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In this paper, a novel approach to feature extraction with wavelet and fractal theories is presented as a powerful technique in pattern recognition. The motivation behind using fractal transformation is to develop a high-speed feature extraction technique. A multiresolution family of the wavelets is also used to compute information conserving micro-features. In this study, a new fractal feature is reported. We employed a central projection method to reduce the dimensionality of the original input pattern, and a wavelet transform technique to convert the derived pattern into a set of subpatterns, from which the fractal dimensions can readily be computed. The new feature is a measurement of the fractal dimension, which is an important characteristic that contains information about the geometrical structure. This new scheme includes utilizing the central projection transformation to describe the shape, the wavelet transformation to aid the boundary identification, and the fractal features to enhance image discrimination. The proposed method reduces the dimensionality of a 2-D pattern by way of a central projection approach, and thereafter, performs Daubechies' wavelet transform on the derived 1-D pattern to generate a set of wavelet transform subpatterns, namely, curves that are non-self-intersecting. Further from the resulting non-self-intersecting curves, the divider dimensions are computed with a modified box-counting approach. These divider dimensions constitute a new feature vector for the original 2-D pattern, defined over the curve's fractal dimensions. We have conducted several experiments in which a set of printed Chinese characters, English letters of varying fonts and other images were classified. Based on the formulation of our new feature vector, the experiments have satisfying results.

Green plant species identification plays an important role in so many aspects, such as ecological environment protection, Chinese medicine preparation, agricultural and horticultural application, etc. A method on green plants recognition based on wavelet transform and variable local edge patterns (VLEP) is proposed in this paper. Firstly, the original image is decomposed by wavelet transformation. Then texture features are extracted using VLEPs. At the same time, block-based and multi-resolution ideas are considered together to extract features after images are transformed by wavelet. Finally, the fused texture features are classified by the nearest neighbor method. The experimental results show that the proposed method is a promising method for recognizing the common green plants with the natural and complex background compared with the other state-of-the-art methods, and combination of block-based and multi-resolution ideas can further improve the accuracy rate effectively.

With the rapid development of digital cameras and smart phones, the image identification system in current times will be of a great impact. This will cause the form of image information to increase serious security issues. Especially, the emergence of the recaptured image makes conventional digital image forensics algorithm invalid. Therefore, a new image forensics algorithm is urgently needed to identify the recaptured image. In this paper, a new recaptured image identifying algorithm is put forward based on wavelet transformation and noise analysis by analyzing the differences between the real and recaptured images generated in the imaging process. First, the proposed algorithm extracts mean value, variance and skewness as wavelet characteristic from the high-frequency images and low-frequency images by wavelet transformation. Meanwhile, the proposed algorithm analyzes the noise image by means of local binary pattern to extract noise characteristic. Finally, the support vector machine is applied to classify the recaptured image with wavelet characteristics and noise characteristics. The results show the presented method can not only identify the recaptured image obtained from different media but also have better identification rate, and the dimension of the characteristic vector is also lower than those obtained by other algorithms.

In order to quantitatively analyze the proportions of independent components in mixtures, it is necessary to extract line spectra corresponding to those components from the spectrum signal of some mixture and evaluate the amplitude of the spectral lines. Multiple factors cause the drift and tilt of a spectrum signal’s baseline, such as environment noises, instrument bias, and sample size, which affect the identification and quantitative analysis of the line spectra superimposed on the baseline. Therefore, the baseline of a spectrum signal should be removed before the line spectra are identified. A baseline correction algorithm based on Catastrophe Point detection and Lipschitz exponent’s analysis is proposed in this paper. With the algorithm, the strong spectral lines are identified and removed, and then the spectral baseline is evaluated without the interference of strong spectrum signals. First, catastrophe points are located based on the local modulus maxima theory of wavelet coefficients. Second, according to the Lipschitz exponent theory, the strong spectral peaks’ regions are identified and removed by a smoothing filter. Then the slowly varying spectrum is segmented adaptively and fitted by the least square fitting method. After the segments are attached and the boundaries are smoothed, the baseline of the spectrum is acquired and extracted finally. The algorithm is more accurate than classical ones because identifying the baseline is implemented after strong peaks are removed, so their influences to baseline extracting are eliminated. The results of experiments show that the algorithm is accurately performed for the spectrum signal of a gas mixture, $S{F}_6$.

