taken the logarithm after the degeneration system normalization of image, obtain：

ln|G^*(μ, v) |=ln | exp [- α (μ²+v²)^β]F^*(μ,v)+N^*(μ,v)| (5)

Wherein, the noise N after normalization is ignored^*(μ v), then obtains following formula：

ln|G^*(μ, v) |=- α (μ²+v²)^β]+ln|F^*(μ,v)| (6)

By in (2) formula substitution (6) ,-α | v | are obtained^2βValue；

Wherein, α, β are the parameter value of the point spread function to be estimated；

2)-α | v | are fitted using least square method^2β, the value of α and β can be obtained from the result of fitting, so that To causing the point spread function of image degradation.

Further, the value of α and β is estimated respectively by selecting μ=0 in four rectilinear directions of v=0, μ=v, μ=- v Meter, arithmetic average is asked for α, is the index characteristic of point spread function due to what β embodied, so geometrical mean is asked for β, Reasonable α and β value are so can obtain, the possibility of distortion is estimated in a single direction so as to avoid.

Further, the step 4) in, according to the point spread function for being obtained, Wiener filtering is carried out to degraded image and is answered Original, image reconstruction is carried out using least mean-square error filter method, and its computing formula is：

Wherein, S is the signal to noise ratio of degraded image, and (μ, v) is the Fourier transformation of original image to F, and (μ v) is Degenerate Graphs to G The Fourier transformation of picture, H (μ, v) be degeneration system point spread function, i.e. the frequency domain presentation of point spread function, μ and v is frequency domain The coordinate in space.

This method rebuilds the original image frequency spectrum of degraded image, then for reconstruction according to the logarithmic relationship of natural image The relation of image and degraded image, point spread function is asked in four straight lines weightings on image spectrum, is expanded according to the point tried to achieve Function pair degraded image is dissipated to be restored.This method is not comprising time-consuming iteration, and method is simple, it is easy to accomplish, so as to reduce Algorithm complex, while obtain accurate point spread function estimating, achieves good image restoration effect.

Its feature of the invention is：

1) this algorithm rebuilds the frequency spectrum of original image using the frequency spectrum of true picture with the double-log linear relationship of frequency, than Traditional algorithm more has physical significance, more accurately.

2) this method is based on the general principle of APEX methods and is improved, to the normalization of the original image of degraded image frequently Spectrum is estimated that the point spread function to being tried to achieve is averaged on four straight lines, improves the stability of estimation.

3) this method is restored instead of SECB algorithms using Wiener filtering to degraded image, in reducing recuperation Interactive session, improves recovery speed, meanwhile, Wiener Filter Method is more preferable to the inhibition of noise than SECB algorithm, improves The recovery effect of image.

Brief description of the drawings

Fig. 1 is the implementation method FB(flow block) that Real-time blind image of the present invention restores.

Fig. 2 is to rebuild picture rich in detail spectrogram by with degraded image frequency spectrum.

Fig. 3 is-α | the v | for obtaining the degeneration system that the original image frequency spectrum of reconstruction substitutes into image^2βThe image of value.

Fig. 4 is p- α | v |^2βIt is fitted the image for obtaining α and β value.

Specific embodiment

The present invention is further described with reference to the accompanying drawings and examples.

As shown in figure 1, realtime graphic blind restoration method of the present invention, comprises the following steps：

1) by degraded image g (x) carry out Fourier transformation obtain blurred picture G (μ, v),

σ=G (0,0) is taken, (μ, v) is normalized, and obtains to G

G^*(μ, v)=G (μ, v)/σ (1)

Wherein, G^*(μ, v) is the normalized spatial spectrum of degraded image, and (μ, is v) degraded image to G, and σ is normaliztion constant, takes σ =F (0,0) ≈ G (0,0), i.e. value of the Fourier transformation of degraded image in origin.

2) the spectrum distribution rule according to natural image, the frequency spectrum to the original image of degraded image is rebuild, original The reconstruction formula (by taking μ=0 as an example) of image spectrum is

Wherein, k is the slope of the picture rich in detail estimated, k values are 0.8 to 1.2, n values when being 6 to 10, and acquirement is estimated Meter effect is preferable.G^*(μ v) is the normalized spatial spectrum of degraded image, F^*(μ, v) be rebuild original image normalized spatial spectrum.g₁ And g₂It is ln | G^*(μ, v) |The value at place, * is convolution symbol, and μ and v is the coordinate of domain space, and the value of n is 6-10, N are image size.

Simultaneously as ln | G^*(0, v) | it is concussion, so g₁, g₂Take ln | G^*(0, n) |, ln | G^*(0 ,-n) | in ln | G^* (0, v) | on weighting smooth value, the picture rich in detail frequency spectrum ln of reconstruction | F^*(0, v) | as shown in Fig. 2 in figure, asterisk point in top is The frequency spectrum of the clear picture rebuild, bottom discrete point is the frequency spectrum of degraded image.

3) normalized spatial spectrum and reconstructed spectrum to degraded image are compared, and ask for the optical transfer function of system, enter And ask for the point spread function of degeneration system.

