KR101433920B1 - Method for recovering signal for reduction of Gibbs phenomenon or ringing artifact and apparatus thereof - Google Patents

Abstract

A signal restoration method and apparatus for removing Gibbs phenomenon and resonance artifacts are disclosed.
In this method, a signal restoration device reconstructs a resolution of the measured signal using a signal measured in an image system and an estimated signal with respect to a original input signal. Then, the process of restoring the resolution is repeated to restore the final image signal so that the total change amount of the restored signal is minimized. Here, the total change amount of the restored signal is the sum of the change amount with the surroundings based on the signal.

Description

[0001] The present invention relates to a Gibbs phenomenon and a signal reconstruction method for removing resonance artifacts, and a Gibbs phenomenon or ringing artifact and apparatus therefor,

The present invention relates to a signal reconstruction method for Gibbs phenomenon and removal of resonance artifacts.

In the case of modern people, the market for high-performance cameras is expanding year by year so that one person owns more than one digital camera per person. In addition, a high-resolution medical imaging system capable of supporting accurate diagnosis of cancer and brain diseases is continuously being developed and developed.

In this way, many image processing systems have a problem of resolution degradation. In order to solve the resolution degradation problem, a resolution restoration technique such as deblurring is developed and used.

However, in the case of a video signal processing system, a signal processing technique using an impulse response function of a corresponding system is commonly applied to recover the original signal. In this signal restoration technique, if a piecewise continuously differentiable periodic function with a discontinuous section is repeatedly restored, a Gibbs phenomenon or a resonance artifact ringing arifact) is common.

Therefore, in order to solve a resolution problem in a video system that causes a reduction in resolution, there is a need for a technique for removing a gibbous phenomenon or a resonance artifact generated when a video signal is restored.

SUMMARY OF THE INVENTION The present invention provides a signal restoration method and apparatus for reducing gibbous phenomena or resonance artifacts occurring in restoring a video signal.

According to an aspect of the present invention,

Reconstructing a resolution of the measured signal using the signal measured in the image system and the estimated signal with respect to the original input signal; And repeating the step of restoring the resolution so that the total amount of change of the restored signal is minimized. The total amount of change of the restored signal is a sum of a change amount with the surroundings based on a signal.

Here, the estimated signal is generated based on a point spread function expressing a degree of resolution degradation of the image system.

The total amount of change is calculated by a derivative of a position of a recovered signal.

Also, the total amount of change is applied when restoring the resolution according to a preset contribution amount.

여기서, p는 상기 측정된 신호이고, S는 상기 점퍼짐 함수이며,

는 상기 복원되는 신호이고,

는 상기 복원되는 신호(

)의 총변화량이며,

는 상기 총변화량(

)의 기여도이고,

는 상기 추정된 신호임에 따라 최종 영상신호를 복원하는 것을 특징으로 한다.In addition, the signal restoration method may include the following signal restoration relation

Where p is the measured signal, S is the jumping load function,

Is the restored signal,

Lt; RTI ID = 0.0 >

), ≪ / RTI >

The total amount of change (

), ≪ / RTI >

And restores the final video signal according to the estimated signal.

)은 다음의 관계식

에 의해 산출되는 것을 특징으로 한다.Further, the total change amount (

) Is expressed by the following relational expression

Is calculated by the following equation.

)는 다음의 관계식

=

여기서, H는 상기 PET 시스템의 기하학적 검출확률이고, G는 상기 PET 시스템의 점퍼짐 함수임을 따르는 것을 특징으로 한다.Further, when the image system is a positron emission tomography (PET) system, the estimated signal

) Is expressed by the following formula

=

Here, H is a geometric detection probability of the PET system, and G is a jumping load function of the PET system.

According to another aspect of the present invention,

Receiving a signal measured by a video system; Estimating a signal to be reconstructed using the measured signal and a jumping function of the image system; Calculating an error between the measured signal and the estimated signal; Calculating a total change amount of the estimated signal, wherein the total change amount represents a sum of a change amount with the surroundings based on a signal; And restoring a video signal when the total amount of change becomes minimum using the sum of the error and the total amount of change.

Here, the video signal is restored by repeating the estimating step, the error calculating step, the total change amount calculating step, and the restoring step to minimize the total change amount.

Also, in the reconstructing step, the inverse problem is solved in the direction of reducing the total amount of change, and the video signal is reconstructed.

