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Reduction of impulse noise using improved weighted average filter.


Digital images are often corrupted by noises. These noises will affect the original information of the image both in quality and quantity. Various types of noise present in the digital images are Gaussian noise, speckle noise, gamma noise, fractal noise, impulse noise. Impulse noise occurred during capturing and transmission of images. This noise is also called as salt and pepper noise where the pixel values are interchanged. Various techniques such as median filters, average filters and fuzzy algorithms are developed to reduce the impulse noise.

Most of impulse noise removal algorithms are variations of median filtering. Best examples are DecisionBased Al0gorithm (DBA) [3], Median-based Switching filter (MS) [9], and Modified Decision Based Unsymmetrical Trimmed Median Filter (MDBUTMF) [10]. Also, due to the nature of impulse noise, some methods are proposed based on fuzzy logics, such as Detail-Preserving Filter (DPF) [6], Noise Adaptive Fuzzy Switching Median (NAFSM) filter [8], and Turbulent Particle swarm optimization based Fuzzy Filtering (TPFF)[13].

Other methods employed different ideas. In [2], Specialized Regularization (SR) method is proposed to restore noisy pixels. Opening- Closing Sequence (OCS) filter is presented in [4] based on mathematical morphology. In [5], Edge -Preserving Algorithm (EPA) is proposed which adopts a directional correlationdependent filtering technique. In [11], Robust Outlyingness Ratio is combined with the Non-Local Means (ROR-NLM) to detect and filter the noisy pixels. In [14], a method is presented which employs an iterative impulse detector and an Adaptive Iterative Mean (AIM) filter to remove the general fixed-valued impulse noise.

Another well -known approach is weighted-average filtering, which exploits the correlation among neighboring pixels to restore the corrupted pixels. The Switching-based Adaptive Weighted Mean (SAWM) filter [7] and the Cloud Model (CM) filter [12] employ this approach for impulse suppression. Both filters adaptively determine the filtering window and use complex weighting rules. In SAWM method, the weights are specified based on the degree of compatibility between pixels, and the CM filter uses the certainty degrees of uncorrupted pixels as their weights. These filters are time-varying; that is they have to perform pixel - by-pixel restoration, rather than processing the image as a whole. This constraint opposes efficient implementation.

In this letter, we propose a two-step method for real- time impulse noise suppression. First, we employ an impulse detector to identify the corrupted pixels. It examines the spatial correlation of suspicious image pixels to decrease the false detection of uncorrupted pixels as corrupted. Second, we restore the image using a weightedaverage filter. The filter operates on the nearest neighboring interpolated image and can be implemented using matrix-based operations.

The rest of this letter is organized as follows. Section II de-fines the impulse noise model. The method is presented in Section III. The experimental results and comparisons are provided in Section IV and Section V

concludes the letter.

I. Impulse Noise Model:

Fixed-Valued Impulse Noise (FVIN), also known as Salt-and-Pepper Noise (SPN), is commonly modeled by [2]:


where, x and x' are the original and corrupted images noise density, respectively, and x(i,j)is the image coordinate. This model implies that the pixels are randomly corrupted by two fixed extreme grey-values, [N.sup.min] and [N.sup.min] with the same probability.

For impulse noise suppression, we first specify the impulse values and locate the corrupted pixels, and then estimate their original values using the information provided by the uncorrupted pixels.

III. Proposed Algorithm:

In this algorithm, we propose a two-step method for real-time impulse noise suppression. First, we employ an impulse detector to identify the corrupted pixels. It examines the spatial correlation of suspicious image pixels to decrease the false detection of uncorrupted pixels as corrupted. Second, we restore the image using a weighted-average filter. The filter operates on the nearest neighboring interpolated image and can be implemented using matrix-based operations.


Impulse detection:

Impulse detection is a method to identify the corrupted pixels. In this, first identify the impulse values Nmax and Nmin. However, marking all pixels with an extreme grey-value as noisy pixels results in a false detection of some uncorrupted pixels as corrupted pixel. Therefore, at the next step, we should locate the noisy pixels by discriminating the uncorrupted pixels which have an impulse value. For this, examine the inclination for each neighborhood and the correlation of each suspicious pixel with its neighbors to distinguish between the corrupted pixels and the uncorrupted ones which have one of the impulse values.

1. The corrupted pixel value is identified by the extreme grey values of the image as (0,255).

2. Then the noise probability is identified to calculate the window size.

Nearest neighbor interpolation:

The simplest interpolation from a computational standpoint is the nearest neighbor, where each interpolated output pixel is assigned the value of the nearest sample point in the input image. This technique is also known as point shift algorithm and pixel replication. This method is used for detecting the corrupted pixels in the image.