By taking μ=0 as an example, details are as follows for the process of asking for of point spread function：

1. when the point spread function of system is G class point spread functions, the frequency domain representation of G class point spread functions is：

H (μ, v)=exp [- α (μ²+v²)^β] (3)

In formula, α and β is the parameter in G class point spread functions, and μ and v is the coordinate of domain space；

By selecting the value of suitable α and β, H (μ, when can v) meet a major class optical transfer function, wherein β=1 couple Gaussian density is answered, in seabed imaging, the aspect such as computer tomography has important application；The exposure long of β=5/6 correspondence Atmospheric turbulance is obscured, and has important application in many-sides such as astronomical observation, remote sensing；The corresponding Lorentzian density functions in β=1/2, It has been applied to be modeled for X-ray scattering phenomenon in medical imaging.In a word, the β for meeting 0 ＜ β≤1 meets many electronics The feature of equipment.

Then the degeneration system of image is expressed as：

G (μ, v)=F (μ, v) H (μ, v)+N (μ, v)=exp [- α (μ²+v²)^β]F(μ,v)+N(μ,v) (4)

In formula, (μ, v) is the optical transfer function of system to H, and (μ v) is the noise of system to N；

To being taken the logarithm after the degeneration system normalization of image, obtain：

ln|G^*(μ, v) |=ln | exp [- α (μ²+v²)^β]F^*(μ,v)+N^*(μ, v) | (5)

Wherein, the noise N after normalization is ignored^*(μ v), then obtains following formula：

ln|G^*(μ, v) |=- α (μ²+v²)^β]+ln|F^*(μ, v) | (6)

By ln | F^*(0, v) | substitute into ln | G^*(0,v)|≈-α(v)^2β-ln|F^*(0, v) | ,-α | v | can be obtained^2βValue, Shown in result of calculation such as Fig. 2.

Wherein, α, β are the parameter value of the point spread function to be estimated；

2.-α | v | are fitted using least square method^2β, the value of α and β can be obtained from the result of fitting, so that To causing the point spread function of image degradation.

Due to-α | v | after β is fixed^2βIt is bell, in-N≤v≤0 curve monotonic increase, in 0≤v≤N inner curve lists Tune successively decreases.Therefore, the not all data of Fig. 3 can be used for estimating the parameter of point spread function, the only data near origin Estimate most effective during point spread function.A threshold value scale and scale ＜ N are set herein, by v ∈ [scale ,-scale] model Enclose interior data from-α | v |^2βIn be extracted (as shown in Figure 4), require scale it so that the point for being taken is all at two Within the scope of " trough ".Discrete point is-α | v | of scale interceptions^2βValue, curve is-α | v |^2βFitting.

- α | v | are fitted using least square method after suitable data are obtained^2β, can be obtained from the result of fitting The value of α and β, so as to obtain causing the point spread function of image degradation.

In the degraded image of reality, due to the influence of degeneration factor and other enchancement factors, the actual turbulent flow of a frame is moved back Change image spectrum information can not possibly Ω=(μ, v) | μ²+v²≤ω²In the range of fully meet radiation symmetric condition, can only Approach to a certain extent or approximately meet radiation symmetric.Therefore, the different straight lines of origin were chosen in Ω planes, to logarithm It is different that spectrum curve is fitted the value for drawing, so as to result in the unstability of point spread function estimation.When selected The direction of straight line by enchancement factor (such as system noise, truncated error etc.) influence it is larger when, it is possible to cause the mistake of APEX methods Effect, it is difficult to estimate go out rational α and β value.By selecting μ=0, estimate respectively in four rectilinear directions of v=0, μ=v, μ=- v, Arithmetic average is asked for α, is the index characteristic of point spread function due to what β embodied, so geometrical mean is asked for β, this Sample can obtain reasonable α and β value, estimate the possibility of distortion in a single direction so as to avoid.

4) image restoration, the present invention is restored using Wiener filtering.

Apex algorithms generally carry out deconvolution image recovery using SECB methods.SECB methods are directed to G class point spread functions The characteristics of number limitlessly detachable and propose, it is relatively time-consuming but due to needing to interact parameter regulation.The present invention is using " most Small mean square error filtering (Wiener filtering) " method carries out image reconstruction.Wiener is filtered by minimizing original image and recovery Mean square error between image obtains recovery image, is considered as a special case of SECB methods, imitates with stronger denoising Really, its computing formula is：

Wherein, S is the signal to noise ratio of degraded image, and (μ, v) is the Fourier transformation of original image to F, and (μ v) is Degenerate Graphs to G The Fourier transformation of picture, H (μ, v) be degeneration system optical transfer function, μ and v for domain space coordinate.

