CN101567079B - Method for restoring motion blurred image based on Hopfield neural network - Google Patents

Abstract

The invention discloses a method for restoring a motion blurred image based on Hopfield neural network, which mainly solves the problem that the prior art cannot converge an overall extreme point whenthe network is stable. The method is achieved according to the following steps: (1) constructing a Toeplitz matrix H; (2) calculating a network weight matrix and an input bias matrix; (3) calculating the input of a network neuron; (4) calculating the output of the neuron by using an updating rule; (5) calculating the output of the network by using a transfer function; (6) judging whether the upda ting of all neurons is finished or not, if so, returning to the step (3), and otherwise, executing the step (7); and (7) judging whether a preset iterations is reached or not, if so, obtaining a restoration result of the blurred image, and otherwise, returning to the step (3) until the preset iterations is reached. The method can obtain a better image restoration result, has better convergence performance, and can be applied to restoring the motion blurred image appearing in the process of digital images.

Description

Method for restoring motion blurred image based on the Hopfield neural network

Technical field

The invention belongs to technical field of image processing, a kind of restoration methods of motion blur image specifically, this method can be used for the recovery to the motion blur image that is occurred in the digital picture process.

Background technology

Image recovers to be meant removal or to alleviate the image quality decrease phenomenon that takes place that in obtaining the digital picture process it is an important and challenging research contents in the Flame Image Process.Recover problem for image, the researcher has proposed a lot of methods.

Traditional restoration methods such as liftering, Wiener filtering, Kalman filtering and generalized inverse singular value decomposition method are widely used in the recovery of image, but these methods require image to satisfy the hypothesis of wide stationary process, and the motion blur image that obtains in the reality can't satisfy such hypothesis fully, thereby has limited these methods to the restorability of motion blur image and application in practice.In addition, these methods require motion blur images to have higher signal to noise ratio (S/N ratio), are only applicable to the image of high s/n ratio as the method for liftering, and this point has further limited the application in practice of traditional restoration methods.

In recent years, the Hopfield neural network has obtained using widely as the means that a kind of image recovers.The scholar Paik of Korea S takes the lead in the image recovery method based on the Hopfield neural network that Zhou proposes is improved, referring to article " Image restoration using a modified Hopfield network ", IEEE Trans.ImageProcessing, 1992, Vol.1, pp.49-63, this method is represented each pixel of image with a neuron, and need not to judge the increase and decrease of Hopfield neural network energy, though these improvement have improved restorability and have reduced the complexity of recovering, but,, make that the speed of convergence of network still is undesirable because the neuron state of this network adopts step to change.After this, the people such as scholar Wu of China improve the method for Paik, referring to article " An Improved Algorithm for Image Restoration Based on Modified Hopfield NeuralNetwork ", Proceedings of the Fourth International Conference on Machine Learning andCybernetics, Guangzhou, August 2005, pp.18-21, the speed of convergence of this method further is improved, but this method is easy to be absorbed in Local Extremum owing to reaching at network when stablizing, can't reach the global extremum point, thereby influenced the quality of recovering image, in addition, the speed of network convergence is still waiting to improve.

Summary of the invention

The objective of the invention is to overcome the deficiency of above-mentioned prior art, proposed a kind of method for restoring motion blurred image, reach the global extremum point when being implemented in network stabilization, improve quality and the speed of convergence of recovering image based on the Hopfield neural network.

The technical scheme that realizes the object of the invention is that the Hopfield neural network of serial is improved, and applies it to then in the middle of the image recovery.Its concrete steps comprise:

(1) sets Hopfield neural network iterations, utilize point spread function structure Toeplitz matrix H;

(2) utilize the Toeplitz matrix H to calculate Hopfield neural network weight matrix W and input bias matrix b;

(3) utilize Hopfield neural network weight matrix W and network input bias matrix b, calculate i neuron input u of this network _i

(4) utilize i neuron input u _iWith Hopfield neural network weight matrix W, calculate neuronic i the neuron output of this network Δ x _i

(5) utilize Hopfield neural network i neuronic output Δ x _iWith Hopfield neural network transfer function f, calculate i output x of whole Hopfield neural network _i, wherein (1,2,3...L), L represents the output number of whole Hopfield neural network to i ∈;

(6) adopt the serial of calculating i+1 to choose neuronic method, and give i, judge whether the i≤L that satisfies condition,, return step (3) if satisfy with the result of calculation assignment; If do not satisfy execution in step (7);

(7) the Hopfield neural network being carried out iteration develops, judge whether to reach the iterations of setting, if reached the iterations of setting, then Hopfield neural network at this moment is output as the restoration result of motion blur image, if do not reach the iterations of setting, return step (3), till the iterations that reaches setting.

