With advance of technology, manipulation and distribution of digital media such as image, audio and video has been widespread explosively. This causes problems like unauthorized copy being more important. Watermarking is a method for copyright protection and hidden information transfer. Wavelet transform has good functionality in various watermarking methods because of its good ability of modeling human visual system. Wavelet transform extensions like basic wavelet are utilized in variety applications of image processing and good results have been reported from them. No comprehensive research has been done in efficiency of extended wavelets on watermarking robustness. In this paper efficiency of wavelet transform extensions is investigated in different attacks. For this purpose a general framework is proposed for embedding and watermark extraction based on bidiagonal singular value factorization. Results show classic wavelets have good robustness against attacks like compression and noises, but they have less robustness against geometric attacks such as rotation and shearing. Unlike classic wavelets, multidirectional wavelet extensions are robust in geometrical attacks.

Evaluation of the road surface distresses is one of the most prominent phases of pavement management process. Over the past decade, a considerable number of researches have been carried out on developing automatic methods for distress detection most of which rely on computer vision and image processing techniques. One of the most important assets comprising computer vision systems is the image feature extraction algorithm. Textural features present more detailed information about the image regions characteristics compared to other features such as color and geometrical (shape) properties. In the past few years, multi-resolutional analysis approaches, such as wavelet transforms have provided an effective tool for fast and accurate image texture representation. In the present study, after acquisition of six different types of asphalt pavement distresses under controlled condition, in order to analyze their structures, three 2-D discrete wavelet transforms including Haar, Daubechies3 and Coiflet1 were utilized. In addition to aforementioned transforms, directional selective dual-tree complex wavelet transform was also applied on the distress images with the purpose of investigating the effectiveness of directional sensitivity increasement. After decomposition of the images by applying the abovementioned transforms, second-order statistics based on gray level co-occurrence matrix and higher-order descriptors based on gray level run-length matrix were employed, in order to characterize the wavelet frequency sub-bands texture.

The purpose of this study is to present a new method of plate damage detection using the wavelet-based contourlet transform method. The contourlet transforms developed based on the Wavelet transform is a new two-dimensional transform that overcomes the limitations of the wavelet transform. The wavelet-based contourlet transform is a new family of contourlet transforms with the same two-step characteristic introduced from the same filter banks, radial, and angular decomposition. This method is used in plate damage detection for the first time. In the first step, the plate using the wavelet transform is decomposed into four sub-bands. Then, a radius decomposition with eight bands in each sub-band of the initial image is introduced using one of the directional filter banks. The radius decomposition in different directions is known as the advantage of this method in comparison with the wavelet transform. This advantage is observed in images with curved lines. In this method, the change in the elastic modulus is considered as damage in plates. The fundamental mode shape of intact and damaged plates is first obtained from the structural frequency analysis. Then, the location, shape, and approximate size of damage are obtained by applying this transform to the responses of the structure.

Seismic data have a variable characteristic. Overlooking this important characteristic will reduce the effectiveness of any signal processing tool. Wavelet transform is a useful tool in seismic data processing and in recent years it has been the subject of attention of geophysicists. In this study we investigate the role of the resolution of the wavelet transform and the Q-factor (Q-factor in band-pass filters is the ratio of central frequency to the bandwidth) of the mother-wavelet on the filter performance with the goal of reducing the random noise and examining the effects of the mother wavelet Q-factor and its oscillatory behavior on the filter performance. We use Rational-Dilation Wavelet Transform (RADWT) and Dual-tree RADWT. These methods have the capability to achieve variable frequency resolution that can also provide a variety of Q-factors. To evaluate the effect of Q-factor of mother wavelet on filter function, the DT-RADWT with different Q-factors is applied on a Ricker Wavelet and synthetic shot gathers and the results are discussed in the manuscript. In the following, we investigate the relationship between seismic signal Q-factor and suitable Q-factor for seismic data processing. The method is applied to high-frequency shallow Sub-Bottom Profiler data and land data. In this study, a new wavelet transform called Rational Dilation Wavelet Transform (RADWT) and its Dual Tree analytical version DT-RADWT is used to attenuate random noise in seismic data. These transforms can achieve a limited range of Q-factor by selecting appropriate parameters p, q and s. The advantage of this transform over the common discrete wavelet transforms is that its rational sampling which provides higher time-frequency resolution. We also investigate the effect of Q-factor of mother wavelet on the performance of wavelet transform filters, and the relation between seismic signal Q-factor and Wavelet transform filter Q-factor. Increasing the Q-factor can reduce the bandwidth of wavelet in each scale. We test the effect of random noise on Q-factor of Ricker wavelet, with different noise levels. The results showed that by changing the level of random noise, the range of Q-factor remains constant. Next, we added the constant noise to Ricker wavelet, and we analyzed the noise-infected wavelet by RADWT and DT-RADWT with different Q-factors, here the soft threshold was used. The result of denoising is presented in Table 2. In last part of manuscript high Q-factor Dual Tree Rational wavelet transform was used to attenuate random noise from synthetic shot gather and marine and land seismic data (figures 9 & 11& 14& 15). Suitable parameters for random noise attenuation, p, q, and s was selected respectively 7, 8, 1 that made WT Q-factor 7.48. This research investigated the role of Q-factor value in suppressing random noise from reflection seismic data. Many Q-factors were tested to evaluate the effect of wavelet transform Q-factor on random noise denoising, and it was observed that with an increase in the Q-factor of the wavelet transform, the signal-to-ratio of filtered trace was improved. The data Q-factor was also calculated, but there was no significant correlation between the appropriate Q-factor of WT for noise reduction and the signal Q-factor. DT-RADWT was better than RADWT in distinguish was the random noise from the signal, due to the use of two parallel filter banks. DT-RADWT with high Q-factor was applied to synthetic data with a variable level of random noise and results are summarized in table4. In addition, the method was also applied to real shallow marine data from sub-bottom profiler with a wide frequency content. Results confirm the effectiveness of WT filter which is increased with the increase of wavelet transform Q-factor.

