**2. Noise consideration**

A signal or an image is unfortunately corrupted by various factors which effects as noise during acquisition or transmission. These noisy effects decrease the performance of visual and computerized analysis. It is clear that the removing of the noise from the signal facilitate

transform are produced from the mother wavelet by scaling and translation operations. When the scaling is chosen as power of two, this kind of wavelet transform is called dyadicorthonormal wavelet transform, which makes a way for discrete wavelet transform (Zou and Tewfik 1993; Blu 1998) . If the chosen mother wavelet has orthonormal properties, there is no redundancy in the discrete wavelet transforms. In addition, this provides the multiresolution algorithm decomposing a signal into scales with different time and

The fundamental concept involved in mutiresolution is to find average features and details of the signal via scalar products with scaling signals and wavelets. The spikes in signal are typically of high frequency and it is possible discriminate the spikes with other noises through the decomposition of multiresolution into different levels. The differences between mother wavelet functions (e.g. Haar, Daubechies, Symlets, Coiflets, Biorthogonal and etc.) consist in how these scaling signals and the wavelets are defined (Zou and Tewfik 1993; Blu

The continuous wavelet transform is computed by changing the scale of the mother wavelet, shifting the scaled wavelet in time, multiplying by the signal, and integrating over all times. When the signal to be analyzed and wavelet function are discredited, the CWT can be realized on computer and the computation time can be significantly reduced if the redundant samples removed respect to sampling theorem. This is not a true discrete wavelet transform. The fundamentals of discrete wavelet transform goes back to sub-band coding theorem (Fischer 1992; Vetterli and Kova evi 1995; Vetterli and Kovacevic 1995). The subband coding encodes each part of the signal after separating into different bands of frequencies. Some studies have made use of wavelet transform as a filter bank in order to

After discovering the signal decomposition of a signal into frequency bands using discrete wavelet transform, the DWT has found many application area, from signal analysis to signal

The one of the first application of the DWT is the denoising process, which aims to remove the small part of the signal assumed as noise (Lang, Guo et al. 1996; Simoncelli and Adelson 1996; Jansen 2001). All kind of the signal obtained from the physical environment has contains more or less disturbing noise. Therefore, wavelet denoising procedure has applied many one or two dimensional signal after particularly soft or hard thresholding methods had proposed (Donoho and Johnstone 1994; Donoho 1995). Such signals some time are onedimensional simple power or control signals (Sen, Zhengxiang et al. 2002; Giaouris, Finch et al. 2008) as well as more complex medical images (Wink and Roerdink 2004; Pizurica, Wink et al. 2006). Especially, wavelet denoising has found an application field about image processing recently (Nasri and Nezamabadi-pour 2009; Chen, Bui et al. 2010; Jovanov, Pi

A signal or an image is unfortunately corrupted by various factors which effects as noise during acquisition or transmission. These noisy effects decrease the performance of visual and computerized analysis. It is clear that the removing of the noise from the signal facilitate

compression (Chang and Kuo 1993; Qu, Adam et al. 2003; He and Scordilis 2008).

frequency resolution (Mallat 1989; Daubechies 1990).

1998; Ergen, Tatar et al. 2010).

separate the signal.

urica et al. 2010).

**2. Noise consideration** 

the processing. The denoising process can be described as to remove the noise while retaining and not distorting the quality of processed signal or image (Chen and Bui 2003; Portilla, Strela et al. 2003; Buades, Coll et al. 2006). The traditional way of denoising to remove the noise from a signal or an image is to use a low or band pass filter with cut off frequencies. However the traditional filtering techniques are able to remove a relevant of the noise, they are incapable if the noise in the band of the signal to be analyzed. Therefore, many denoising techniques are proposed to overcome this problem.

The algorithms and processing techniques used for signals can be also used for images because an image can be considered as a two dimensional signal. Therefore, the digital signal processing techniques for a one dimensional signal can be adapted to process two dimensional signals or images.

Because the origin and nonstationarity of the noise infecting in the signal, it is difficult to model it. Nevertheless, if the noise assumed as stationary, an empirically recorded signal that is corrupted by additive noise can be represented as;

$$y(i) = \mathbf{x}(i) + \sigma \mathbf{z}(i) \; , \; i = 0, 1, \dots, n - 1 \tag{1}$$

Where *y i*( ) noisy signal, *x i*( )is noise free actual signal and ( )*i* are independently normal random variables and represents the intensity of the noise in *y*( )*i* . The noise is usually modeled as stationary independent zero-mean white Gaussian variables (Moulin and Liu 1999; Alfaouri and Daqrouq 2008).

When this model is used, the objective of noise removal is to reconstruct the original signal *x i*( ) from a finite set of *y*( )*i* values without assuming a particular structure for the signal. The usual approach to noise removal models noise as high frequency signal added to an original signal. These high frequencies can be bringing out using traditional Fourier transform, ultimately removing them by adequate filtering. This noise removal technique conceptually clear and efficient since depends only calculating DFT (Discrete Fourier Transform)(Wachowiak, Rash et al. 2000).

However, there is some issue that must be under consideration. The most prominent having same frequency as the noise has important information in the original signal. Filtering out these frequency components will cause noticeable loss of information of the desired signal when considered the frequency representation of the original signal. It is clear that a method is required in order to conserve the prominent part of the signal having relatively high frequencies as the noise has. The wavelet based noise removal techniques have provided this conservation of the prominent part.
