Adaptive-hierarchical filtering approach for noise removal
Tsung-Nan Lin
*, Kai-Jie Chan
Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan Received 7 April 2006; received in revised form 25 July 2007; accepted 8 August 2007
Available online 15 August 2007
Abstract
In this paper, our contribution is to propose an adaptive-hierarchical filter that can remove the impulse noise while preserving the details in an image. The global image structure, which is estimated from a set of pyramid images, can be used as prior information in order to apply different filters adaptively. The proposed filter outperforms other methods in that it can make use of both local and global information efficiently. Experimental results show that the proposed method produces better performance than many other well-known methods do.
2007 Elsevier B.V. All rights reserved.
Keywords: Adaptive filter; Noise removal
1. Introduction
Digital images are often corrupted by impulsive noise due to errors generated in noisy communication channels or sensors [1]. It is essential to remove corrupted pixels before some subsequent processing. Many techniques [2– 5]have been proposed to remove impulse noise from the corrupted images. Median filter[4], which exploits the rank order information of the input data, was initially intro-duced to effectively remove impulse noise. Despite its effec-tiveness of noise removal, it tends to modify both noisy pixels and uncorrupted good pixels. Weighted median
and center weighted median [3] use a set of weighting
parameters in order to preserve more image signal details. Ideally, the filtering should be applied to noisy pixels only. Therefore, various switching techniques are introduced
[2,5–8]in order to avoid the damage of good pixels by first classifying image pixels as corrupted and uncorrupted and then passed through the noise-removal filters and identify filters, respectively.
Sun and Neuvo proposed impulse detectors, Switching I and Switching II, with a decision rule based on first order
statistics by estimating the difference between the current pixel and output of the median filter [5]. Florencio and Schafer introduced a decision measure according to a sec-ond order statistic called normalized deviation [8]. Pok et al. proposed the notion of a homogeneity level, which is defined on the basis of the pairwise correlations between neighboring image pixels, to identify the salt and pepper impulse noise[9].
Such kinds of algorithms are proved to be more effective than uniformly applied methods when the noisy pixels are sparsely distributed in the image. However, if images are highly corrupted, a large number of impulse noise may connect into noise blotches. In such cases, it becomes very difficult to detect and eliminate the noise. Additionally, the error will propagate around the nearby regions. Besides, a noise identification scheme is often based on information within a local window so that such an approach is unable to reflect the real global structure of a region. Therefore, the noise cancelation filters are not very effective in preserv-ing the detailed areas.
In this article, our contribution is to propose a novel approach of an adaptive-hierarchical filtering technique to effectively remove the noise while keeping the detailed image information preserved at the same time. The hierar-chical filters generate a set of pyramid images. From the 0141-9382/$ - see front matter 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.displa.2007.08.001 *
Corresponding author. Tel.: +886 2 33663612; fax: +886 2 23677238. E-mail address:tsungnan@ntu.edu.tw(T.-N. Lin).
www.elsevier.com/locate/displa Displays 29 (2008) 209–213
pyramid structure of an image, the global information of the true image can be effectively differentiated from the noise information. Pixels corrupted by noise in the upper level images will diminish because of the down-sampling process. However, the global information of the image is preserved across all levels of the pyramid.
After estimating the global structure as the prior infor-mation, different noise decision filters and error cancelation filters are designed adaptively depending on the global structure of an image. This procedure is applied iteratively to remove noise and preserve the fine detailed information effectively. This iterative reconstruction makes it possible to use partial results as context information to resolve ambiguities in estimating the global structure. The noise pixels processed in the current iteration are used to help better estimate accurate prior information in the subse-quent iterations. One main advantage of such an approach is that some impulse pixels located in the middle of large noise blotches can also be properly detected and filtered. Our approach can be illustrated in Fig. 1. Experimental results indicate the proposed algorithm provides better results over many other well-known methods on problems of both uniform random and fixed value (salt-and-pepper) noise.
