Wavelet denoising¶. Wavelet denoising relies on the wavelet representation of the image. Gaussian noise tends to be represented by small values in the wavelet domain and can be removed by setting coefficients below a given threshold to zero (hard thresholding) or shrinking all coefficients toward zero by a given amount (soft thresholding). Setting to the universal threshold (about 3.3 for these datasets and noise level) gives the output for the VisuShrink wavelet shrinkage algorithm. For more information on wavelet transformations and applications to denoising, see P. Van Fleet, Discrete Wavelet Transformations, Hoboken, NJ: John Wiley & Sons, Inc., 2008.
AndABSTRACTThe development of wavelet theory in recent years has motivated the emergence of applications such as in signal processing, image and function representation, finance, economics, etc. One of the dvantages wavelet as compared with Fourier is, it has fast algorithm to evaluate the series expansion. In the present study, we will discuss the applications of fast wavelet algorithm namely Discrete Wavelet Transform (DWT) in finance such as denoising the time series by using wavelet thresholding. Some numerical results by using real data will be presented. Howto cite this article:S.A.A. Sulaiman, 2011.
Application of Wavelet Method in Stock Exchange Problem. Journal of Applied Sciences, 11: 1331-1335.DOI:URL:Received:October 18, 2010; Accepted: December 24, 2010;Published: March 09, 2011INTRODUCTIONWavelets are relatively new in pure and applied mathematics field of research;they have, with respect to theory and applications, strong relations with FourierTransform. Wavelets have emerged in the last twenty years as a synthesis ofideas from fields such as electrical engineering, statistics, physics, computerscience, economy, finance and mathematics. Have beautifuland deep mathematical properties, making them well-adapted tool for a wide rangeof functional spaces, or equivalently, for very different types of data.
Onthe other hand, they can be implemented via fast algorithms, essential to converttheir mathematical efficiency into truly practical tool (;; ).Temperature, water level or closed market prices over a period of time are an example of time series data. In its descriptive form, time series data may be defined as a set of data collected or arranged in a sequence of order over a successive equal increment of time.
An example of a financial time series that will be used in this study is the Kuala Lumpur Composite Index (KLCI). We use daily closing data covering the period of 1 January 1995 to December 31, 2008 (the total data sets are 3706). The index is denominated in local currency units, extracted from the Bloomberg Database. It is undeniably, the daily data contain too much noise and are subject to the problem of non-synchronous infrequent trading.
KLCI time series moves on the basis of supply and demand for shares. Therefore, the supply and demand curve will be surrounded by noise created by random order signal.Noise is an unwanted modulation of the carrier whose presence interferes withthe detection of the desired signal. Noise is extraneous information in a signal that can be filteredout via the computation of averaging and detailing coefficients in the wavelettransformation. In fact many statistical phenomena have wavelet structure. Oftensmall bursts of high frequency wavelets are followed by lower frequency wavesor vice versa. The theory of wavelets reconstruction helps to localize and identifysuch accumulations of small waves and helps thus to better understand reasonfor these phenomena. In addition, wavelet theory is different from Fourier analysisand spectral theory since it is based on a local frequency representation.MATERIALS AND METHODSIn this section we will review the basic definition of Wavelet theory by usingMultiresolution Analysis (MRA) approach.
For more detail the reader can referredthe books on wavelet by, and.Until recently wavelet analysis via MRA approach has been found to be a reliable method in financial and economic analysis, in particular for stock market and foreign exchange. Applications of wavelets in finance can be seen in the study of non-stationary and non-linearity property of financial time series because of structure change, volatility and long-memory process. Furthermore, wavelet methods have also being use as a tool for forecasting. In addition, wavelets decompositions of a signal or data can be adopted to improve the hypothesis testing on existing theories and can also provide insights of financial phenomena and enhance the development of theories.Based on,and, suppose that there exists a functionφ(t) ε L 2 (R), such that the family of functions.
(7)In this study, we use the symlet 4 wavelet (8 filter coefficient). To show the power of DWT, we apply the symlet 4 to denoise time series data up to seven level of approximation.show the example of symlet 4 scaling function andits corresponding wavelet function.
Meanwhile showthe wavelet decomposition for the original time series data (KLCI data). Forthis data set, the best level of decomposition is 7. We can see clearly from, even at level 7, the wavelet decomposition alreadycontains the main patterns of the original time series that is appear very volatileand various point of spike.
3:Denoised original signal using DWT (various thresholding approach)Where, I is the usual indicator function. In other words, hard means keep orkill while soft means shrink or kill (; ).The rule that usually being adopted is the soft thresholding.Although the hard thresholding is able to preserve the peak, it also produce greater spurious oscillations and close discontinuties.
There are a few methods can be use to find the threshold value.
Click Below to Get this Project with Synopsis, Report, Video Tutorials & Other details:-Subscribe to See Latest Project Videos:-Project Description:A very large portion of digital image processing is devoted to image denoising. This includes research in algorithm development and routine goal oriented image processing. Image restoration is the removal or reduction of degradations that are incurred while the image is being obtained. Degradation comes from blurring as well as noise due to electronic and photometric sources. Blurring is a form of bandwidth reduction of the image caused by the imperfect image formation process such as relative motion between the camera and the original scene or by an optical system that is out of focus. Image denoising is often used in the field of photography or publishing where an image was somehow degraded but needs to be improved before it can be printed. For this type of application we need to know something about the degradation process in order to develop a model for it.
When we have a model for the degradation process, the inverse process can be applied to the image to restore it back to the original form. In this project technique for image restoration or image denoising will include BayesShrink Algorithms for wavelet thresholdingTo Get More Details: www.techpacs.comContact Details are:Mobile No.