Analysis of earth science data using different transform methods such as Fourier and wavelet transform, are useful for the extraction of hidden information imbedded in the data. Fortunately, the uses of such transforms have been expanding as reported in recent studies. Wavelets and wavelet transform in signal processing, offer important advantages that are highly useful in transient data analysis. These include multiresolution analysis of data for extraction of different information that reside in different frequency bands as well as extraction of localized features, a distinct property of wavelet transform as compared with other transforms. Furthermore, in wavelet transform, availability of alternative mother wavelets each with its own distinct featuremakes wavelets highly suitable for their usage in different application environment for maximal information extraction. Therefore selection of appropriate mother wavelet for maximal information extraction in a given data analysis, is considered to be an important and necessary step when working with wavelets.Areview of literature in earth science on the subject of optimal wavelet selection reveals little work has been done on the subject. In this paper, we have attempted to overcome this shortcoming in which we have investigated various approaches and considerations for the selection of optimum mother wavelet. In this investigation the results of a case study for selection of optimum mother wavelet for decomposition of set of petrophysical logs gathered from one of the Iranian south oil elds are presented. The signicance of optimum mother wavelet selection in this oil eld is shown.

Wavelet transform is a new and useful method for signal analysis. Wavelet function is a composition of basic functions which can separate a signal in time and frequency. Therefore, wavelet transforms are capable of detecting many of unknown aspects of information which can not be detected through other methods. A wavelet-based nondestructive method for damage detection in structures that is effective and accurate is presented in this text. The proposed method is based on the analysis of the response signal of damaged structures. The main idea is to extract the damage location from the coefficients of the wavelet transform applying on the signals coming from the structural responses. After analysis of the structure by ABAQUS software, displacement response of structure was extracted along its longitudinal axis. Afterwards, the response was used for the wavelet analysis by the wavelet toolbox of the MATLAB software and the detection of damage in the structures was investigated. The results of wavelet analysis showed that the wavelet coefficients plots have considerable rise at or around the damage location. A sudden change or peak on the wavelet coefficients plot can indicate the location of a crack. Based on the obtained simulation results, it appears that this method can provide an advantageous alternative to classical methods for structural damage detection, such as Fourier transform.

Inspection of the pavement distresses is one of the most prominent phases of pavement management process in regard with determining optimum pavement maintenance strategies. Over the past few decades, a considerable number of efforts have been carried out on developing automatic methods for objectively distress detection all of which rely on machine vision and image processing techniques. One of the most important assets comprising machine vision systems is the feature extraction process. In the past few years, multi-resolutional analysis approaches, namely wavelet transforms has provided a great tool for fast and accurate image texture representation. In the present study, after acquisition of six different types of asphalt pavement distresses under controlled condition, in order to identify and categorize them, four 2-D multi-resolution transforms including Haar discrete wavelet, Daubechies3 discrete wavelet, Coiflet1 discrete wavelet and dual-tree complex wavelet were utilized. After decomposition of the distress images by applying the aforementioned transforms, first-order statistical indices based on histogram and second-order statistics based on gray level co-occurrence matrix were employed, in order to describe the wavelet frequency sub-bands texture. The distress classification results based on minimum Mahalanobis distance classifier indicate that extracting second-order statistics from the sub-bands of the dual-tree complex wavelet and Haar discrete wavelet transforms, yielding classification accuracy of 99% and 95% respectively, outperform other feature extraction algorithms in distress recognition. Furthermore, statistical indices acquired from gray level co-occurrence matrix with average classification rate of 87%, obtained superior performance in distress images discrimination compared to histogram statistics.