Comparatively study on image noising and Denoising

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Dipika Sharma, IJRIT-40

International Journal of Research in Information Technology

(IJRIT)

www.ijrit.com ISSN 2001-5569

Comparatively study on image noising and Denoising

Dipika sharma , Miss shalini kapoor and Mr. jujhar singh M.tech , CSE, Kurukshetra university kurukshetra

G.I.T.M, Karnal , Haryana ,India [email protected]

H.O.D, CSE , Kurukshetra university kurukshetra G.I.T.M, Karnal , Haryana, India

Assistant lecturer , CSE, kurukshetra university kurukshetra G.I.T.M, Karanl , Haryana ,India

[email protected]

Abstract

Visual information transmitted in the form of digital images is becoming a major method of communication in the modern age, but the image obtained after transmission is often corrupted with noise. The received image needs processing before it can be used in applications. Image Denoising involves the manipulation of the image data to produce a visually high quality image. Different noise models include Gaussian noise, salt and pepper noise, speckle noise and Brownian noise. Hence, it is necessary to have knowledge about the noise present in the image so as to select the Appropriate Denoising algorithm. The filtering approach has been proved to be the best when the image is corrupted with salt and pepper noise. The wavelet based approach finds applications in Denoising images corrupted with Gaussian noise. In the case where the noise characteristics are complex, the multifractal approach can be used.

Keywords-median filter,weiner filter,Gaussian noise and salt and pepper noise.

1. Introduction

COMPARITIVE STUDY BETWEEN FILTERS IN IMAGE NOISING AND DENOISING USING MATLAB.

1.1 Objective:

The main objectives of the project work are shown below:

 while comparing filters it will be seen that which Denoising technique is better for removing which noise and speed for Denoising also matters. 

 Different size of images will be used so as to know effect of Denoising technique on small and large image. 

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 All the images taken care of different formats so that it can be better understood that which Denoising technique better works for which format.

1.2 Median Filter

The Median filter is a nonlinear digital filtering technique, often used to remove noise. Such noise reduction is a typical preprocessing step to improve the results of later processing (for example, edge detection on an image). Median filtering is very widely used in digital image processing because under certain conditions, it preserves edges whilst removing noise. The main idea of the median filter is to run through the signal entry by entry, replacing each entry with the median of neighboring entries. Note that if the window has an odd number of entries, then the median is simple to define: it is just the middle value after all the entries in the window are sorted numerically. For an even number of entries, there is more than one possible median. The median filter is a robust filter. Median filters are widely used as smoothers for image processing, as well as in signal processing and time series processing.

A major advantage of the median filter over linear filters is that the median filter can eliminate the effect of input noise values with extremely large magnitudes. (In contrast, linear filters are sensitive to this type of noise - that is, the output may be degraded severely by even by a small fraction of anomalous noise values).

The output y of the median filter at the moment t is calculated as the median of the input values corresponding to the moments adjacent to t: y(t) = median((x(t-T/2),x(t-T1+1),…,x(t),…,x(t +T/2)). where t is the size of the window of the median filter. Since the median value must actually be the value of one of the pixels in the neighborhood, the median filter does not create new unrealistic pixel values when the filter straddles an edge. For this reason the median filter is much better at preserving sharp edges than the mean filter. These advantages aid median filters in denoising uniform noise as well from an image.

1.3 Wiener Filter

The goal of the Wiener filter is to filter out noise that has corrupted a signal. It is based on a statistical approach. Typical filters are designed for a desired frequency response. The Wiener filter approaches filtering from a different angle. One is assumed to have knowledge of the spectral properties of the original signal and the noise, and one seeks the LTI filter whose output would come as close to the original signal as possible [5]. Wiener filters are characterized by the following:

 a.Assumption: signal and (additive) noise are stationary linear random processes with known spectral characteristics.

 Requirement: the filter must be physically realizable, i.e. causal (this requirement can be dropped, resulting in a non-causal solution)

 Performance criteria: minimum mean-square error.