2. Prior information estimation: a hierarchical approach It has been well observed that edges contain the most important information of an image. Estimating the true global edge information from a corrupted image is a chal-lenge. In this paper, we propose a hierarchical approach to effectively estimate the true edge.
Using a simple 2· 2 average filter, it is easy to construct a set of pyramid images. It is important to note that the true edge of an image will not disappear in the higher level images while the edges produced by noisy pixels will decrease in the higher level images. Therefore, hierarchical edge detection (HED) scheme shown inFig. 2 is used to estimate the global true edge information. Sobel edge oper-ators are used[10]. The Sobel operator performs a 2-D spa-tial gradient measurement on an image and so emphasizes regions of high spatial gradient that correspond to edges. Typically it is used to find the approximate absolute gradi-ent magnitude at each point in an input gray-scale image. Edge value in the upper level image can be set to zero if it is smaller than some predefined values which result from noise.Fig. 3demonstrates the effectiveness of HED to mate the structure from a corrupted image. After the esti-mation, each pixel can be classified as ‘‘Weak Edge’’, ‘‘Medium Edge’’ or ‘‘Strong Edge’’ based on the local sta-tistics. In this paper, we choose to calculate the mean of a 3· 3 window centered about each pixel. Namely,
Weak Edge: HED(i, j) < T1
Medium Edge: T1 < HED(i, j) < T2 Strong Edge: T2 < HED(i, j)
The T1 and T2 are the pre-specified thresholds for the above switching operation. T1 and T2 are two thresholds which indicate the fuzziness of the edge information. When the value of HED is greater than T2, it is an indication that the context is a global edge. When the value of HED is in between, it indicates it is median edge. The thresholds are determined based on the statistic data from a lot of images.
Noisy image
Prior edge information estimation
Edge orientedmedian based filter
iteration
Weak edge region Medium edge region
Strong edge region
Output image
Fig. 1. Adaptive-hierarchical filtering to remove noise iteratively.
Level 0
Level 1
Level 2 Edge det.
Edge det. Edge det. Original size of image
threshold
threshold
threshold the modified edge
We choose T1 = 20, T2 = 180 experimentally for a three-layer HED as shown inFig. 2. The edge value is evaluated within a layer. Since the true edge of an image will not dis-appear in the higher layer level images while the edges pro-duced by noisy pixels will decrease in the higher level images as shown in Fig. 2. HED is proposed to estimate the prior edge information. Noise decision filters and noise cancelation filters can be designed adaptively according to the global structure of an image after such prior informa-tion can be accurately estimated.
3. Adaptive filters of noise detection and cancelation Many switching-based approaches ([8,5]) identify noisy pixels by comparing the output of the median filter or the average value of the filter windows to the value of center pixel. When the distance exceeds a threshold, the center pixel is regarded as a noise pixel. However, using a fixed threshold would lack of adaptivity to noise density varia-tion. Besides, when the noise density is high, a lot of mis-classifications will occur and result in more degraded filtering performance.
We apply different noise-detection and noise-cancelation filters according to the image structures adaptively. For pixels belonging to weak and median-edges, noisy pixels are identified based on the distance between the center pixel and the output of a 3· 3 median filter. The threshold is determined adaptively based on the statistics of the local image structure. We compare the distance to the standard
deviation of the edge information within the 3· 3 filter. Namely, the noisy pixels in smooth and median-edge regions can be identified as follows:
jxði; jÞ Medijj > K qij ð1Þ
where qijdenotes the standard deviation of edge
informa-tion within the 3· 3 block and Medij is the output of the
median filter within the block. Eq.(1)identifies noisy pixels by comparing to the local statistics of neighbor pixels. The threshold is not fixed but adaptive to the local image struc-ture. Intuitively, the threshold should be small when the pixels are in the smooth regions. In the median-edge re-gions, the threshold should be larger to accommodate the local variation in the image texture.
