CN109712098B - Image restoration method based on statistical reasoning - Google Patents

Abstract

The invention relates to an image restoration method based on statistical reasoning, which comprises the following steps: s1: applying basic statistical reasoning to the signal reconstruction by a machine learning algorithm; s2: the deep neural network algorithm is used for avoiding the prior statistical modeling of the traditional loss signal, and a convolutional neural network regression model is built by training a large number of damage inputs and clear target output parameters; s3: by minimizing the risk of experience, learning maps the corrupted observations onto the observed sharp signals, and thus results in the possibility of repairing the image in this way, in the usual case, by observing only the corrupted data, even if no sharp signals are observed. The invention is based on the principle of statistical reasoning, only damaged target data can be trained for image restoration under the condition that complete target data is not observed, and the image restoration performance close to the use of the complete data can be obtained under the normal condition.

Description

Image restoration method based on statistical reasoning

Technical Field

The invention belongs to the field of image restoration, and relates to an image restoration method based on statistical reasoning.

Background

With the continuous development of computer and multimedia technologies, information mainly based on images becomes the mainstream media of information exchange, and the life style of people is greatly influenced. Image restoration is an important research branch in the field of image processing, and has wide applications in various fields such as medical care, military security, public management, and the like. The image restoration is to fill up an unknown area or remove redundant objects in an image by using some intact information existing in a damaged image, so that the restored image approaches or reaches the visual effect of the original image, and the image information can still completely express the content contained in the image information. In the conventional image restoration method, complete target data needs to be collected for training, but it is difficult to collect complete undamaged target data in the real world, especially in the fields of astronomical imaging, nuclear magnetic resonance imaging and the like. The development of the deep neural network avoids the traditional image restoration method of prior modeling of the damaged signal, and the same performance of training by using a complete signal can be obtained by training the damaged data immediately.

Disclosure of Invention

In view of the above, the present invention aims to provide an image restoration method based on statistical inference, which can train only damaged target data to perform image restoration without observing complete target data, and can achieve image restoration performance close to that of using complete data under normal conditions.

In order to achieve the purpose, the invention provides the following technical scheme:

an image restoration method based on statistical reasoning comprises the following steps:

s1: applying basic statistical reasoning to the signal reconstruction by a machine learning algorithm;

s2: the deep neural network algorithm is used for avoiding the prior statistical modeling of the traditional loss signal, and a convolutional neural network regression model is built by training a large number of damage inputs and clear target output parameters;

s3: by minimizing the risk of experience, learning maps the corrupted observations onto the observed sharp signals, and thus results in the possibility of repairing the image in this way, in the usual case, by observing only the corrupted data, even if no sharp signals are observed.

Further, step S1 includes the steps of:

s11: preparing a set of data-corrupted target data values (y)₁,y₂…), the complete unknown data value is estimated by finding the number z with the smallest mean deviation from the measured value according to some loss function L, as follows:

argmin_zE_y{L(z,y)}

wherein, L (z, y) is a loss function, which represents the loss caused by adopting the parameter with the value of z to replace the real value when the real value of the parameter is y; argmin_zE_yIt is shown that the parameter z is chosen such that the expected loss of the loss function L (z, y) is minimal.

S12: for the loss function L₁：

L(z,y)＝(z-y)²

The minimum of this loss function is found at the arithmetic mean of the observations:

z＝E_y{y}

s13: for the loss function L₂：

L(z,y)＝|z-y|

The minimum of the loss function is found at the median of the observations;

s14: a general class bias minimization estimator is a known M estimator, and from a statistical point of view, a collective estimate using these common loss functions can be considered an ML estimate by interpreting the loss functions as negative log-likelihoods.

Further, step S2 includes the steps of:

s21: training neural network regressors is a generalization of ML estimation, where the following is a set of input target pairs (x),y) In which the network parameter f_θ(x) Parameterized by θ:

argmin_θE_(x,y){L(f_θ(x),y)}

using f which only outputs a learning scalar if input data is not used_θ(x) Then the task is equal to step S11;

s22: the complete training will yield the same minimization problem in each training sample, and the task is equivalent to the following equation:

argmin_θE_x{E_y|x{L(f_θ(x),y)}}

the network minimizes this loss by solving the point estimation problem separately for each input sample, with the properties of the potential loss inherited by the neural network training.

Through the equation in step S11, in a limited number of input-target pairs (x),y) By training the regression metric, it can be found that the mapping between the input and the target is multivalued. For example, in a super resolution task, a low resolution image may be interpreted by many different high resolution images y. Using L₁Loss, training a neural network regressor using training pairs of low resolution images and high resolution images, it can be found that if random numbers are usedThe matching random numbers replace the target, and the estimated value remains unchanged.