When the imaging system is a positron emission tomography (PET) system, the signal is estimated using the jumping function and the geometric detection probability of the PET system in the estimating step.

According to another aspect of the present invention,

A video input unit receiving a signal measured by the video system; An image estimator for estimating a signal to be reconstructed using the measured signal and a jumping function of the image system; An error calculator for calculating an error between the measured signal and the estimated signal; A total change amount calculating unit for calculating a total change amount of the estimated signal, wherein the total change amount indicates a sum of a change amount with the surroundings based on a signal; And a signal reconstruction unit for reconstructing a video signal when the total amount of change becomes minimum using a sum of an error calculated by the error calculating unit and a total change amount calculated by the total change amount calculating unit.

Here, the signal decompression unit repeatedly performs a process of reducing the sum of the error and the total change amount, thereby restoring the video signal when the total change amount becomes minimum.

According to the present invention, it is possible to reduce the gibbous phenomenon or resonance artifacts generated in restoring a video signal.

Therefore, the diagnostic accuracy can be improved in the case of the diagnostic apparatus.

As a result, the sales competitiveness of video systems is improved.

1 is a diagram illustrating a concept of measuring a video signal in a general video system.
2 is a diagram illustrating a concept of a general signal restoration system restoring a video signal using a measured signal.
3 is a diagram illustrating a concept of a signal restoration method according to an embodiment of the present invention.
4 is a diagram illustrating a signal restoration apparatus according to an embodiment of the present invention.
5 is a flowchart of a signal restoration method according to an embodiment of the present invention.
FIG. 6 is a view for comparing images restored by a general method with respect to a PET system and images restored by a method according to an embodiment of the present invention.
Fig. 7 is a view showing a result of drawing a profile in the x-axis direction with respect to the image of Fig.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art can easily carry out the present invention. The present invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. In order to clearly illustrate the present invention, parts not related to the description are omitted, and similar parts are denoted by like reference characters throughout the specification.

Throughout the specification, when an element is referred to as "comprising ", it means that it can include other elements as well, without excluding other elements unless specifically stated otherwise. Also, the terms " part, "" module," and " module ", etc. in the specification mean a unit for processing at least one function or operation and may be implemented by hardware or software or a combination of hardware and software have.

1, in the case of an image system 10 that processes or measures a video signal f, the detection characteristics of the system, in particular, the degree of resolution degradation, is determined through a point spread function (S) Can be defined.

In order to solve the resolution degradation problem of the system itself and to reconstruct and restore the original input signal, the image system 10 includes a jumping function S representing the degree of resolution degradation and a measurement data a signal recovery system that improves the resolution of a video signal by repeatedly solving the inverse problem of the image detection process using the p (p) is used.

[Equation 1]

)에 고주파의 신호를 반복적으로 더해가게 되는 반면 k번째 반복 연산에서 복원된 영상신호(

) 내 불연속 구간을 가진 연속 미분 가능한 주기함수(piecewise continuously differentiable periodic function)를 복원하고자 할 경우 불연속 구간 주위로 크게 진동(oscillation)하는 신호가 발생하는 기브스 현상 (Gibbs phenomenon) 혹은 공명 인공산물(ringing arifact)이 발생하게 된다. According to this signal restoration technique, as shown in FIG. 2,

), While the reconstructed image signal in the k-th iterative operation (

In case of attempting to recover a piecewise continuously differentiable periodic function with a discontinuous section within a discontinuous section, a Gibbs phenomenon or a ringing aifact, in which a large oscillating signal is generated around the discontinuous section, ).

Such vibration signals or resonance artifacts degrade the quality of the images, which may degrade the accuracy of the diagnosis in the case of medical images. In the case of digital cameras, the quality of the images may deteriorate and adversely affect sales performance. Therefore, there is a need for a technique capable of removing such Gibbs phenomenon or resonance artifacts.

Now, a detailed description will be given of a Gibbs phenomenon and a signal restoration method for removing resonance artifacts according to an embodiment of the present invention.

In the embodiment of the present invention, a total variation (TV) of a signal to be restored is used in order to reduce a gibbous phenomenon or a resonance artifact generated when a original input signal is restored by using a jumping load function in an image system. Here, the total change amount of the signal is represented by a value obtained by measuring the amount of change with the surroundings for each position of the signal. Particularly, in the embodiment of the present invention, the video signal is restored such that the total change amount of the signal to be restored is minimized.