To get a good estimation of the K value, we calculate the local statistics of several uncorrupted images. From exper-iments, it is noted that 97–99% pixels (x(i, j)) satisfy the condition that jx(i, j) Medijj < K*qij if the value K is set
between 1.5 and 2 for smooth and median-edge regions. Therefore, we choose the value K to be 1.5 and 2 for smooth and median-edge regions, respectively. If the noisy pixel is in the smooth region, it is replaced by the output of
the 3· 3 median output. For median-edge region (the
information is estimated by HED as shown in Section2), directional noise-cancelation filters are applied depending on the edge orientation. We utilize the 1-D based median filter (1· 3 or 3 · 1 depending on the edge orientation obtained from the Sobel operator) since it can preserve the edge information better when compared to the 2-D filter.
The third noise detection module distinguishes the con-sidered pixel as non-isolated impulse noise or impulse noise on the edge pixel. Non-isolated impulse noise refers to the considered pixel that belongs to a noise blotch. Noise on the edge can be identified by exploring the property of edge information. Intuitively, it is noted that the generic edge intensity is almost homogeneous along the edge orienta-tion. In other words, if we calculate the variance test of the center pixel xi,j along all possible edge orientations
according to Eq. (2), it can easily seen the value will go smaller if the center pixel is a uncorrupted edge pixel. On the other hand, a large value indicates that the center pixel Fig. 3. Comparison of image structure estimation (a) 40% noise density
without HED (b) 40% noise density with HED. 40% noise density means 40% pixels are corrupted by noises.
is a corrupted edge pixel. In the following experiments (Section4), the value is set as 65%.
In essence, the characteristics of a noise blotch (a block of non-isolated noisy pixels) is similar to that of edge pixels since both are high frequency signals. However, they dis-play different characteristics in the pyramid structure. The characteristics of edge pixels behave consistently in the pyramid structure. A noise blotch, on the other hand, becomes an isolated noise, which can be identified based on Eq.(2) similarly, in the upper level images of the pyra-mid structure. If a pixel is classified as an corrupted edge pixel, the 1-D based median filter (1· 3 or 3 · 1 depending on the edge orientation obtained from the Sobel operator) is used to remove the noise based on its edge orientation. For a noise blotch, the 2-D median filter of 5· 5 is used.
d1¼ jxi1;j1 xi;jj þ jxiþ1;jþ1 xi;jj
d2¼ jxi1;j xi;jj þ jxiþ1;j xi;jj
d3¼ jxi1;jþ1 xi;jj þ jxiþ1;j1 xi;jj
d4¼ jxi;j1 xi;jj þ jxi;jþ1 xi;jj
dmin¼ minðd1; d2; d3; d4Þ
ð2Þ
4. Experimental results
The performance of the proposed algorithm is evaluated based on simulations. Three commonly used gray-scale images as shown in Fig. 4 (Lena, Bridge, and Airplane)
are experimented. Fixed-value noise and random-valued noise with uniform distribution are tested. Simulations are carried out for various noise density levels ranging from 10% to 30%.
Table 2
Restoration results in PSNR for fixed-valued impulse noise densities ranging from 10% to 30%
Algorithm Lena Bridge Airplane
10% 20% 30% 10% 20% 30% 10% 20% 30% Median (3· 3) 33.65 29.57 23.89 26.22 24.57 21.59 34.54 29.73 23.79 Median (5· 5) 30.86 30.22 29.47 24.01 23.67 23.28 30.54 29.87 29.13 [8] 26.09 18.59 14.27 25.30 18.16 14.00 25.44 18.12 14.00 Switching I[5] 35.05 30.08 24.02 26.55 24.76 21.66 35.53 30.02 23.85 Switching II[5] 34.51 25.83 20.06 28.23 23.63 19.28 34.36 25.58 19.9 CWM[3] 33.86 25.75 20.04 27.92 23.54 19.26 34.03 25.53 19.89 MSM[7] 36.2 26.04 20.03 30.05 24.15 19.35 35.94 25.78 19.87 CSAM[9] 35.43 31.57 25.4 28.31 26.6 24.03 38.61 33.17 28.87 Proposed 35.5 32.3 29.8 28.0 26.6 24.6 37.8 33.2 29.5
Fig. 5. Iterative restoration performance of airplane image (a) original image corrupted by 20% random-valued impulse noise. (b) After the first iteration. (c) After the second iteration. (d) Restored image after the third iteration.