Further, step S3 includes:

the training target that destroys neural networks with zero mean noise without changing the network learning, combined with the corrupted input from the formula in step S1, results in an empirical risk minimization task:

input xAnd object yAre derived from a corrupted distribution with potentially unknown integrity data yIs a condition such that

Given limited data, the problem can be solved using the above-described method. For limited data, the estimated variance is the average variance of corrupted data in the target divided by the number of training samples in many image recovery tasks, the expectation of corrupted input data is the complete target that we seek to recover. The above results show that in these cases we can use this method for image inpainting, as long as we can view each source image twice.

The invention has the beneficial effects that: based on the principle of statistical reasoning, only damaged target data can be trained for image restoration without observing complete target data, and image restoration performance close to that of the complete data can be obtained under the normal condition.

Drawings

In order to make the purpose, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:

FIG. 1 is a contrast graph of image restoration with Gaussian noise added, where (a) represents the original, (b) represents the noise graph, (c) the method of the present invention, and (d) the mean filtering denoising algorithm.

Fig. 2 is a comparison graph of image inpainting with poisson noise added, where (a) represents the original, (b) represents the noise map, (c) the method of the present invention, and (d) the median filtering algorithm.

FIG. 3 is a graph of image restoration contrast with random value impulse noise added, where (a) represents the original image, (b) represents the noise map, (c) the method of the present invention, and (d) the BM3D algorithm;

fig. 4 is a schematic flow chart of an image restoration method based on statistical inference according to an embodiment of the present invention.

Detailed Description

Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

As shown in fig. 4, a method for repairing an image based on statistical inference includes the following steps:

s1: applying basic statistical reasoning to the signal reconstruction by a machine learning algorithm;

s2: the deep neural network algorithm is used for avoiding the prior statistical modeling of the traditional loss signal, and a convolutional neural network regression model is built by training a large number of damage inputs and clear target output parameters;

s3: by minimizing the risk of experience, learning maps the corrupted observations onto the observed sharp signals, and thus results in the possibility of repairing the image in this way, in the usual case, by observing only the corrupted data, even if no sharp signals are observed.

Optionally, step S1 includes the steps of:

s11: preparing a set of data-corrupted target data values (y)₁,y₂…), the complete unknown data value is estimated by finding the number z with the smallest mean deviation from the measured value according to some loss function L, as follows:

argmin_zE_y{L(z,y)}

wherein, L (z, y) is a loss function, which represents the loss caused by adopting the parameter with the value of z to replace the real value when the real value of the parameter is y; argmin_zE_yIt is shown that the parameter z is chosen such that the expected loss of the loss function L (z, y) is minimal.

S12: for the loss function L₁：

L(z,y)＝(z-y)²

The minimum of this loss function is found at the arithmetic mean of the observations:

z＝E_y{y}

s13: for the loss function L₂：

L(z,y)＝|z-y|

The minimum of the loss function is found at the median of the observations;

s14: a general class-bias-minimization estimator is the known M estimator, and from a statistical point of view, a collective estimate using these common loss functions can be considered as an ML estimate by interpreting the loss functions as negative log-likelihood.

Optionally, step S2 includes the steps of:

s21: training neural network regressors is a generalization of ML estimation, where the following is a set of input target pairs (x),y) In which the network parameter f_θ(x) Parameterized by θ:

argmin_θE_(x,y){L(f_θ(x),y)}

using f which only outputs a learning scalar if input data is not used_θ(x) Then the task is equal to step S11;

s22: a complete training will yield the same minimization problem in each training sample, and the task is equivalent to the following equation:

argmin_θE_x{E_y|x{L(f_θ(x),y)}}

the network minimizes this loss by solving the point estimation problem separately for each input sample, with the properties of the potential loss inherited by the neural network training.

By the equation in step S11, in a limited number of input-target pairs (x),y) By training the regression metric, it can be found that the mapping between the input and the target is multivalued. For example, in a super resolution task, a low resolution image may be interpreted by many different high resolution images y. Using L₁Training a neural network regressor using a training pair of low resolution images and high resolution images, one finds that the estimate remains unchanged if the target is replaced with a random number that matches the random number.

Optionally, step S3 includes:

the training target that destroys the neural network with zero mean noise without changing the network learning, in combination with the corrupted input from the formula in step S1, results in an empirical risk minimization task:

input xAnd object yAre derived from a corrupted distribution with potentially unknown integrity data yIs a condition such that

Given limited data, the problem can be solved using the above-described method. For limited data, the estimated variance is the average variance of corrupted data in the target divided by the number of training samples in many image recovery tasks, the expectation of corrupted input data is the complete target that we seek to recover. The above results show that in these cases we can use this method for image inpainting, as long as we can view each source image twice.

