# An Efficient Adaptive Denoising Algorithm for  Remote Sensing Images

Authors: Xiujie Qu; Fu Zhang; Huan Jia
Journal: Mathematical Problems in Engineering
 (2013)

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## Abstract

Typically, after the capturing, imaging, and transferring processes have been accomplished, the digital images will contain a variety of noise, caused by both the equipment itself and by the complex working environment. Consequently, it is necessary to perform a de-noising process to facilitate the extraction of useful information. This paper presents a fast and efficient denoising algorithm, which combines the advantages of traditional median filters and weighted filter algorithms. In this algorithm, the noise in the figure is determined, and those results are applied to adaptively change the size of the window, while assigning different weights to the pixels in the filter window. The experimental results show that we can significantly remove almost all salt and pepper noise, while retaining full image textures, edges, and other minutiae.


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## Body

## 1. Introduction

Drivers’ behavior analysis is increasingly becoming important in the study of intelligent transportation systems (ITS) [1]. Due to the importance of driving behavior to vehicle safety, many researchers have attempted to model driving behavior [2]. Ding et al. took the neural network to learn and incorporate the uncertainties to predict the driver’s lane-changing behavior more accurately [2]. To make a good prediction, remote sensing technology, according to Ewan et al. [3], is a critical component since advances in road weather remote sensing technologies have made noninvasive road weather sensors a valuable component in many ITS applications. Specifically, satellite land remote sensing has been widely used in the infrastructure and system engineering of highway transportation systems. Hence, there is a necessity for greater accuracy in remote sensing images. With the fast development of hyper spectral remote sensing technology, the image can describe the characteristics of Earth objects more comprehensively and explicitly [4]. However, the images obtained directly from the sensors, are limited by the performance of the sensor device itself, as well as by the impact of the postprocessing circuit, which contains significant amount of noise interference [5]. Although over the last decades the development of imaging spectrometers is rapid, remote sensing image is still affected by many complex factors during the processing of acquisition and transmission, which will produce a mass of noises [6].In order to improve identification and to more effectively reflect objective reality, it is necessary for the digital image to go through a denoising procedure. The factors that impact the quality of the remote sensing images are the undercurrent of the Charge Coupled Device (CCD) camera, the zero response offsets, and the response inconsistency [7]. The noise in imaging systems is usually either additive or multiplicative. After processing by a readout circuit, there are mainly Gaussian and impulse noises remaining. The particle properties of the salt and pepper noise will seriously interfere with the characteristics of very small targets in remote sensing images, severely reducing the credibility of the image data [8, 9]. Therefore, effective denoising processing is very important.The impulse noise degrades the original image by replacing some image pixels by the noise value. This value could be the maximum and minimum gray level of the image that is known as salt and pepper noise, and a random pixel value in the image gray level that is random-valued impulse noise [10]. It is generated during imaging, transmission, and decoding processes. Additionally, the image cutting process will also produce salt and pepper noise.The first efficient method in impulse is to carry out a low-pass filter process, based on the median filtering algorithm, which is still in the core of many recent denoising methods and can removes the high-frequency portion of the image [11]. The median filter (MF) replaces each pixel with the median of the neighborhood pixels in the square sliding window that is around it. By using this filter, impulse noise can be discarded, but one of its shortcomings is that in a high-density impulse noise, the number of noisy pixels is greater than that of the noise free ones in the window, and so the median value can also be noisy [12]. The other problem of median filter is that when a pixel is noise-free in nature, it may be altered and replaced by the median value that could lead to the blurring of the image [13]. Another common denoising procedure uses a weighted filter (WF) algorithm [14]. The weighted filter algorithm assigns different weights to the pixels that are in the neighborhood of the center pixel, and then takes a mean value instead of the center pixel’s value, to achieve denoising [15]. This algorithm is fast in removing noise. However, it loses much of the image detail and yields an imperfect result at the same time. There are some other denoising methods, such as wavelet transformation [16, 17] and sparse representation [18]. As frequency domain transforms algorithms, the wavelet transform (WT) is a mathematical tool which has been widely used in image processing, and the sparse representation is recent and widely used in image segmentation and is usually based on the over-complete dictionary. Both of the two algorithms are effective in removing noise, but are not easy to implement on hardware.In this paper, we combine the advantages of these two types of algorithms (MF and WF) and propose a fast and more effective and adaptive filtering denoising algorithm. This algorithm can effectively remove the salt and pepper noise, and obtain a good denoising effect, while preserving details of the image such as textures and contours.


