**5.8.2 Objective evaluation**

466 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

Butterworth wavelets with nonlinear phase, orthogonal Coiflets wavelets with near linear phase, and biorthogonal Spline wavelets with linear phase (Daubechies, 1989, 1992). All of

 This transform cross-multiplies a function against the Haar wavelet with various shifts and stretches, like the Fourier transform cross-multiplies a function against a sine wave

 Daubechies wavelets are a family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of vanishing moments for some

Meyer's wavelet construction is fundamentally a solvent method for solving the two-

Coiflets are discrete wavelets designed by Ingrid Daubechies, to have scaling functions

biorthogonal wavelet is a wavelet where the associated wavelet transform is invertible

Fig. 4. (a) Haar wavelet (b) Daubechies wavelet (c) Meyer Wavelet (d) Symlet wavelet (e)

Coiflets wavelet (f) Bi orthogonal wavelet (g) Reverse Bi orthogonal

Symlet wavelet is only nearly symmetric, and is not exactly symmetrical.

them are associated with FIR filters except Butterworth wavelets.

Haar wavelet is the simplest of the wavelet transforms.

**5.7 Wavelet families in SAR images** 

given support.

scale equation.

with vanishing moments.

**5.8 Performance evaluation 5.8.1 Subjective evaluation** 

but not necessarily orthogonal.

Reverse biorthogonal is a spline wavelet filters.

with two phases and many stretches.

Fig. 5. Peak to Signal noise ratio for wavelet methods

Fig. 6. Mean square error rate for wavelet methods

Fig. 7. PSNR values for shrinkage method based on coiflet Wavelet family

Image Denoising Based on Wavelet Analysis for Satellite Imagery 469

and resolution of the images. Finally, it is concluded that the selection of wavelet for image denoising depends on size, contents and resolution of the images for desired image quality.

Automation in river ice image classification assists the ice experts in extracting geophysical information from the increasing volume of images. Rivers and streams are the key elements in the terrestrial re-distribution of water. An ice cover has significant impact on rivers such as modifies ecosystem, affects microclimate, cause flooding, restrict navigation, impact hydropower generation. The regions that are affected by ice are fishing industry, coastal

High reflectance, thermal insulation, storage of water extent (areal coverage), depth,

Environmental monitoring/prediction – flood forecasting, severe weather(blowing

Satellite-based Synthetic Aperture Radar (SAR) provides a powerful vessel surveillance capability in front of time consuming traditional methods. SAR images are larger in volume. SAR images typically consist of 32 bit complex pixels with large dimensions. The entropy of SAR images is higher than optical images (Sery et al., 1996).. SAR images carry information in low frequency bands as well as high frequency bands. SAR images have larger dynamic range than optical images. SAR sea images are highly heterogeneous and this fact affects to the viability of the approach. The major advantages of SAR are (i)Sensitive to texture (ii) Good for vegetation studies (iii) Ocean waves, winds, currents(iv) Seismic Activity and Moisture content.

This is the first and lowest level operation to be done on images. The input and the output are both intensity images. The main idea with the preprocessing is to suppress information in the image that is not relevant for its purpose or the following analysis of the image (Subashini &Krishnaveni, 2010). The pre-processing techniques use the fact that neighboring pixels have essentially the same brightness. There are many different pre-processing methods developed for different purposes.Interesting areas of pre-processing for this work is image filtering for noise suppression. Two shrinkage methods are used over here to calculate new pixel values in a local neighborhood. Shrinkage is a well known and appealing denoising technique. On the experiment evaluation, Daubechies wavelet family of orthogonal wavelets is concluded as the appropriate family for shrinkage method as it is defined as a discrete wavelet transform and characterized by a maximal number of

Snowfall/solid precipitation .Indicator of climate variability and change

Socio-economic – hydropower production/management, agriculture, tourism

**6. Wavelet analysis for ice classification in SAR imagery** 

Impacts both global/regional energy and water cycles.

water equivalent (water content), wet/dry state.

Input/validation of models – NWP, hydrological, climate

snow), soil moisture/drought, forest fire risk, wildlife

zone and lake water levels and navigation.

**6.3 SAR image denoising using Wavelet** 

vanishing moments for some given support.

**6.1 Importance of ice covers** 

**6.2 SAR basics** 

Fig. 8. MSE values for shrinkage method based on coiflet Wavelet family

The wavelet transform is computed separately for different segments of the time-domain signal at different frequencies. Discrete wavelet transform (DWT), which transforms a discrete time signal to a discrete wavelet representation. The reconstruction of image is far better in wavelet by analysis and it is implemented with the given SAR image. Some of the parameters taken for analysis of wavelet on SAR images are

Mean Square error rate - MSE is called **squared error loss**.

**MSE** of an estimator is one of many ways to quantify the amount by which an estimator differs from the true value of the quantity being estimated.

**PSNR -**This ratio is often used as a quality measurement between the original and a compressed image. The higher the PSNR, the better the quality of the compressed or reconstructed image.

The *Mean Square Error (MSE)* and the *Peak Signal to Noise Ratio (PSNR)* are the two error metrics used to compare image quality. The MSE represents the cumulative squared error between the compressed and the original image, whereas PSNR represents a measure of the peak error. The lower the value of MSE, the lower the error.

From the above got results the coiflets of wavelet denoising method out performs the rest of the wavelet families. This study presented an analysis and comparison of the wavelet families using for image denoising considering PSNR and visual quality of image as quality measure. The effects of bio orthogonal , Reverse bio orthogonal, Daubechies, coiflets and symlets wavelet families on the test images have been examined. The PSNR and visual image quality for wavelet functions of each family is also presented. The PSNR is taken as the objective measure for performance analysis of wavelets using for images denosinig. Here it is analyzed –the results for a wide range of wavelets families and found that the wavelet coifilets provides best performance for SAR images.The computational time required for the Bio orthogonal and reverse bio orthogonal wavelet families is more in comparison to other wavelet families is more in comparison to other wavelet families. The performance of wavelet function depends not only size of the image but also on the content and resolution of the images. Finally, it is concluded that the selection of wavelet for image denoising depends on size, contents and resolution of the images for desired image quality.
