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  Invisibility, robustness and payload are three indispensable and contradictory properties for any image watermarking systems. Recently, to achieve the tradeoff among above three requirements, statistical watermarking schemes have gained a lot of attention. Most existing approaches, however, often bear a number of drawbacks, in particular: (i) They all employ directly transform coefficients, which are always fragile to some attacks, for watermark embedding and statistical modeling; (ii) The adopted model cannot capture accurately the statistical distributions of the transform coefficients; (iii) Most of them simply use the linear function for watermark embedding, which often either miss higher capacity or may cause visible distortions. This has motivated us to introduce in this paper a novel non-linear statistical image watermark detector based on undecimated discrete wavelet transform (UDWT)-polar complex exponential transform (PCET) magnitude and the exponentiated Cauchy-Rayleigh distribution. We begin with a detailed study on the robustness and statistical characteristics of local UDWT-PCET magnitudes of natural images. This study reveals the strong robustness and highly non-Gaussian marginal statistics of local UDWT-PCET magnitudes. We also find that, with a small number of parameters, the new exponentiated Cauchy-Rayleigh model can capture accurately the statistical properties of the robust UDWT-PCET magnitudes of the image. Meanwhile, the statistical model parameters can be computed effectively by using the genetic simulated annealing (GSA)-based maximum likelihood (ML) estimation. Based on these findings, we finally develop a new non-linear statistical image watermark detector using the exponentiated Cauchy-Rayleigh PDF and locally most powerful (LMP) decision rule. Also, we use the exponentiated Cauchy-Rayleigh statistical model to derive the closed-form expressions for the watermark detector. Extensive experimental results show the superiority of the proposed blind watermark detector over most of the state-of-the-art methods recently proposed in the literature.

An image watermarking scheme is typically evaluated using three main conflicting characteristics: imperceptibility, robustness, and capacity. Developing a good image watermarking method is challenging because it requires a trade-off between these three basic characteristics. In this paper, we propose a statistical image watermark decoder in undecimated discrete wavelet transform-polar complex exponentiated transform magnitude domain, wherein a probability density function based on the exponentiated Cauchy–Rayleigh distribution is used, in view of the fact that this probability density function provides a better statistical match to the empirical probability density function of the robust undecimated discrete wavelet transform-polar complex exponentiated transform magnitudes of the image. In watermark embedding, we first perform the undecimated discrete wavelet transform on the carrier image. We then select the maximum energy subband and divide it into blocks, and compute the polar complex exponentiated transform for each block. Finally, we embed watermark in undecimated discrete wavelet transform-polar complex exponentiated transform magnitudes using nonlinear multiplicative approach. In the decoding process, we first analyze the robustness and statistical characteristics of undecimated discrete wavelet transform-polar complex exponentiated transform magnitudes. We then observe that, with a small number of parameters, the new exponentiated Cauchy–Rayleigh model can capture accurately the statistical distributions of the robust undecimated discrete wavelet transform-polar complex exponentiated transform magnitudes of the image. Meanwhile, statistical model parameters can be estimated effectively by using genetic simulated annealing based maximum likelihood approach. Motivated by our modeling results, we finally design a new statistical image watermark decoder using the exponentiated Cauchy–Rayleigh distribution and maximum likelihood decision rule. Experimental results on extensive test images demonstrate that the proposed watermark decoder provides a performance better than that of most of the state-of-the-art methods recently proposed in the literature.

Invisibility, robustness and payload are three indispensable and contradictory properties for any image watermarking systems. To achieve the tradeoff among the three requirements, statistical watermarking approaches have received increasing attention in recent years. But, most existing schemes often bear a number of drawbacks, in particular: (1) They mainly utilize transform coefficients, which are always fragile to some attacks, especially global geometric transforms, for watermark inserting and statistical modeling; (2) the adopted statistical models always cannot capture accurately both marginal distribution and various strong dependencies between coefficients; and (3) the used parameter estimation usually has high time complexity and poor computational accuracy. This has motivated us to introduce in this paper a novel statistical image watermarking in singular value decomposition (SVD)-undecimated discrete wavelet transform (UDWT) difference domain using vector Alpha Skew Gaussian (VB-ASG) distribution. We begin with a detailed study on the robustness and statistical characteristics of local SVD-UDWT difference coefficients of natural images. This study reveals the excellent robustness, highly non-Gaussian marginal statistics and strong dependencies of local SVD-UDWT difference coefficients. We also find that conditioned on their generalized neighborhoods, the local SVD-UDWT difference coefficients can be approximately modeled as vector Alpha Skew Gaussian (VB-ASG) variables. Meanwhile, model parameters can be estimated effectively by using approximate maximum likelihood estimation (AMLE) approach. Based on these findings, we model local SVD-UDWT difference coefficients using VB-ASG model that can capture marginal statistics and strong dependencies. Finally, we develop a new statistical image watermark decoder using the VB-ASG model and maximum likelihood (ML) decision rule. Our experimental evaluation results validate that our image watermarking leads to performance improvements comparable to several state-of-the-art statistical watermarking methods and some approaches based on convolutional neural networks. In particular, under the condition of the same watermarking capacity, the imperceptibility and robustness of this method show certain superiority compared with other algorithms.