2. Image noise

Image noise is the random variation of brightness or color information in images produced by the sensor and circuitry of a scanner or digital camera. Image noise can also originate in film grain and in the

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Dipika Sharma, IJRIT-42 unavoidable shot noise of an ideal photon detector. Image noise is generally regarded as an undesirable by- product of image capture. Although these unwanted fluctuations became known as "noise" by analogy with unwanted sound they are inaudible

and actually beneficial in some applications, such as dithering. The types of Noise are following:-

• Gaussian noise

• Salt-and-pepper noise

2.1 Gaussian noise

The standard model of amplifier noise is additive, Gaussian, independent at each pixel and independent of the signal intensity. In color cameras where more amplification is used in the blue color channel than in the green or red channel, there can be more noise in the blue channel .Amplifier noise is a major part of the

"read noise" of an image sensor, that is, of the constant noise level in dark areas of the image.

Gaussian noise is evenly distributed over the signal. This means that each Pixel in the noisy image is the sum of the true pixel value and a random Gaussian Distributed noise value. As the name indicates, this type of noise has a Gaussian distribution, which has a bell shaped probability distribution function given by,

Gaussian distribution

Gaussian noise

(Mean=0, variance 0.05)

(Mean=1.5, variance 10)

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2.2 Salt-and-pepper noise

An image containing salt-and-pepper noise will have dark pixels in bright regions and bright pixels in dark regions this type of noise can be caused by dead pixels, analog-to-digital converter errors, bit errors in transmission, etc. This can be eliminated in large part by using dark frame subtraction and by interpolating around dark/bright pixels. Salt and pepper noise is an impulse type of noise, which is also referred to as intensity spikes. This is caused generally due to errors in data transmission. It has only two possible values, a and b. The probability of each is typically less than 0.1. The corrupted pixels are set alternatively to the minimum or to the maximum value, giving the image a “salt and pepper” like appearance. Unaffected pixels remain unchanged. For an 8-bit image, the typical value for pepper

noise is 0 and for salt noise 255. The salt and pepper noise is generally caused by malfunctioning of pixel Elements in the camera sensors, faulty memory locations, or timing errors in the digitization process. The probability density function for this type of noise is shown figure. Salt and pepper noise with a variance of 0.05 is shown in Image.

Salt and pepper noise

Salt & paper noise and median filter:

Image with noise recovered image

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Dipika Sharma, IJRIT-44 Salt and pepper noise with weiner filter

Image with noise Recovered image

Weiner filter with Gaussian noise

Image with noise Recovered image

Median filter with Gaussian noise

images with noise Recovered Image

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3. Conclusion

We used the sunset title Image in “jpg” format, adding three noise (Gaussian and Salt & Pepper) with standard deviation (0.025). In this image, De-noised all noisy images by all filters and conclude from the results that:

(a)The performance of the Wiener Filter after de-noising for Speckle and Gaussian noisy image is better than Median filter.

(b)The performance of the Median filter after de-noising for Salt & Pepper noisy image is better than Wiener filter.

4. Scope for future work

There are a couple of areas which we would like to improve on. One area is in improving the denoising along the edges as the method we used did not perform so well along the edges. The future work of research would be to implement Wiener Filter in Wavelet Domain.

5. References

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4. C. Sidney Burrus, Ramesh A. Gopinath, and Haitao Guo. Introduction to Wavelets and Wavelet Transforms A Primer. New Jersey: Prentice-Hall Pub., 1998, p. 6.

5. David L. Donoho. “De-noising by soft-thresholding.” IEEE Trans. on Information Theory, Vol 41, No. 3, May 1995.

6. David L. Donoho. “Unconditional bases are optimal bases for data compression and for statistical estimation.” Applied and Computational Harmonic Analysis, Vol. 1, No. 1, pp. 100-115, Dec.

1993.

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http://www.beyonddiscovery.org/content/view.page.asp?I=1959, 2001 [May 6, 2010].

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Internet: http://www.resonancepub.com/wavelets.htm [May 06,2010].87

9. Stephane G. Mallat. “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation.” IEEE Transactions on Pattern Analysis and Machine Intelligence,Vol. 11, No. 7, Jul. 1989.