## 2. Weighted Filter Denoising

Shang and Sui [14], proposed an adaptive weighted filter algorithm that assigns different weights to the pixels that are in the neighborhood of the center spot and determines the importance of the center pixel to achieve denoising. First, assume a point p(x,y) in the source image, the function of which is given as
(1)q(i,j)={p(x+i,y+j):-1≤i,j≤1,i∪j≠0}.
This function represents a 3*3 set of pixels surrounding the center pixel, labeled as neighborhood Q, which is defined as
(2)Ai,j=|p(x,y)-q(i,j)|,-1≤i,j≤1,i∪j≠0,
where Ai,j represents the absolute differences between the point p(x,y) and other points in neighborhood Q. Then, the Ai,j differences are organized in ascending order, the first four smallest differences are added into the operator ROAD(x,y). The value of ROAD(x,y) represents the similarities of the nearest four pixels in the neighborhood. Then, an evaluation must be made based on the center pixel. If the point is valid, we do nothing; otherwise, it is followed with a smooth filter process. The criterion is given as follows:(3)f(x,y)={Φ(p(x,y)),if(ROAD(x,y))>σr,p(x,y),if(ROAD(x,y))≤σr.
That is to say, if the value of ROAD(x,y) is higher than that of the threshold, then the corresponding point, p(x,y), can be considered to be a noise, and there is a need for denoising; otherwise, we take it as an effective message and there is no need for any transformation. The smaller the threshold selected, the more stringent the noise determination is, but the easier it is to lose the details. The algorithm can automatically assign different weights to the pixels in a designated neighborhood, according to their validity. The closer the pixel is to the center pixel, the higher the weight it is assigned. However, some desirable details were also replaced, especially when the window size was large, yielding the restored image being blurred [15].


## 3. Adaptive Median Filter

A traditional median filtering algorithm is based on the type of pixels in the neighborhood and takes a gray median value to replace the original pixel [11]. The major drawback of standard median filter is that the filter is only effective to work at low noise densities [15]. That is to say, if the pulse noise density was not too large (the probability distribution of the positive and negative pulses was less than 0.2), then the median filter has a good denoising capability, but the filter size needs to be set in advance. If the area has intensive noise distribution, a small filter window will result in an unobtrusive denoising effect, while a large window will smooth out the details of the edge region.Nair and Mol [12], has suggested a new adaptive median filtering algorithm as an improvement. The algorithm can automatically modify both the size and shape of the filter window, which can, to a certain extent, avoid the lack of median filtering. If, however, the filter template is large, then a mean filter can be used to effectively improve the filtering performance. The functions of the algorithm are as follows.(1)
Calculate the median value,Zmed,  the maximum value, Zmax, and the minimum value, Zmin, of the pixels in the window. When the size of the window reaches its maximum, calculate the mean value instead.(2)
Calculate theA1=Zmed-Zmin and A2=Zmed-Zmax, and if A1>0 and A2<0, then the median value is not a noise, and the algorithm is terminated and taken as an output; otherwise, move on to step (3).(3)
If the template size is greater than (or equal to) the maximum value, then calculate the mean value. Otherwise, increase the template size and change its shape. If the increased result is less thanSmax, then go to step (1); otherwise, output the mean value as the final result.The methodology of Masood et al.’s paper [13] is suitable for a different degree of noise scale. It can adaptively change the size and shape of the filter window to achieve the removal of salt and pepper noise, but the algorithm is limited by the size of the window. When the window becomes too large, the mean filter is essentially a smoothing filter, and is largely responsible for the loss of image details. At the same time, for the actual noise, it still uses a traditional median filtering algorithm to carry out the denoising process, which while also removing some minor objective edges, contours, and other minutiae, it only improves the image denoising visual effects to a limited extent.


