Image Denoising Using M-Band Wavelets A Study on M-Band Wavelet and its Application for Image Denoising Kaushik Sinha Assistant Professor, Dept. of IT College of Engineering and Management, Kolaghat KTPP Township, West Bengal, India Debalina Jana Assistant Professor, Dept. of AEIE College of Engineering and Management, Kolaghat KTPP Township, West Bengal, India Abstract—This work addresses to a study on the different techniques of noise removal from an image using M-Band Wavelet Transform. The standard wavelet transform technique has already proven its capability for different image processing problems such as image denoising. Noise removal from image is best done in the frequency domain. Psychophysical results indicate human visual processes an image by decomposing into multiple channels corresponding to its frequency and orientation components at different scales. It is also capable of preserving both local and global information. So, multi scale wavelet analysis is an ideal approach to describe noise removal. In this paper, the capability of M-Band Wavelet Transform is discussed in the process of noise removal from different images. Keywords—M-Band Wavelet Transform; Additive White Gaussian noise; Thresholding; Image Denoise I. INTRODUCTION Many types of noises due to sensor or channel transmission errors often corrupt images and noise suppression becomes a particularly delicate and a difficult task [5-6]. Applied noise removal techniques should take into account a trade-off between noise reduction and preservation of actual image content in a way that enhances the diagnostically relevant image content. The need for efficient image restoration methods has grown with the massive production of digital images and movies of all kinds, often taken in poor conditions. No matter how good cameras are, an image improvement is always desirable to extend their range of action [4]. The two main limitations in image accuracy are categorized as blur and noise. Blur is intrinsic to image acquisition systems, as digital images have a finite number of samples and must satisfy the Shannon–Nyquist sampling conditions. The second main image perturbation is noise. There are different types of noises that can affect an image. Some of them are A. Salt and pepper noise It is the type of noise where some black and white pixels occurs randomly on an image. A false saturation gives a white spot (salt) and a failed response gives a black spot in the image (pepper) [3], [9]. B. Gaussian white noise This is the most common type of noise [3], [7-9] which can be generated artificially using the formula Y = X + sqrt(variance) × random(s) + mean; (1) Where, X is the input image, Y is the output image, s is the size of X. The value of mean and variance is taken as input. C. Poisson noise In probability theory and statistics, Poisson distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed interval of time and/or space. If the expected number of occurrences in a particular time interval is λ, then probability that there are exactly k (k = 0, 1, 2 …) occurrences is given by (, )=    −  ! (2) D. Speckle noise Within each resolution cell, a number of elementary scatters reflect the incident wave towards the sensor. The received image is thus corrupted by a random granular pattern, called Speckle. A speckle noise can be modelled as  =  (3) Where, v is the speckle noise, f is the noise-free image and ϑ is a unit mean random field. In this paper, the experimental work is done with Gaussian white noise [9]. In the field of Image Processing, the wavelet transform has emerged with a great success [10]. The M-band wavelet transform[24] is a specific area of wavelet transform which has so many advantages over standard wavelet transform [17- 23]. II. M-BAND WAVELET TRANSFORM The term wavelet means a small wave. The smallness refers to the condition that this (window) function is of finite length (compactly supported). The wave refers to the Vol. 3 Issue 6, June - 2014 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 www.ijert.org IJERTV3IS060953 International Journal of Engineering Research & Technology (IJERT) 782