In this paper, we have proposed an application of sparse-based morphological component analysis (MCA) to address the problem of classification of the epileptic seizure using time series electroencephalogram (EEG). MCA was employed to decompose the EEG signal segments considering its morphology during epileptic events using undecimated wavelet transform (UDWT), local discrete cosine transform (LDCT), and Dirac bases forming the over-complete dictionary. Frequency-modulated time frequency features were extracted after applying the Hilbert transform. Feature root mean instantaneous frequency square (RMIFS) and its parameters and parameters ratio are used in two different pairs for classification using support vector machine (SVM), showing good and comparable results.

It is a great challenge to maintain details while suppressing and eliminating noise of the image. Considering the nonconvexity property of the diffusion function and the hypersensitivity of the Laplace operator to noise in the Y-K model, a fourth-order PDE image denoising model (Con_G&L model) is proposed in this paper. This model is constructed by a new convexity-preserving diffusion function which guarantees the corresponding energy functional has a globally unique minimum solution. At the same time, the Gaussian filter is combined with the Laplace operator in this model, and as a result, the noisy image is smoothed before the diffusion process, which improves the ability of capturing the details and edges of the noisy image greatly. Furthermore, by analyzing the statistical properties of the undecimated discrete wavelet transform (UDWT) coefficients of noisy image, we observe that the noise information is mainly distributed in the high-frequency sub-bands, and based on this, the proposed Con_G&L model is applied in the high-frequency sub-bands of the UDWT to get the denoising method. The proposed method removes the image noise effectively with the image texture and other details of the image being maintained. Meanwhile, the generation of false edges and the staircase effect can be suppressed. A large number of simulation experiments verify the effectiveness of the proposed method.

In this study, the wavelet transform is applied to the seismic refraction data to provide an accurate first break picking result. The goal is not to apply the threshold to filter the data for the random noise suppression. We tried to introduce the wavelet domain as a replacement for the time domain. Thus, changing the domain is so hazardous; because the kernel effects of each transform could change the first break, which means that an erroneous refraction interpretation but note that DWT approaches have divided into many types based on frames, filter Banks and dimensions. In this way, this study has found one of the suitable domains of DWT that could provide a reliable result. Another aspect of this study that should be mentioned is that there is no reconstruction performed after decomposition. Our finding shows that to provide a better decomposition for the first break, picking the wavelet type must be short enough to avoid the effect of the kernel selection. We are, therefore, test db2 as a mother wavelet. After the decomposition, the data will be provided to a number of scales. Each scale has its frequency content, which means that random noise concentration will be at particular scales. These scales that contain more random noise will be eliminated and the best scale with the lowest possible amount of random noise will be chosen by the statistical approaches. After this selection, the first break selection will proceed to provide accurate interpretations. Subsequently, the velocity of each layer will be estimated using these first arrival times. Another achievement in this study is to find a true scale in DWT domain to avoid redundancy aspects. To select the true scale, a statistical approaches proved that we can find best scale for analysis.

Fiber signal denoising technology is one of the key technologies the OTDR or distributed fiber optic sensors, fiber optic equipment. Actual project application, proposed an improved undecimated discrete wavelet transform (UDWT) denoising technology, relative to traditional wavelet transform denoising technology, has the following characteristics: Denoised curve is more smooth; Better peak detection capability; Better small attenuation maintain capability; Better denoising capability. This technology has achieved very good results in OTDR equipment, beside it can be applied to other optical signal processing.

hrough analyzing problems brought on change detection methods of high-resolution remote sensing images, a novel change detection algorithm is proposed. First, feature images of image’s objects extracted using oriented-object method serve as data of input vector to estimate sub-space for Independent Component Analysis(ICA), which can improve effect of noise suppression, simultaneously, a new algorithm using self-adapted weight is proposed in order to extract image’s object, which optimizes processing method on oriented-object deeply；new partitioning scheme using undecimated discrete wavelet transform(UDWT) overcomes effectively prominent problem which shrinking of the size of input vector becomes leads to unprecisely estimation of sub-space for ICA. Compared with typical algorithm, such as ICA and UDWT, simulation results show that new algorithm improves robust and veracity of change detection for high-resolution images greatly.

The success of the oil and gas industry depends on utilizing a good geological model. The traditional interpretation of a geological model requires the use of both seismic and well log data. Since seismic data is an indirect measure of the lithology, it can miss out on some important lithological boundaries due to absence of high‐frequency data in the deeper section. Well log data, on the other hand, is a direct measure of the lithology and can be a good addition to demarcate lithological boundaries. This paper identifies the lithological boundaries using gamma‐ray log based on two different techniques without much involvement from the interpreter. The workflow considers the amplitude spectrum of the seismic data to tie with the well‐derived output. This data‐driven automated process can help an interpreter draw and develop a geological model quickly and efficiently.