JPH07110802A - Method for restoring information - Google Patents

Abstract

PURPOSE:To restore original information and to specify the factor of deterioration when the factor of the deterioration is unknown. CONSTITUTION:Temperature T is set up to a high temperature (step 1) and the initial state of a picture system (x) consisting of an original picture and a deterioration function (step 2). A transiting state candidate (y) is selected in accordance with probability P (x, y) (steps 3, 4), a current state is updated to (y) in accordance with received probability A (x, y) (steps 5 to 7) and the temperature T is slightly reduced (step 8). The energy of the picture system is minimized by repeating the steps 3 to 8 to restore an optimum picture.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an information restoration method for restoring information such as image patterns and voice patterns.

[0002]

2. Description of the Related Art Conventionally, a deterioration factor is known, a pixel in an image is used as a random variable, an estimated deterioration image is created using an estimated original image and a deterioration function, and an actual deterioration image is compared with an estimated deterioration image. There is a method to restore the image by defining the energy of the estimated original image using a priori information about the image (for example, line process) and minimizing the energy by statistical relaxation method or genetic algorithm. .

Regarding the above-mentioned technique, for example, "optimal image restoration by genetic algorithm-introduction of line process" (IEICE NC92-21 (reference 1)), "parallel operation and visual image processing" (neuro) Basic Theory of Computing Chapter 7 pp.235-265
(Company) Japan Industrial Technology Promotion Association, edited by Neurocomputer Research Section, Kaibundo Publishing (Reference 2)).

[0004]

However, the above-mentioned conventional technique has a problem that it cannot be used unless the cause of deterioration is completely known.

An object of the present invention is to provide an information restoration method for restoring original information and identifying a deterioration factor at the same time when the deterioration factor is unknown.

[0006]

In order to achieve the above object, the invention according to claim 1 provides an information restoration method for performing restoration processing on deterioration information in a state in which original information is deteriorated due to some deterioration factor. , The estimated deterioration factor and the estimated original information are random variables, and the estimated original information is multiplied by the estimated deterioration factor to be the estimated deterioration information, and the actually obtained deterioration information is compared with the estimated deterioration information. Is performed to define the estimated deterioration factor and the energy of the estimated original information, and the energy is minimized to restore the information.

The invention according to claim 2 is characterized in that the energy is minimized by using a statistical relaxation method.

According to a third aspect of the present invention, the energy is minimized by using a genetic algorithm.

[0009]

The temperature is set to a high temperature, and the initial state of the image system x consisting of the original image and the deterioration function is set. The next transitional state y is selected according to the probability P (x, y), the current state is updated to y at the acceptance probability A (x, y), and the temperature is lowered slightly. The energy of the image system is minimized by repeating the process of changing the state, calculating the acceptance probability, selecting the state, and lowering the temperature. As a result, even when the deterioration factor is unknown, it is possible to restore the optimum image.

[0010]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be specifically described below with reference to the drawings. The case where the information restoration method of the present invention is applied to image restoration will be described below as an example. That is, as the information to be restored, it is assumed that the original image f is the deteriorated image g that has deteriorated through the deterioration process h. Further, here, the energy is minimized by using the statistical relaxation method, but it is basically the same even if the energy is minimized by using another method.

First, the deterioration process will be briefly described.
When an image deteriorates due to blurring or noise, the deterioration process can be modeled by the following equation.

G (x, y) = ∬h (x, y, x ′, y ′) · f (x ′, y ′) dx′dy ′ + n (x, y) (1) Place in the deterioration function h If there is no dependency, it can be easily expressed in the Fourier transform domain, and G (u, v) = H (u, v) .F (u, v) + N (u, v) (2). Here, g represents a deteriorated image, h represents a deterioration function, f represents an original image, n represents random noise, and G, H, F, and N represent Fourier transforms of g, h, f, and n, respectively.

When there is no noise and H ≠ 0, F (u, v) = G (u, v) / H (u, v) (3) is calculated, and an inverse Fourier transform is performed to obtain a complete image. A restoration is obtained. This image restoration is called an inverse filter.

However, in the case of the ideal low-pass filter, H (u, v) = 1; u * 2 + v * 2≤ω0 * 2 H (u, v) = 0; u * 2 + v * 2> ω0 * 2 (4) (however, * 2 represents the square), which is one of the ill-posed problems in which the zero point exists in H and the inverse filter cannot be used. If the deterioration function h is a space-variant filter with location dependence, the inverse function (1 / H
It is difficult to obtain (u, v)), and image restoration becomes a more difficult problem. Furthermore, if there is noise,
The noise is amplified in the region of H≈0, and when the inverse Fourier transform is performed, there arises a problem that the image is almost restored to noise. If the deterioration function h is unknown, such a method cannot be used.

In the present invention, the deterioration function itself may be unknown. However, it is possible to construct a model of the deterioration function that has been parameterized based on the a priori information.

The image is regarded as a random variable, and the image is subjected to MRF.
With the (Markov Random Field) model, the conditional probability distribution of the original image when the degraded image is given can be accurately represented by the energy of the image (here, the line process is not considered, but the line process is considered). The same is true when the concept of process is introduced).

Now, consider an image system x composed of an image f and a deterioration function h. The energy of the image system x = (f, h) when the degraded image g is given is defined as follows.