The present invention has the following advantages compared with prior art:

1, the present invention has broken through image and must satisfy the condition of wide stationary process because the method that has adopted iteration to develop is compared with classical image recovery method, and has reduced in the image recovery process requirement to high s/n ratio;

2, the present invention is owing to adopt serial to choose neuron, utilize the neuron input and the Hopfield neural network weight matrix of Hopfield neural network to calculate this network output, compare with existing serial Hopfield neural net method, can when network stabilization, reach the global extremum point, have better restorability and speed of convergence, can obtain the restoration result of motion blur image comparatively fast, preferably.

Description of drawings

Fig. 1 is a process flow diagram of the present invention;

Fig. 2 is the former picture rich in detail that the present invention and existing three kinds of methods are used in emulation experiment;

Fig. 3 is the present invention and existing three kinds of motion blur images that method is used in emulation experiment;

Fig. 4 is the present invention and the signal to noise ratio (S/N ratio) improvement amount trend graph of existing three kinds of methods under different iterationses;

Fig. 5 is the present invention and the trend graph of the Y-PSNR of existing three kinds of methods under different iterationses;

Fig. 6 is the recovery image enlarged drawing of the present invention under different iterationses;

Fig. 7 is the recovery image enlarged drawing of existing serial Hopfield neural network under different iterationses;

Fig. 8 is the enlarged drawing of the recovery image of Hopfield neural network restoration methods under different iterationses of existing P aik;

Fig. 9 is the enlarged drawing of the recovery image of Hopfield neural network restoration methods under different iterationses of existing Zhou.

Embodiment

With reference to Fig. 1, specific implementation step of the present invention is as follows:

Step 1 is set Hopfield neural network iterations, utilizes point spread function structure Toeplitz matrix H.

At first, rule of thumb value is set Hopfield neural network iterations, is generally 300 to 400 times;

Secondly, determine motion blur yardstick d, the motion blur angle

, these two parameters of supposition are known in the emulation experiment, fuzzy yardstick d value between 1 to 15, motion blur angle

Value between 1 to 90 degree is used following formula like this, just constructed point spread function h (x, y); (x y) uses following formula construction to go out the Toeplitz matrix H to utilize point spread function h then;

$h(x,y)=\left\{\begin{array}{cc}1/d& -d/2\≤r\≤d/2\\ 0& \mathrm{otherwise}\end{array}\right.$

Wherein,

Step 2 utilizes the Toeplitz matrix H to calculate Hopfield neural network weight matrix W and input bias matrix b.

The computing formula of weight matrix W is: W=-H ^TH (1)

The computing formula of input bias matrix b is: b=H ^TG (2)

Wherein, g is a motion blur image, H ^TIt is the H transposed matrix.

Step 3 is utilized Hopfield neural network weight matrix W and network input bias matrix b, calculates i neuron input u of this network _i

I neuronic input u _iComputing formula be: $u_i=b_i+\underset{j}{\mathrm{\Σ}}{w}_{\mathrm{ij}}{f}_j\left(t\right)---\left(3\right)$

Wherein, w _IiBe the element among the Hopfield neural network weight matrix W, b _iBe the element among the Hopfield neural network weight matrix b, f _j(t) be the current output valve of j neuron of Hopfield neural network behind the t time iteration process network.

Step 4 is utilized i neuron input of Hopfield neural network u _iWith Hopfield neural network weight matrix W, calculate neuronic i the neuron output of this network Δ x _i

(4a) utilize i neuron input of Hopfield neural network u _i, calculate the neuronic i of this network neuronic modifying factor: Δ x ' _i=2u _i

(4b) utilize i neuron input of Hopfield neural network u _i, the element w among the Hopfield neural network weight matrix W _IiWith i neuronic modifying factor Δ x ' _i, calculate neuronic i the neuron output of this network: Δ x _i=d (u _iThe u of)=- _i/ w _Ii-Δ x ' _i

Step 5 is utilized Hopfield neural network i neuronic output Δ x _iWith Hopfield neural network transfer function f, calculate i output x of whole Hopfield neural network _i, wherein i ∈ (1,2,3...L), L represents the output number of whole Hopfield neural network, and its computing formula is as follows:

$x_i=f\left({\mathrm{\&Delta;x}}_i\right)=\left\{\begin{array}{cc}0& {\mathrm{\&Delta;x}}_i<0\\ {\mathrm{\&Delta;x}}_i& 0\&le;{\mathrm{\&Delta;x}}_i\&le;255\\ 255& 255<\mathrm{\&Delta;}{x}_i\end{array}\right..---\left(4\right)$

Step 6 adopts serial to upgrade neuronic method the neuron in the Hopfield neural network of the present invention is upgraded.