This method is very efficient, even if the quality of image is very poor. It is because the Fourier Transform of a rectangular function is equivalent to a sinc function; with its gain in pass band falls off quickly. Also, it has prominent side lobes are in the logarithmical scale.

Nearest Neighbor interpolation is applicable when we want to increase the size of an image, it duplicates each column. This doubles the image size in the horizontal direction. Then duplicate each row of the enlarged image to double the size in the vertical direction.

Weighted average filter:

Instead of averaging all the pixel values in the window, considering the closer-by pixels higher weighting, and far-away pixels lower weighting is a weighted average filter.


This type of operation is in fact 2 linear convolution of f(m,n) by a filter h(m,n).Weighted average filter retains low frequency and suppresses high frequency and it acts as low-pass filter.


Weighted averaging:

In this given example the weights are sum to one. The basic idea is to give higher weight to some samples, according to their position with respect to the center of the window. Each sample is given a weight according to its spatial position in the window.


Steps involved in the removal of noise are detection of impulse then it is removed and restored.

1. The original image is captured and the noise is added to the originalimage

2. After addition of noise the noise probability is identified to calculate the windowsize.

3. The impulse noise is identified by using the impulse detector.

4. Impulse detector identifies the two extreme grey values as noise.

5. The identified noise is replaced by using the Nearest Neighbor interpolation.

6. Then the image is applied to weighted average filter.

7. In weighted average filter the weights are different for corrupted and uncorrupted pixels

8. After the filtering process the image is restored by this weighted average filter.

Image Restoration:

For image restoration, we propose an Efficient Weighted-Average (EWA) filter. In the proposed method, first we construct an initial image using the Nearest Neighboring Interpolation (NNI). In this image, each noisy pixel takes the grey-value of its nearest known pixel. We then improve the initial image by employing a weighted-average filter, which applies different procedures for weighting the known and noisy pixels.

Weight Assignment Procedures:

Weights of Known Pixels:

The weight assignment to known pixels is based on the fact that due to the spatial correlation of image pixels, the information of adjacent pixels overlaps. In other words, two separate pixels have more information than two adjacent pixels.

Weights of Noisy Pixels:

The weight assignment to noisy pixels is based on this image property that farther image pixels have lesser correlation with each other. Thus in the initial image, noisy pixels which are farther from their nearest known pixel take less accurate value.

IV. Simulation Results:

The propose algorithm is compared with the images of various noise levels. The comparison is

Measuring parameters:

Mean Squared Error:

The quality of the image measures the change between the original image (X) and denoised image (Y) is a mean squared error and it is given by


The Mean Squared Error widely used to quantify image quality. When image is used alone, it does not correlate strongly enough with perceptual quality. The statistics states that the mean squared error of an estimator is one of many ways to quantify gray value difference between the images. MSE is implied by an estimator and the true values of the quantity being estimated. MSE corresponds to the expected value of the squared error loss or quadratic loss.

Image        Noise density   PSNR (db)    MSE    Time delay (sec)

Camera Man        20%         29.250     77.89          2
                  40%         28.374     95.29         3.5
                  60%         27.904     106.1         4.5
                  80%         27.627     113.1          5


Peak Signal to Noise Ratio:

The Peak Signal to Noise Ratio (PSNR) is the ratio between maximum possible power and corrupting noise that affect representation of image. PSNR is usually expressed as decibel scale. PSNR defined via the Mean Square Error (MSE) and corresponding distortion matric, the Peak Signal to Noise Ratio is given by, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Here, MAXI is the maximum possible pixel value of the image. The pixels are represented using 8 bits per sample, this is 255. The PSNR is basically the SNR when all pixel values are equal to the maximum possible value.


Impulse noise removal is based on weighted average filter with the nearest neighbor interpolation. This method first step is construct initial image using nearest neighbor interpolation. From the initial image, detect the impulse noise. Then noisy image is reconstructed using the weighted average filter. The experimental result verifies that this method performs best compared to the previous algorithm in terms of quantitative and qualitative approach. The effectiveness of this algorithm is compared with the quantitative measures are PSNR and MSE. This method reduces the computational complexity and the time delay.


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(1) Aarthi T. and (2) Gayathri R.

(1) M.E.-Applied Electronics, Saveetha Engineering College, Chennai.

(2) Associate professor, Department of Ece. Saveetha Engineering College, Chennai.

Received 25 April 2016; Accepted 28 May 2016; Available 5 June 2016

Address For Correspondence:

Aarthi T., M.E.- Applied Electronics, Saveetha Engineering College, Chennai.

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Author:Aarthi, T.; Gayathri, R.
Publication:Advances in Natural and Applied Sciences
Date:Jun 15, 2016
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