The total amount of change of the signal to be restored in the restoration technique using the jumping function is used as a prior function as shown in the following Equation (2) Thereby restoring the image signal from which the resonance artifact is removed.

&Quot; (2) "

는 측정 데이터로부터 복원하고자 하는 영상신호이고,

는 복원하고자 하는 영상신호(

)의 총변화량이며,

는 총변화량(

)의 기여도를 결정하는 파라미터를 나타낸다. 여기서,

는 측정 데이터(p)에 대해 추정된 데이터를 나타낸다.Here, p is data measured using an image system, S is a jumping function representing the degree of resolution degradation of the image system,

Is a video signal to be recovered from the measurement data,

The video signal to be restored

), ≪ / RTI >

The total amount of change (

) ≪ / RTI > here,

Represents data estimated for the measurement data p.

는 측정 데이터와 추정 데이터 사이의 오차를 산출하기 위한 항(term)이고,

는 복원하고자 하는 영상신호의 총변화량을 기여도

만큼 적용한 항(term)이다.Further, in the above-mentioned equation (1)

Is a term for calculating an error between the measured data and the estimated data,

The total amount of change of the video signal to be restored

Is the term to which the term is applied.

)의 총변화량(

)은 다음의 [수학식 3]과 같이 복원하고자 하는 영상신호(

)를 위치마다 미분하여 계산할 수 있다.On the other hand, in the embodiment of the present invention,

) Of total variation (

) Is expressed by the following equation (3): < EMI ID = 3.0 >

) Can be calculated by differentiating for each position.

&Quot; (3) "

)가 최종 복원한 영상이 되는 것이다. As shown in FIG. 3, the signal restoration method according to an embodiment of the present invention includes a process of calculating an error between measured data and estimated data to restore a resolution, and a process of calculating a total change amount of a video signal to be restored Lt; / RTI > In particular, referring to FIG. 3, when the sum of the error and the total amount of change calculated in the square brackets is the smallest,

) Is the final restored image.

)에서 발생하는 기브스 현상은 영상 내 경계선과 같이 급격한 변화가 있는 구간 주변으로 물결무늬와 같은 신호를 발생시키므로 이로 인하여 영상의 총변동량(

)은 증가하게 된다. 그러므로 총변화량(

)을 줄이는 방향으로 역문제를 풀면 해상도를 복원함과 동시에 기브스 현상을 제거할 수 있다.Resolution restoration process (

) Causes a signal like a wave pattern around a region having a sudden change such as a boundary line in the image. As a result, the total variation of the image

) Is increased. Therefore,

), It is possible to recover the resolution and remove the gibbous phenomenon.

4 is a flowchart of a signal restoration apparatus according to an embodiment of the present invention.

4, a signal restoring apparatus according to an embodiment of the present invention includes an image input unit 100, an image estimating unit 200, an error calculating unit 300, a total change amount calculating unit 400, (500).

The image input unit 100 receives image data, that is, measurement data, which is input through an image system (not shown).

The image estimating unit 200 estimates image data using measurement data input through the image input unit 100 and a jumping function of the image system and outputs estimated data.

)을 사용하여 오차를 산출한다.The error calculator 300 calculates an error between the measurement data output from the image input unit 100 and the estimation data output from the image estimator 200. [ The error calculator 300 calculates the error (?) In Equation (2)

) Is used to calculate the error.

)을 사용하여 총변화량을 산출한다.The total change amount calculation unit 400 calculates the total change amount of the estimated data output from the video estimation unit 200. [ The total change amount calculating unit 400 calculates the total change amount calculating unit 400 based on the equation (2)

) Is used to calculate the total change amount.

The signal restoring unit 500 applies Equation 2 to the error calculated by the error calculating unit 300 and the total change amount calculated by the total change calculating unit 400 so that the sum of the error and the total change amount is minimized And outputs the restored video signal.

The signal restoring unit 500 repeats the process of applying Equation 2 so that the sum of the error calculated by the error calculating unit 300 and the total change amount calculated by the total change calculating unit 400 is reduced And restores and outputs the video signal. Here, the number of repetitions can be set statistically or experimentally.

Hereinafter, a signal restoration method according to an embodiment of the present invention will be described with reference to FIG.

First, the image input unit 100 receives data measured by a video system (not shown) (S100).