## 4. This Paper’s Algorithm

In this paper, the advantages of the weighted filter and the improved adaptive median filter algorithms have been combined, with help from the proposed fast noise suppression algorithm, to produce an improved adaptive weighted correction algorithm. The main concept was to use weighted filters to assign different weights to the pixels in the filter window, and to utilize a median filter (for its good salt and pepper noise removal abilities), to replace the center pixel. At the same time, the concept of noise detection was introduced, and an evaluation of the previous noise point was then used to adaptively change the window size. With a premise of removing noise, improvements have been made to the signal-to-noise ratio of the postprocessing image, while preserving the textures, contours, and other feature details.For a source image, first a pointp(x,y) is assumed, and evaluated to determine whether it is a suspected noise point (p(x,y)=255 or p(x,y)=0), and if not, skip to the next point; otherwise, calculate the number of nonextreme points in the window, which are marked as S_length. If the value of S_length is higher than that of the preset threshold, then reserve the coordinates of the point, while expanding the filter window to continue calculations, or otherwise execute a filtering process. That is to say, center on that point and take its 3*3 neighborhood as a filter window. Then, calculate the absolute differences between the point p(x,y) and other points in the neighborhood, and add the differences into the operator ROAD(x,y). At the same time, set a threshold Q_t (using the best result of 100 experimental results), and if ROAD(x,y) is greater than Q_t, make a denoising process; otherwise, output the original value. The criterion is the same for function (3). During the denoising process, different weights must be assigned to the pixels in the neighborhood, according to their correlation to the center. The higher the correlation is, the greater the weight is, and vice versa. The weight is calculated as
(4)ωi,j=e-ROAD(i,j)2/3×σw3.
In which σω is an experimental constant, and set the σω=63, in order to achieve an ideal removal. Obtain the final weight coefficient for each pixel through normalization. The function is
(5)ρi,j=ωi,j∑i=-11∑j=-11ωi,j.
Then, multiply the gray value of each pixel with the corresponding weight coefficient, and add them to get a new center Z_weight, calculated as
(6)f(x,y)=∑i=-11∑j=-11ρi,j×q(i,j).
Take the new result as a replacement for the center pixel and through median filtering, obtain a final value Z_med as the output. We can cycle through all the above steps, until all the pixels have been calculated. The flowchart of the algorithm is shown in Figure 1.Figure 1
The flowchart of the algorithm.


## 5. Experimental Results and Analysis

In this paper, we took a remote sensing image as a source, and added salt and pepper noise with different densities from 2 to 20%. Through the application of this new algorithm to the denoising process, and by taking the weighted filter algorithm, and the adaptive median filter algorithm as a comparison, the experimental results shown in Figures2(a) through 2(d) were obtained, assuming a noise density of 10% for the example.(a) Remote sensing image with 10% salt and pepper noise. (b) Weight filter result (3*3 in size of window). (c) Adaptive median filter result. (d) This papers algorithm result.
(a)
(b)
(c)
(d)Judging by the visual effects, the results obtained by the weighted algorithm showed that much of the noise had been removed, but the edges, contours of the runway, houses, and other small targets on the ground, had become blurred, while also losing a large amount of the texture message from the lawns and sandy lands. All of these will be detrimental to the quality and value of a collection of remote sensing information. The denoising results obtained by the adaptive median algorithm were very poor, having only removed some of the noise, and having blurred the contours of the image. Among the three groups, the experimental results obtained with this paper’s algorithm were the best. This algorithm removed almost all the noise, and retained some of the interesting features of small targets such as the tag lines on the runway and the support vehicles, and did not filter out the contours and edges of the remotely sensed images.Judging from the evaluation index, the greatest value of peak signal-to-noise ratios was obtained by this paper’s improved algorithm, when compared with the other two algorithms discussed. With the continuously improving accuracy of the CCD imaging devices, remote sensing image noise density will remain at a low level. The experimental results in Table1 show that when the noise density is low (less than 10%), the value of the PSNR will be significantly improved by this new algorithm. Therefore, the improved algorithm in this paper has a great practical value.Table 1
Comparison of several de-noising algorithms in PSNR value.
S & P noise density
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Adaptive median filter
27.9188
27.8494
27.7736
27.5341
27.3256
27.0771
26.9283
26.4809
26.1196
25.6974
Weight filter
33.7074
29.2102
26.0911
23.7517
21.5619
20.5428
19.1369
18.0877
17.2054
16.3512
This paper’s algorithm
41.3948
38.7249
37.2327
36.485
34.5214
33.3825
32.684
32.0604
31.7249
31.0123


## 6. Conclusion

In this paper, the advantages of the weighted filter and the improved adaptive median filter algorithms have been combined to propose an improved fast weighted-median filter algorithm. The major reason why the proposed method can significantly improve the performance of noise removing is that it adds a noise-detection before the denoising process. By this way, the procedure can quickly find out the noise pot and just directly do the removing process on the noise instead of processing the effective pixels that save a lot of time. This new algorithm can better distinguish the noise and effective information than traditional algorithms, and clean out nearly all salt and pepper noise in the remotely sensed images, while retaining some of the interesting features of small targets such as the contours, edges, and textures. The results obtained by processing with this new algorithm have a high PSNR value, as shown in Figure3, containing various useful messages which do help to identify the small targets.Figure 3
PSNR graph.



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*Source: 207461-2013-11-13.xml*