At first, change i+1 neuron over to, give i with its result of calculation assignment again from i current neuron; Judge whether the i≤L that satisfies condition then,, return step (3) if satisfy; If do not satisfy execution in step (7); Wherein, L is neuronic sum, for the purpose of the present invention, and owing to each pixel is represented by a neuron, so the number of the pixel of image just equals the size of L.

Step 7, the Hopfield neural network is carried out iteration to be developed, judge whether to reach the iterations of setting, if reached the iterations of setting, then Hopfield neural network at this moment is output as the restoration result of motion blur image, if do not reach the iterations of setting, return step (3), till the iterations that reaches setting.

This algorithm is a kind of method of iteration, all x after each iteration _iVariation has all taken place, and after reaching set iterations and reaching, the output of Hopfield neural network is exactly the restoration result to motion blur image.

Effect of the present invention is found out by following The simulation experiment result.

1) simulated conditions: the used image of emulation experiment derives from the standard picture storehouse, be example only below with the part of Lena image, former picture rich in detail and the motion blur image used among the present invention are described, with reference to Fig. 2 and Fig. 3, they are respectively former picture rich in detail and the motion blur images that the present invention is applied in emulation experiment.

In emulation experiment, used the quality that two evaluation indexes are estimated restoration result, they are respectively signal to noise ratio (S/N ratio) improvement amount ISNR, Y-PSNR PSNR.Their definition is respectively:

Signal to noise ratio (S/N ratio) improvement amount: $\mathrm{ISNR}=10{\mathrm{<figure-callout\; id="10"\; label="log"\; filenames="H2009100228676E00023.png"\; state="\{\{state\}\}">log</figure-callout>}}_{10}\frac{{\left|\right|g-f\left|\right|}^2}{{\left|\right|f\left(t\right)-f\left|\right|}^2}---\left(5\right)$

Y-PSNR: $\mathrm{PSNR}=10{\log }_{10}\left(\frac{{255}^2\&times;M\&times;N}{\mathrm{\&Sigma;}{\left|\right|f\left(t\right)-f\left|\right|}^2}\right)---\left(6\right)$

Wherein: f is a picture rich in detail, and g is a motion blur image, and f (t) is t the image after the iteration, and M and N are the size of picture size.

2) simulation result

Fig. 4 be the present invention with the Hopfield neural network restoration methods of Zhou, the Hopfield neural network restoration methods of Paik and the trend graph of the signal to noise ratio (S/N ratio) improvement amount of serial Hopfield neural net method under different iterationses.

Fig. 5 be the present invention with the Hopfield neural network restoration methods of Zhou, the Hopfield neural network restoration methods of Paik and the trend graph of serial Hopfield neural net method Y-PSNR under different iterationses.

The ISNR that the present invention and three kinds of control methodss are obtained when different iterations and the data of PSNR value are as shown in table 1.Method of the present invention and existing serial Hopfield neural net method carry out 50 times the experiment after statisticss as shown in table 2.Wherein, Alg1 is a method of the present invention, and Alg2 is a serial Hopfield neural net method, and Alg3 is the Hopfield neural network restoration methods of Paik, and Alg4 is the Hopfield neural network restoration methods of Zhou.

Fig. 6 (a), Fig. 6 (b), Fig. 6 (c) and Fig. 6 (d) represent respectively the present invention carry out 100 times, 150 times, 200 times and 250 iteration after the recovery image; Fig. 7 (a), Fig. 7 (b), Fig. 7 (c) and Fig. 7 (d) represent respectively serial Hopfield neural net method carry out 100 times, 150 times, 200 times and 250 iteration after the recovery image; The Hopfield neural network restoration methods that Fig. 8 (a), Fig. 8 (b), Fig. 8 (c) and Fig. 8 (d) represent Paik respectively carry out 100 times, 150 times, 200 times and 250 iteration after the recovery image; The Hopfield neural network restoration methods that Fig. 9 (a), Fig. 9 (b), Fig. 9 (c) and Fig. 9 (d) represent Zhou respectively carry out 100 times, 150 times, 200 times and 250 iteration after the recovery image.

From Fig. 4 and Fig. 5 as seen, the present invention and other three kinds of methods all can reach stable status, but recovery effects of the present invention obviously is better than other three kinds of existing methods.