Claims (5)

1. a kind of realtime graphic blind restoration method, it is characterised in that comprise the following steps：

1) Fourier transformation is carried out to degraded image, then obtains the normalized spatial spectrum of degraded image；

2) the spectrum distribution rule according to natural image, the frequency spectrum to the original image of degraded image is rebuild, and estimates original The normalized spatial spectrum of beginning image；

Step 2) in, the reconstruction formula of original image normalized spatial spectrum is：

$\ln \left|F^{*}(\mathrm{\&mu;},\mathrm{\&nu;})\right|=\left\{\begin{array}{cc}\ln \left|G^{*}(\mathrm{\&mu;},\mathrm{\&nu;})\right|& \left|\sqrt{{\mathrm{\&mu;}}^2+{\mathrm{\&nu;}}^2}\right|<n\\ g_1+k*\log \left|n\right|-k*\log \left|\sqrt{{\mathrm{\&mu;}}^2+{\mathrm{\&nu;}}^2}\right|& n\&le;\sqrt{{\mathrm{\&mu;}}^2+{\mathrm{\&nu;}}^2}\&le;N-1\\ g_2+k*\log \left|n\right|-k*\log \left|\sqrt{{\mathrm{\&mu;}}^2+{\mathrm{\&nu;}}^2}\right|& -N\&le;\sqrt{{\mathrm{\&mu;}}^2+{\mathrm{\&nu;}}^2}\&le;-n\end{array}\right.---\left(2\right)$

Wherein, k is the slope of the picture rich in detail estimated, G^*(μ, ν) is the normalized spatial spectrum of degraded image, F^*(μ is v) what is rebuild Original image normalized spatial spectrum, g₁And g₂It is ln | G^*(μ, ν) |The value at place, * is convolution symbol, and μ and ν is frequency The coordinate of domain space, the value of n is 6-10, and N is image size；

g₁, g₂Take ln | G^*(0, n) |, ln | G^*(0 ,-n) | in ln | G^*(0, v) | on weighted average；

3) normalized spatial spectrum and the original image normalized spatial spectrum of reconstruction to degraded image is compared, and asks for degeneration system Optical transfer function, and then ask for the point spread function of degraded image；

4) according to the point spread function for being obtained, image reconstruction is carried out using Wiener filtering to degraded image.

2. realtime graphic blind restoration method according to claim 1, it is characterised in that step 1) in, to degraded image g X () carries out Fourier transformation and obtains G (μ, v), (μ, v) is normalized, and obtains to G：

G^*(μ, v)=G (μ, v)/σ (1)

Wherein, σ is normaliztion constant, takes σ=F (0,0) ≈ G (0,0), and G (0,0) is the Fourier transformation of degraded image in origin Value, F (0,0) for original image Fourier transformation origin value.

3. realtime graphic blind restoration method according to claim 1, it is characterised in that step 3) in, ask for degraded image Point spread function realized by following process：

1) when the point spread function of degeneration system is G class point spread functions, the frequency domain representation of G class point spread functions is：H(μ, V)=exp [- a (μ²+v²)^β],a>0,0<β≤1, (3)

In formula, α and β is the parameter in G class point spread functions；

Then the degeneration system of image is expressed as：

G (μ, ν)=F (μ, ν) H (μ, ν)+N (μ, ν)=exp [- α (μ²+ν²)^β]F(μ,ν)+N(μ,ν) (4)

In formula, (μ, v) is the Fourier transformation of degraded image to G, and (μ, v) is the Fourier transformation of original image to F, and (μ is v) to move back to H The optical transfer function of change system, N (μ, ν) is the noise of system；

To being taken the logarithm after the degeneration system normalization of image, obtain：

ln|G^*(μ, v) |=ln | exp [- α (μ²+v²)^β]F^*(μ,v)+N^*(μ,v)| (5)

Wherein, the noise N after normalization is ignored^*(μ v), then obtains following formula：

ln|G^*(μ, v) |=- α (μ²+v²)^β+ln|F^*(μ,v)| (6)

By in (2) formula substitution (6) ,-α | v | are obtained^2βValue；

2)-a | ν | are fitted using least square method^2β, the value of α and β can be obtained from the result of fitting, so as to be led Cause the point spread function of image degradation.

4. realtime graphic blind restoration method according to claim 3, it is characterised in that to the value of α and β by selection in μ Estimate respectively in four rectilinear directions of=0, ν=0, μ=ν, μ=- ν, arithmetic average is asked for α, geometric average is asked for β Value.

5. realtime graphic blind restoration method according to claim 1, it is characterised in that step 4) in, degraded image is adopted Image reconstruction is carried out with Wiener filtering, its computing formula is：

$F(\mathrm{\&mu;},\mathrm{\&nu;})=\&lsqb;\frac{1}{H(\mathrm{\&mu;},\mathrm{\&nu;})}\frac{|H(\mathrm{\&mu;},\mathrm{\&nu;}){|}^2}{|H(\mathrm{\&mu;},\mathrm{\&nu;}){|}^2+S}\&rsqb;G(\mathrm{\&mu;},\mathrm{\&nu;})---\left(7\right)$

Wherein, S is the signal to noise ratio of degraded image, and F (μ, ν) is the Fourier transformation of original image, and G (μ, ν) is degraded image Fourier transformation, H (μ, ν) is the optical transfer function of degeneration system, the i.e. frequency domain presentation of point spread function.