)를 초기화하고(S110), 반복 회수(k)를 0으로 초기화한다(S120).After that, the signal restoring unit 500 restores the initial video signal (

Is initialized (S110), and the number of iterations k is initialized to zero (S120).

Then, the image estimating unit 200 estimates the image data using the measured data input in the step S100 and the jumping function of the image system, and calculates the estimated data (S130).

)를 [수학식 4]를 통해 산출한다(S140). Thereafter, the error calculator 300 calculates an error between the measurement data input in the step S100 and the data estimated in the step S130

) Is calculated through [Equation 4] (S140).

&Quot; (4) "

)을 [수학식 5]를 통해 산출한다(S150).Subsequently, the total change amount calculating unit 400 calculates the total change amount (i.e.,

) Is calculated through Equation (5) (S150).

&Quot; (5) "

)와 상기 단계(S150)에서 산출된 총변화량(

)을 사용하여 k=1일 때의 영상신호를 복원한다(S160). 이 때, 신호 복원부(500)는 다음의 [수학식 6]에 따른 신호 복원 기법을 사용한다.Then, the signal restoring unit 500 corrects the error calculated in the step S140

) And the total amount of change calculated in the step S150

) To restore the video signal when k = 1 (S160). At this time, the signal restoring unit 500 uses the signal restoration technique according to Equation (6).

&Quot; (6) "

Thereafter, the signal restoring unit 500 determines whether signal restoration should be stopped (S170). The judgment for stopping the signal restoration can be judged by various criteria. For example, the number of repetitions k may be set in advance as a threshold value, and the signal restoration may be stopped when the threshold value is reached, or the signal restoration may be stopped when the resolution of the restored signal exceeds a preset resolution can do. As a criterion for such a stoppage, it can be applied variously according to the image system.

If the condition for stopping signal restoration is not satisfied, the number of repetitions k is incremented by 1 in step S180, and the steps S130, S140, S150, and S160 are repeated to restore the image corresponding to the number of repetitions k do.

However, if the condition for stopping the signal restoration is satisfied, the restoration of the video signal is stopped, and the restored video signal is output as the final video signal in step S160 when k is the threshold value in step S160.

Therefore, the final image signal output in the step S190 is a high-resolution image signal which is removed from the image signal measured in the above-described step S190, and the Gibbous phenomenon or the resonance artifact is removed.

Hereinafter, a signal restoration method according to an embodiment of the present invention will be described in detail using a positron emission tomography (PET) system, which is a representative nuclear medicine imaging system useful for diagnosis of cancer and brain diseases.

In case of PET (Positron emission tomography) signal restoration, reconstruction is performed using a system specific point spread function. When such a signal restoration technique is used, a gibbous phenomenon, that is, Resonant artifacts are observed around.

Since the resonance artifacts are a factor for lowering the accuracy of diagnosis, the resolution of the reconstructed image signal is reduced as well as the resolution as shown in Equation (7) after applying Equation (2) Is included in the signal restoration algorithm.

&Quot; (7) "

는 복원하고자 하는 PET의 단면 영상을 의미한다. 또한, PET 시스템의 검출 특성은 점퍼짐 함수 G와 PET 데이터의 기하학적 검출 확률을 의미하는 H를 이용하여 표현된다. In Equation (7), p denotes data measured in the PET system,

Sectional image of the PET to be reconstructed. In addition, the detection characteristics of the PET system are expressed using the jumper load function G and H, which means the geometric detection probability of the PET data.

The inverse problem for restoration of PET data that removes resolution restoration and gibbsite phenomenon is a closed-form solution as shown in Equation (8) below using an OSL-EM (Algorithm of One Step Late-Expectation Maximization) It is possible to derive an expressive update equation that expresses it.

&Quot; (8) "

를 이용하여 총변화량의 기여도를 결정할 수 있다. Here, the OSL-EM algorithm restores the resolution using the jumping function, calculates the total change amount of the current estimation image, and reduces the artifacts in the normalization process. Here, the parameter for determining the contribution of the total change amount

Can be used to determine the contribution of the total variation.

On the other hand, in the OSL-EM algorithm, the partial differential term of the total change amount with respect to the current estimated image is expressed by the following equation (9).

&Quot; (9) "

FIG. 6 shows experimental results for a disease model having three spherical sources with a diameter of 1 mm in a cylinder, uniformly distributing the source in a cylindrical shape, and having an intensity of 8: 1 between a spherical source and a cylindrical background source .