E (x) ≡‖g−hf‖ * 2 (5) where ‖‖ * 2 represents the square of the norm.

The probability (perturbation probability) of selecting the next candidate y from the image system x is P (x, y), and P (x, y) satisfies the following condition.

∀x, y∈S: P (x, y) ≧ 0 (6) ∀x∈S: Σ P (x, y) = 1 (7) y∈S ∀x∈S: P (x, x) = 0 (8) ∀x, yεS: P (x, y) = P (y, x) (9) ∀x, yεS, ∃s: P * s (x, y)> 0 (10) Here, S represents a state space taken by the image system (note that Expression 10 represents that a certain state x is moved to an arbitrary state y with a certain probability by s trials). Further, the probability that the system takes y as the next state (acceptance probability; Boltzmann distribution) is defined as follows.

A (x, y) ≡exp (− (E (y) −E (x)) / T) / {1 + exp (−E ((y) −E (x)) / T)} (11) The image system x (that is, the image f and the deterioration function h) is considered as a random variable, and the state transition is performed according to the following transition rule. The operating procedure is: 1. The initial state of the image system x is arbitrarily set. 2. Set temperature T to high temperature. 3. Select the next transitional state candidate y according to the perturbation probability P (x, y). 4. Update the current state to y with acceptance probability A (x, y) The temperature T is lowered a little. By repeating the above 3 to 5, the energy of the image system can be minimized and an optimum image system can be obtained. Further, the deterioration function can be identified and the original image can be estimated at the same time. The "optimal image system" is an image system (f, h) having the maximum posterior probability when the deteriorated image g is given. At this time, it has been proved that if the temperature T is lowered in proportion to 1 / lnN, where N is the number of repetitions, it is possible to reach the state of giving the minimum value of the energy function with probability 1 (see the above-mentioned document. (See 7.3 Markov random field and Gibbs distribution in (2)).

FIG. 1 is a processing flowchart of the information restoration method of the present invention when the statistical relaxation method is used. First,
The temperature parameter T is set to a sufficiently high temperature (step 1). Next, each pixel is regarded as a random variable, and the parameter of the parameterized deterioration function is regarded as a random variable. The pixel and the deterioration function are combined into one image system, and a solution candidate x is one in which the random variable has a unique state (step 2).

Since x has a unique state, the energy E (x) of x can be calculated (step 3). Next, the pixel of the solution candidate x or the parameter of the deterioration function is partially changed by using a random number to create another solution candidate y (step 4). The perturbation probability can satisfy the above condition by using a random number and not placing a constraint on the changing place and the changing amount. The energy E (y) of the newly created solution candidate y is calculated (step 5), and the acceptance probability A of equation (11) can be calculated using the energies E (x) and T of x (step 5). 6).

A random number for selecting y with the acceptance probability A is generated and y is selected as the next state, or the original state x
Is determined (step 7). The temperature T is lowered according to the annealing schedule, the process returns to step 3, and the process of changing the state, calculating the acceptance probability, and selecting the state is repeated. As the annealing schedule, if the number of iterations is set to N and T is lowered so as to be proportional to 1 / lnN, it is possible to reach the state of giving the minimum value of the energy function with probability 1, but it takes a considerable amount of calculation time.

In the above process, the line process (line process; a stochastic process representing the existence of edges is introduced into the evaluation function to solve the discontinuity problem) is not used. However, when the line process is introduced, pixels, It is exactly the same except that one image system is formed by combining the random variables representing the edges and the deterioration function. Further, if the parameters of the image and the deterioration factor are incorporated into the genotype and the energy is minimized by the genetic algorithm, the minimum value search can be performed at higher speed (for the genetic algorithm, refer to the reference 1). , For example, David E. Gold
Berg, Genetic Algorithms, Addison-Wesley, 19
89 etc.).

The present invention is not limited to the above, and the estimated deterioration factor (h) and the estimated original factor are evaluated by evaluating the estimated original information using, for example, foreseeable information (eg, line process) related to the original information. The energy (x = (f, h)) of the information (f) may be defined, and the information may be restored by minimizing the energy.

[0027]

As described above, according to the first aspect of the present invention, the pixel and the deterioration function are combined into one image system, and the energy of the system is minimized. Information can be restored even when unknown, and at the same time, the cause of deterioration can be identified.

According to the second aspect of the present invention, by using the technique known in the statistical relaxation method, it is possible to identify the optimum image restoration and deterioration factor with the probability 1.

According to the third aspect of the invention, by using the genetic algorithm, it is possible to restore a good image at a higher speed and identify the deterioration factor.

[Brief description of drawings]

FIG. 1 is a processing flowchart of an information restoration method of the present invention.

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Claims (3)

[Claims] 1. An information restoration method for performing restoration processing on deterioration information in a state where original information has deteriorated due to some deterioration factor, wherein the estimated deterioration factor and estimated original information are random variables, and the estimated original Information obtained by applying the estimated deterioration factor to the estimated deterioration information is defined, and the estimated deterioration factor and the estimated original information energy are defined by comparing the actually acquired deterioration information with the estimated deterioration information, An information restoration method characterized by restoring information by minimizing the energy. 2. The information restoration method according to claim 1, wherein the energy minimization is performed by using a statistical relaxation method. 3. The information restoration method according to claim 1, wherein the energy minimization is performed by using a genetic algorithm.