International Journal of Science and Research (IJSR) ISSN (Online): 2319-7064 Index Copernicus Value (2013): 6.14 | Impact Factor (2015): 6.391 Volume 5 Issue 6, June 2016 www.ijsr.net Licensed Under Creative Commons Attribution CC BY Comparing Wavelet and Wavelet Packet Image Denoising Using Thresholding Techniques Tapan Kumar Hazra 1 , Rajib Guhathakurta 2 1 Department of Information Technology, Institute of Engineering and Management, Salt Lake, Kolkata-700091 2 Department of Information Technology, Institute of Engineering and Management, Salt Lake, Kolkata-700091 Abstract: Image denoising has remained a fundamental problem in the field of image processing. With Wavelet transforms, various algorithms for denoising in wavelet domain were introduced. Wavelets gave a superior performance in image de-noising because here multi-resolution analysis is possible. Wavelet thresholding is a signal estimation technique that exploits the capabilities of wavelet transform for signal denoising. The aim of this project was to study various denoising techniques using wavelet and wavelet packets and compare them to determine the better one for image denoising. Performance of denoising algorithm is measured using quantitative performance measures such as Signal-to-Noise Ratio (SNR) and Mean Square Error (MSE). Keywords: Multi-resolution, Sub-Band Coding, Discrete Wavelet Transform, Continuous Wavelet Transform, Wavelet Packet 1. Introduction In many applications, image denoising is used to produce good estimates of the original image from noisy observations. The restored image should contain less noise than the observations while still keep sharp transitions (i.e. edges). Wavelet transform, due to its excellent localization property, has rapidly become an indispensable signal and image processing tool for a variety of applications, including compression and denoising. Wavelet denoising attempts to remove the noise present in the signal while preserving the signal characteristics, regardless of its frequency content. It involves three steps: a linear forward wavelet transform, nonlinear thresholding step and a linear inverse wavelet transform. Wavelet thresholding[1, 2] (first proposed by Donoho is a signal estimation technique that exploits the capabilities of wavelet transform for signal denoising. It removes noise by killing coefficients that are insignificant relative to some threshold, and turns out to be simple and effective, depends heavily on the choice of a thresholding parameter and the choice of this threshold determines, to a great extent the efficacy of denoising. Researchers have developed various techniques for choosing denoising parameters and so far there is no “best” universal threshold determination technique. The aim of this project was to study various thresholding techniques such as SureShrink, VisuShrink and BayesShrink and determine the best one for imagedenoising. 2. Motivation Wavelet theory is one of the most modern areas of mathematics. Masterfully developed by French researchers, such as Yves Meyer, Stéphane Mallat and Albert Cohen, this theory, is now used as an analytical tool in most areas of technical research: mechanical, electronics, communications, computers, biology and medicine, astronomy and so on. In the field of signal and image processing, the main applications of wavelet theory are compression and denoising. In the context of denoising, the success of techniques based on the wavelet theory is ensured by the ability of decorrelation (separation of noise and useful signal) of the different discrete wavelet transforms. Because the signal is contained in a small number of coefficients of such a transform, all other coefficients essentially contain noise. By filtering these coefficients, most of the noise is eliminated. Thus, each method of image denoising based on the use of wavelets follows the classic method, in three steps: computing a discrete wavelet transform of the image to be denoised, filtering in the wavelet domain and the computation of the corresponding inverse wavelet transform. Throughout recent years, many wavelet transforms (WT) have been used to operate denoising. The first one was the discrete wavelet transform; it has three main disadvantages, lack of shift invariance, lack of symmetry of the mother wavelet and poor directional selectivity. These disadvantages can be diminished using a complex wavelet transform. More than 20 years ago, Grossman and Morlet developed the continuous wavelet transform .A revival of interest in later years has occurred in both signal processing and statistics for the use of complex wavelets and complex analytic wavelets, particularly in it may be linked to the development of complex-valued discrete wavelet filters and the clever dual filter bank. The complex WT has been shown to provide a powerful tool insignal and image analysis. 3. Denoising Procedure The procedure to denoise an image is given as follows: De-noised image = W−1 [T{W (Original Image + Noise)}] Step 1: Apply forward wavelet transform to a noisy image to get decomposed image. Step 2: Apply non-linear thresholding to decomposed image to remove noise. Step 3: Apply inverse wavelet transform to threshold image to get a denoised image in spatial domain. 4. Wavelet Transform Wavelet transform is a relatively new concept (about 20 – 25 years old ). Mathematical Transformations are applied Paper ID: NOV164305 http://dx.doi.org/10.21275/v5i6.NOV164305 790