# Non Uniformity Correction Neural Network Algorithm Computer Science Essay

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In the infrared thermal imaging system because of the material and producing technology, it is very difficult that every detector in the IRFPA reach the same response to the same radiant point, which was defined as infrared non-uniformity, and it has negative impacts on result of the infrared image in the IRFPA. There are two categories for non-uniformity correction in the IRFPA: reference-based non-uniformity correction (NUC) algorithm and scene based NUC algorithms. The first category is included multi-point NUC algorithm, two-point NUC algorithm. The intrinsic responsivity of every detector drifts with time and operation temperature, which results in the drift of correction parameters. The correction parameters need periodically recalibration. In the second category, the algorithms often used are neural network algorithm, mean filtering algorithm and Kalman filtering algorithm. These algorithms are based on scene and that the data to compute correction parameters are not derived from reference source but for the estimation of scene. As the result, it has such advantage that it needn't correct frequently and could adapt by oneself to change the correction parameters with the change of time and environment. So the second category was studied widely. However, the neural network algorithm has some defects, for example: slow speed of convergence and not good in correction accuracy. It is therefore very important to study non-uniformity correction algorithm in infrared focal plane array (IRFPA). In order to improve the convergence speed and non-stability Non-uniformity correction algorithm, a new scene based non-uniformity correction algorithm for IRFPA is proposed in this paper. Improvement is achieved by employing an optimization techniques in the process of estimating the desired image f(n), and using a new algorithm estimate convergent scope of the convergence constant. The proposed algorithm is better than other three algorithms as evident by different corrected images. It does not need any reference source and could obtain the same result with the two-point NUC algorithm.

Key words- Infrared focal plane array, Non-uniformity correction, convergence constant

## I. Introduction

The process of infrared image correction is taken as a linear model , it means that the output response of the i line and j column in the IRFPA are written as follows:

(1)

Where variables xij(n)and yij(n) are used to represent raw infrared pixel and corrected infrared pixel respectively in the IRFPA. Where kij(n) and bij(n) are gain coefficient and offset coefficient of (i,j)th detector, and n is frame number in an infrared image sequence.

By using the method of steepest descent algorithm, iterative equations for optimizing correction parameters can be got. They have the following representations:

(2)

(3)

Where u is a convergence constant which control the speed of the convergence. The error function Eij(n) is designed by employing corrected image output yij(n)and its desired value fij(n). And it has the following format:

(4)

## II. Improved non-uniformity correction algorithm based on neural network

A. Ordering mean filter algorithm

This is the first step to process the infrared image. Traditional mean filter algorithm is that in which every pixel gray value and its neighboring pixel's gray value are used to compute their means. It has such defect that this will miss a lot of details and make the infrared image blur. An improved mean filter algorithm is presented .Take a pixel's gray value xij(n) and its 8 neighboring pixel's gray values, and arrange this 9 pixel's value from small to big. As its neighboring pixel's gray values may not change rapidly, then compute the mid 5 values' mean in this new sequence of numbers as the pixel's new gray value. It has the following format:

(5)

This algorithm not only could preserve some details in some sense and make the image more clear, but also could delete some bad pixels.

B. Estimating the convergence constant

It is a very important parameter u to the convergent speed of the NUC neural network algorithm. As long as u is chosen in an adapted scope, the iterative equations will be convergence. It could certify as follow:

In the process of talking about the convergence, we firstly suppose it has a large interval between two frame images, so we think these two frame image aren't correlated. At the same time, because kj is only a function of inputs xj+1 xjâ€¦x0, kj is also not correlated with xj. While kj is stochastic, so we must use their aggregated mean, and it could be presented as follows:

(6)

Considering both k j and x j aren't correlated, so we can get:

(7)

Supposing P= E [ dj xjt and R= [ E xj xjT] , we can get:

(8)

Supposing preliminary value k ï€½ï€ k0 , we could get:

(9)

Where R is a real symmetric matrix and its Eigen value could be expressed as follows:

is diagonal matrix that is made of R's eigenvalue:

Then we can get

(10)

In order to reach convergence, from the above function we can conclude that it must abide by such rule:

This mean that u has to be less than reciprocal of the largest R's eigen value and more than 0, then the iterative equations will be convergence.

C. Improved neural network NUC algorithm

In the process of improved neural network algorithm, the smallest correction error mean square value was considered by the adjustment of gain coefficient and offset coefficient as a guide line. It has the following format from the fourth function:

(11)

Where yij(n) is an output gray value in the infrared image and fij(n) is a desired gray value that is compute by using above new ordering mean filter algorithm, and the infrared image has MÃ-N pixels. In the process of the correction, to make sure that the mean of the gain coefficient's reciprocal was 1.0, we design new function as following:

(12)

Where M means the lines and N means the columns in the IRFPA. According to the steepest descent algorithm, it could get a new format:

(13)

(14)

Where u is a convergence constant, and n is the number of frame.