ISNR and PSNR value that table 1. the present invention and control methods are obtained when different iterations

As can be seen from Table 1, method of the present invention is bigger than ISNR and the PSNR value that other three kinds of control methodss obtain.

From Fig. 6 (a), Fig. 7 (a), Fig. 8 (a) and Fig. 9 (a) also as can be seen, carry out 100 times iteration in neural network after, use the image graph 6 (a) after method of the present invention is recovered more much better on visual effect than other three kinds of method image restored Fig. 7 (a), Fig. 8 (a) and Fig. 9 (a).From Fig. 6 (b), Fig. 7 (b), Fig. 8 (b) and Fig. 9 (b) also as can be seen, carry out 150 times iteration in neural network after, use the image graph 6 (b) after method of the present invention is recovered more much better on visual effect than other three kinds of method image restored Fig. 7 (b), Fig. 8 (b) and Fig. 9 (b).From Fig. 6 (c), Fig. 7 (c), Fig. 8 (c) and Fig. 9 (c) also as can be seen, carry out 200 times iteration in neural network after, use the image graph 6 (c) after method of the present invention is recovered more much better on visual effect than other three kinds of method image restored Fig. 7 (c), Fig. 8 (c) and Fig. 9 (c).From Fig. 6 (d), Fig. 7 (d), Fig. 8 (d) and Fig. 9 (d) as can be seen, carry out 250 times iteration in neural network after, use the image graph 6 (d) after method of the present invention is recovered more much better on visual effect than other three kinds of method image restored Fig. 7 (d), Fig. 8 (d) and Fig. 9 (d).

Because in three kinds of control methodss, the restorability of serial Hopfield neural net method is better than the restorability of the Hopfield neural network restoration methods of the Hopfield neural network restoration methods of Zhou, Paik, therefore, the present invention and serial Hopfield neural net method have carried out 50 times contrast experiment, and the data that experiment obtains are as shown in table 2.Wherein, after Δ PSNR is illustrated in identical iterations, the PSNR value that the present invention obtains is than the raising amount of the PSNR value of serial Hopfield neural net method acquisition, after Δ ISNR is illustrated in identical iterations, the raising amount of the ISNR value that the resulting ISNR value of the present invention obtains than serial Hopfield neural net method.

Table 2. the present invention is carrying out the statistics after the experiment 50 times

Fuzzy yardstick	Fuzzy angle	ΔPSNR	ΔISNR
				1-15	1-90	0.1-0.7(dB)	0.1-0.65(dB)

Table 2 is that method of the present invention and existing serial Hopfield neural net method are being carried out the statistics after the experiment 50 times.Also as can be seen, the present invention has restorability preferably than serial Hopfield neural net method from table 2.

Claims (1)

1. the method for restoring motion blurred image based on the Hopfield neural network comprises the steps:

(1) sets Hopfield neural network iterations, utilize point spread function structure Toeplitz matrix H;

(2) utilize the Toeplitz matrix H to calculate Hopfield neural network weight matrix W and input bias matrix b;

(3) utilize Hopfield neural network weight matrix W and input bias matrix b, calculate i neuron input u of this network _i

(4) utilize i neuron input u _iWith Hopfield neural network weight matrix W, calculate neuronic i the neuron output of this network Δ x _i:

(4a) utilize i neuron input of Hopfield neural network u _iCalculate the neuronic i of this network neuronic modifying factor: Δ x ' _i=2u _i

(4b) utilize i neuron input of Hopfield neural network u _i, the element w among the Hopfield neural network weight matrix W _IiWith i neuronic modifying factor Δ x ' _i, calculate neuronic i the neuron output of this network: Δ x _i=d (u _iThe u of)=- _i/ w _Ii-Δ x ' _i

(5) utilize Hopfield neural network i neuronic output Δ x _iCalculate i of whole Hopfield neural network output x with Hopfield neural network transfer function f _i, wherein (1,2,3...L), L represents the output number of whole Hopfield neural network to i ∈;

(6) adopt i+1 neuronic serial choosing method of calculating, and give i neuron, judge whether the i≤L that satisfies condition,, return step (3) if satisfy with the result of calculation assignment; If do not satisfy execution in step (7);

(7) the Hopfield neural network being carried out iteration develops, judge whether to reach the iterations of setting, if reached the iterations of setting, then Hopfield neural network at this moment is output as the restoration result of motion blur image, if do not reach the iterations of setting, return step (3), till the iterations that reaches setting.

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