In the case of the disease model with background source, it can be seen that the degradation of resolution is transferred to the reconstructed image as it is in EM without resolution restoration for original image.

In the case of the EMR RR for resolution restoration and the OSL-TV-RR for which the total variation amount is applied according to the embodiment of the present invention, the resolution is gradually improved.

In addition, in the case of EM-RR that only performs resolution restoration, a gabbing phenomenon occurs around the boundary line. On the other hand, according to the embodiment of the present invention, OSL-TV- There is a number.

7, when the profile is plotted on the x-axis of the reconstructed image in the PET system, the value of the OSL-TV-RR applied with the total amount of change according to the embodiment of the present invention changes abruptly It can be confirmed that the Gibbs phenomenon is reduced in the section.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, It belongs to the scope of right.

Claims (13)

Reconstructing a resolution of the measured signal using the signal measured in the image system and the estimated signal with respect to the original input signal; And
And restoring the resolution so that the total amount of change of the restored signal is minimized,
Wherein the total amount of change of the restored signal is the sum of the amount of change with respect to the periphery based on each position corresponding to the restored signal,
And restoring the resolution so that the total change amount is minimized, restoring the original input signal by solving an inverse problem in a direction of decreasing the total change amount,
The total amount of change is applied in restoring the original input signal according to a preset contribution
Wherein the signal restoration method comprises the steps of: The method according to claim 1,
Wherein the estimated signal is generated based on a point spread function expressing a degree of resolution degradation of the image system. 3. The method of claim 2,
Wherein the total amount of change is calculated by differentiating the positions of the recovered signals. delete 3. The method of claim 2,
The signal restoration method includes the following signal restoration relation

Where p is the measured signal,
S is the jumping load function,

Is the restored signal,

Lt; RTI ID = 0.0 >

), ≪ / RTI >

The total amount of change (

), ≪ / RTI >

Is the estimated signal
And reconstructing the final image signal according to the reconstructed image signal. 6. The method of claim 5,
The total change amount (

) Is expressed by the following relational expression

here,

Is a signal corresponding to the (x, y) position of the reconstructed image
And the signal is reconstructed by the reconstructing unit. 6. The method of claim 5,
If the imaging system is a positron emission tomography (PET) system, the estimated signal

) Is expressed by the following formula

=

Where H is the geometric detection probability of the PET system,
G is the jumping load function of the PET system
To the signal. Receiving a signal measured by a video system;
Estimating a signal to be reconstructed using the measured signal and a jumping function of the image system;
Calculating an error between the measured signal and the estimated signal;
Calculating a total change amount of the estimated signal, wherein a total change amount indicates a sum of a change amount with a periphery based on an angular position corresponding to a restored signal; And
And restoring a video signal when the total amount of change becomes minimum using the sum of the error and the total amount of change,
In the restoring step, the inverse problem is solved in the direction of decreasing the total change amount to restore the video signal,
The total amount of change is applied in restoring the video signal according to a predetermined contribution amount
Wherein the signal restoration method comprises the steps of: 9. The method of claim 8,
Wherein the estimating step, the error calculating step, the total change amount calculating step, and the restoring step are repeated to restore the video signal when the total change amount becomes minimum. delete 10. The method of claim 9,
Wherein when the imaging system is a positron emission tomography (PET) system, the signal is estimated using the jumping function and the geometric detection probability of the PET system in the estimating step. A video input unit receiving a signal measured by the video system;
An image estimator for estimating a signal to be reconstructed using the measured signal and a jumping function of the image system;
An error calculator for calculating an error between the measured signal and the estimated signal;
A total change amount calculating unit for calculating a total change amount of the estimated signal, wherein the total change amount represents a sum of a change amount with the surroundings based on an angular position corresponding to a restored signal; And
And a signal reconstruction unit for reconstructing a video signal when the total amount of change becomes minimum using a sum of an error calculated by the error calculating unit and a total change amount calculated by the total change amount calculating unit,
Wherein the signal restoring unit restores the video signal by solving an inverse problem in a direction of reducing the total change amount,
The total amount of change is applied in restoring the video signal according to a predetermined contribution amount
Wherein the signal restoration device comprises: 13. The method of claim 12,
Wherein the signal restoring unit repeatedly performs a process of reducing the sum of the error and the total change amount to restore the video signal when the total change amount becomes minimum.

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