## III. Result

In the experiment we use the MÃ-N LWIR un cooled micro bolometer detector and its non-uniformity in the IRFPA, and compute the former 150 frame infrared images by above several algorithms. Its results and analysis was presented as following.

A. Analysis of the estimated convergence constant

Using un cooled micro bolometer detector, 100 frame 380Ã-240 infrared images are collected randomly in the different situation. Considering 380Ã-240 isn't a square matrix, we can't compute its eigen value. But we could choose the matrix of 80Ã-80ã€110Ã-110ã€150Ã-150ã€ 200Ã-200 ã€240Ã-240 etc, from this matrix of the 380Ã-240. We compute their mean of the largest eigen value in 10 frame images respectively, and it is presented in table.1.

Table.1: The largest matrix's eigen value

Matrix

Matrix

(80 x 80)

Matrix

(110 x 110)

Mean of the largest matrix's eigen value

1.0074 x 104

1.4054 x 104

Matrix

(150 x 150)

Matrix

(200 x 200)

Matrix

(240 x 240)

1.8656 x 104

2.3802 x 104

2.7439 x104

From Table.1, we could know that the largest matrix's eigen values in this 5 category matrixes are more than 104, and there is such a performance that the largest matrix's eigen values will be increased with the matrix's scale increasing. After finished this experiment we compute the largest matrix's eigen values of the 320Ã-320 matrix of an infrared image. And its largest matrix's eigen values is 5.9289 Ã-104.

With the above algorithm we could precisely estimate the scope of the u when the iterative equations reach convergence: 0< u < 3.0Ã-10-5. If u's value is more than this scope, the iterative equation will not reach a good effect. By estimated u's value, we could quickly find u's scope, which is the key to improve the convergent speed.

B. Correction accuracy and error analysis

To compare the corrected results quantitatively, the NUC algorithms are applied to one image created by IRFPA with uniform illumination, and the residual non uniformity of corrected image is computed by the following equation:

(15)

Where U is the residual non-uniformity of corrected image and y ( x) is the average of corrected image. So the value of U indicates validity and correction accuracy of different correction algorithms. Table.2 shows the residual non-uniformity values' mean that was calculated to correct the same symmetrical radiant point by different correction algorithms in the different temperatures.

Table.2: Computing value of the U by different algorithms

raw image

mean filter

improved neural network

0.4594

0.4520

0.4192

Two-point UNC

Proposed improved neural network algorithm

0.3718

0.3254

From Table.2, it is obvious that the non-uniformity of the corrected image by the proposed algorithm is the smallest and by mean filter algorithm is the largest. And the corrected result of the proposed algorithm is better then others. It is concluded that the main error source of the NUC algorithm based on neural network is the estimation error of the desired image. The larger the estimation error, the larger is the correction error. Though the two points NUC algorithm that belong to reference-based NUC algorithm is also have a good result, its result is not as good as the proposed algorithm.

(a) The raw image

(b) The image by mean filter algorithm

(c) The image by improved neural network algorithm

(d) The image by two-point UNC algorithm

(e) The image by the proposed algorithm

Fig.1 Corrected images by different algorithms

We could find it from the vision as well: in the Fig.1& 2, these images that were collected at 150th frame when the gain coefficient and the offset coefficient are basically steady-going, show the corrected results as follows by four different algorithms:

(a) The raw image

(b) The image by mean filter algorithm

(c) The image by improved neural network algorithm

(d) The image by two-point UNC algorithm

(e) The image by the proposed algorithm

Fig.2 Corrected images by different algorithms

From Fig.1 & Fig. 2, we could get the following analysis: as a whole, the corrected result of image by the proposed algorithm is better than the corrected results by other three algorithms. Compared with the raw image, it's obvious that the upright stripe in the corrected image by the proposed algorithm is disappeared, and the color distribution is also well-proportioned than it of the raw image. Compared with the image by the second algorithm, it could find that the mean filter algorithm can't completely eliminate the upright stripe of the image and the corrected image is also lost lots of details and become blurring. Compared with the image by the traditional neural network, it know that the convergence speed by the propose algorithm is quicker than it by the traditional algorithm. Though the image by the two-point NUC algorithm looks clearer, it can't eliminate the bad pixels in the image. Therefore, we could get such conclusion that the proposed algorithm has a good NUC result.

## IV. Conclusions

In this paper, an improved non-uniformity correction (NUC) algorithm based on neural network is proposed. This NUC algorithm is improved in correction accuracy and convergence speed by employing an optimization technique in the process of estimating the desired image f (n), and using a new algorithm estimate convergent scope of the convergence constant. The proposed algorithm is better than other three algorithms as evident by different corrected images. The proposed algorithm does not need any reference source and could obtain the same result with the two-point NUC algorithm. So the proposed algorithm has a better value in applications.