In fig. 1, the original clear picture is added with gaussian noise with an average value of 0 and a variance of 0.05, and a median filtering algorithm and two algorithms of image restoration based on statistical inference proposed by the invention are adopted to perform a comparison experiment on a denoising result.

From the simulation result, the two image restoration methods both effectively remove noise to a certain extent, and basically restore the original appearance of the image, but cannot completely restore the original image. Although the overall effect of the median filtering algorithm is good and the repairing speed is fast, it can be seen from fig. 1(c) that a large amount of details are lost in the denoising process and a good denoising effect cannot be achieved. The image restoration algorithm based on statistical reasoning has good restoration effect on the image, not only ensures the definition of the image, but also effectively removes noise, and the detailed part information of the image is well stored.

Fig. 2 is a simulation experiment performed by using an airplane picture, adding salt-pepper noise with a mean value of 0 and a variance of 0.03 to an original clear picture, and performing a comparison experiment on a denoising result by using a mean filtering algorithm and an image restoration algorithm based on statistical reasoning provided by the invention.

From the simulation result, the two image restoration methods effectively remove the noise to a certain extent, and basically restore the original appearance of the image. From fig. 1(c), it can be seen that the two algorithms have good overall effect and high restoration speed, and although the details of the part are lost, the noise can be removed well. This means that the performance of image inpainting can be guaranteed without observing the complete target data.

In fig. 3, the original clear picture is added with bernoulli noise with a mean value of 0 and a variance of 0.7, and a comparison experiment is performed on the denoising result by adopting a BM3D algorithm and an image repairing algorithm based on statistical reasoning provided by the invention.

From the simulation result, the two image restoration methods effectively remove the noise to a certain extent, and basically restore the original appearance of the image. The two algorithms have good image restoration effect, ensure the definition of the image, effectively remove noise and keep the information of the detail part of the image in good condition. Thus further illustrating that complete target data is not entirely necessary in image inpainting.

Finally, it is noted that the above-mentioned preferred embodiments illustrate rather than limit the invention, and that, although the invention has been described in detail with reference to the above-mentioned preferred embodiments, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the scope of the invention as defined by the appended claims.

Claims (2)

1. An image restoration method based on statistical reasoning is characterized in that: the method comprises the following steps:

s1: applying basic statistical reasoning to signal reconstruction by a machine learning algorithm, comprising the steps of:

s11: preparing a set of data-corrupted target data values (y)₁,y₂…), the complete unknown data value is estimated by finding the number z with the smallest mean deviation from the measured value according to some loss function L, as follows:

argmin_zE_y{L(z,y)}

wherein, L (z, y) is a loss function, which represents the loss caused by adopting the parameter with the value of z to replace the real value when the real value of the parameter is y; argmin_zE_yMeans to select a suitable parameter z such that the expected loss of the loss function L (z, y) is minimal;

s12: for the loss function L₁：

L(z,y)＝(z-y)²

The minimum of this loss function is found at the arithmetic mean of the observations:

z＝E_y{y}

s13: for the loss function L₂：

L(z,y)＝|z-y|

The minimum of the loss function is found at the median of the observations;

s14: the general class-bias minimization estimator is a known M estimator, and a summary estimate using common loss functions is considered as an ML estimate, interpreting the loss functions as negative log-likelihood;

s2: training damage input and target output parameters by using a deep neural network algorithm, and establishing a convolutional neural network regression model;

s3: learning to map corrupted observations onto observed sharp signals by a method that minimizes empirical risk, repairing the image by observing corrupted data, destroying the training targets of the neural network with zero mean noise without altering the network learning, and combining the corrupted inputs from the formula in step S1, to arrive at an empirical risk minimization task:

2. the statistical inference-based image inpainting method of claim 1, wherein: step S2 includes the following steps:

s21: training neural network regressors is a generalization of ML estimation, where the following is a set of input target pairs (x)_i,y_i) In which the network parameter f_θ(x) Parameterized by θ:

argmin_θE_(x,y){L(f_θ(x),y)}

using f which only outputs a learning scalar if input data is not used_θ(x) Then the task is equal to step S11;

s22: the task is equivalent to the following formula:

argmin_θE_x{E_y|x{L(f_θ(x),y)}}

the network minimizes this loss by solving the point estimation problem separately for each input sample, with the properties of the potential loss inherited by the neural network training.

Images