Table 1
Restoration results in PSNR for random-valued impulse noise densities ranging from 10% to 30%
Algorithm Lena Bridge Airplane
10% 20% 30% 10% 20% 30% 10% 20% 30% Median (3· 3) 33.82 31.41 28.11 26.22 25.06 23.49 34.55 31.62 27.49 Median (5· 5) 30.7 30.03 29.16 23.99 23.58 23.05 30.47 29.77 28.8 [8] 29.17 23.75 20.09 26.78 22.74 19.15 28.46 22.84 19.41 Switching I[5] 35.53 32.05 28.34 26.59 25.26 23.59 35.47 32.02 27.6 Switching II[5] 35.89 30.44 25.66 28.53 25.73 21.35 36.09 29.74 24.73 CWM[3] 35.17 30.32 25.66 28.26 25.64 22.91 35.74 29.73 24.76 MSM[7] 35.71 30.39 25.84 29.94 26.48 23.38 35.81 29.8 25.04 CSAM[9] 19.39 16.16 14.47 18.83 15.82 14.05 18.74 15.67 13.85 Proposed 35.9 33.71 30.88 28.65 26.3 25.17 34.1 31.98 29.44
Peak SNR (PSNR) is used to give a quantitative evalu-ation. The PSNR performance of the proposed mechanism is compared to that of the 3· 3 median filter, 5 · 5 median filter, Florencio and Schafer’s switching scheme, Sun and Neuvo’s switching scheme-I and scheme-II, 3· 3 CWM fil-ter ([3]), MSM filter ([7]), and CSAM ([9]) filter.
Tables 1 and 2demonstrates the PSNR results for ran-dom-valued noise and fixed value noise, respectively. Both simulation results show the proposed filtering outperforms other filtering schemes. We apply three iterations of the proposed to restore the corrupted image. Fig. 5 demon-strates the noise is removed gradually in the interative pro-cess since the filtered image in the current iteration provides
better estimation of image global structure in the next iter-ation. The consistency of the performance from Tables 1 and 2 indicates that the proposed filter is fairly robust against wide variations of noise densities.
A subjective visual comparison of the noise reduction and image detail-preserving using ‘‘Bridge’’ image is pre-sented inFig. 6. We can observe that outputs of Switching I and median filter have the edge blurring effect. On the contrary, even though Florencio and MSM have better edge preserving result, it is observed fromTables 1 and 2
that PSNR will decrease substantially in the high noise density.
5. Conclusions
In this paper, we present an adaptive-hierarchical filter-ing technique to remove the impulse noise effectively while preserving the detailed image information at the same time. The global image structure is estimated as prior informa-tion which can be used to apply different filters adaptively. A noisy pixel can be effectively removed by either a stan-dard median filter or the edge directional filter depending on the local statistics of the image structure. The procedure is applied iteratively. The iterative reconstructions make it possible to use partial results as context information to resolve ambiguities in estimating the global structure. The proposed filter outperforms other methods in that it can make use of both local and global information efficiently. Experimental results show that the proposed method pro-duces better performance than many other well-known methods do.
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Fig. 6. Restoration results for various methods. (a) Original image. (b) Image corrupted by 20% random value noise. (c) 5· 5 median filter. (d) 3· 3 median filter. (e) Sun’s switching scheme-I. (f) Sun’s switching scheme-II. (g) Florencio’s filter. (h) MSM filter. (i) The proposed filter.