This paper introduces a method for detection and identification of IGBT-based drive open-circuit fault of DTC induction motor drives. The detection mechanism is based on soft set theory and wavelet decomposition, if it is detailed, ⊼-product decision making method and sym2 wavelet decomposition have been used in the detection mechanism. In this method, the stator currents have been used as an input to the system. The stator current has been used for the detection of the fault. The signal analysis has been performed up to the six level details wavelets decomposition. Faulty switch is detected by applying soft set theory to sixth level wavelets transformation. This is the first time applied to inverter in induction motor drives fault detection. The results demonstrate that the proposed fault detection and diagnosis system has very good capabilities.

We consider the problem of cancer classification from gene expression data. We propose using a mutual information-based gene or feature selection method where features are wavelet-based. The bootstrap technique is employed to obtain an accurate estimate of the mutual information. We then develop a nonlinear probit Bayesian classifier consisting of a linear term plus a nonlinear term, the parameters of which are estimated using the Gibbs sampler. These new methods are applied to analyze breast-cancer data and leukemia data. The results indicate that the proposed gene and feature selection method is very accurate in breast-cancer and leukemia classifications.

The process of retinal vessel segmentation is important for detection of various eye conditions including the effect of diabetes on eyes, or diabetic retinopathy. As we know, the retinal microvasculature is unique since it is the only part of the human circulation system that can be directly and non-evasively visualized in vivo; readily photographed as well as subjected to digital image analysis. This paper explores a new technique for detecting the idiosyncrasies of retina images, for which we have reviewed some well-known image segmentation algorithms that help in detecting retinal abnormalities. In this work, we have also focused on the extraction of the vessel from retina images and developed an automated diagnostic system for diabetic retinopathy. This paper represents techniques, such as the snake model that was used for auto-extraction of retinal blood vessels and use of wavelet decomposition and back propagation neural network to extract the retinal vessels features and analyze the dataset. Finally, an analysis of performance of the vessel segmentation algorithm and wavelet analysis on standard image databases has been done. In this context, we have used F-score for validation of the result.

In this paper, a novel denoising method based on wavelet, extended adaptive Wiener filter and the bilateral filter is proposed for digital images. Production of mode is accomplished by the genetic algorithm. The proposed extended adaptive Wiener filter has been developed from the adaptive Wiener filter. First, the genetic algorithm suggest some hybrid models. The attributes of images, including peak signal to noise ratio, signal to noise ratio and image quality assessment are studied. Then, in order to evaluate the model, the values of attributes are sent to the Fuzzy deduction system. Simulations and evaluations mentioned in this paper are accomplished on some standard images such as Lena, boy, fruit, mandrill, Barbara, butterfly, and boat. Next, weaker models are omitted by studying of the various models. Establishment of new generations performs in a form that a generation emendation is carried out, and final model has a more optimum quality compared to each two filters in order to obviate the noise. At the end, the results of this system are studied so that a comprehensive model with the best performance is to be found. Experiments show that the proposed method has better performance than wavelet, bilateral, Butterworth, and some other filters.

In this paper, a novel similar image retrieval scheme based on wavelet transformation will be presented. Our scheme is built upon a block-based query system. Our new scheme employs the wavelet transformation technique to transform each block in the spatial domain to the wavelet domain. Then, from each transformed block, the mean value and the edge types are extracted. These extracted features are then used to compute the similarity between a query image and the images in the database. In order to increase the similarity in the query result, the current block can be further divided into many sub-blocks, and then features can be extracted from these sub-blocks. Finally, the query result will be a set of ranked images in the database with respect to the query. According to our experiment, the proposed scheme can obtain satisfactory results.

The main objective of this paper is to investigate the fractional Hankel wavelet transformation and to study some basic properties. An inversion formula for this fractional Hankel wavelet transformation is also obtained. Some examples of fractional Hankel wavelet transformation are given.

An adaptive digital watermarking algorithm was proposed, in which Gold codes was applied, and the watermark was inserted into the wavelet domain of the carrier image according to the analysis of human visual system. The robustness and efficiency of the algorithm is enhanced because of the introduction of CDMA. At first, Gold codes were generated by m-sequences, and the watermark was encoded through CDMA technique, then the encoded information was inserted into the wavelet domain adaptively according to JND (Just Noticeable Difference). Experiment results show that the embedded watermark is invisible, and can resist to Gaussian Noise, JPEG compression and median filtering.

This paper puts forwards the detecting algorithm and the extracting algorithm for hidden information, which are respectively based on domain of variation and still color digital image. Efforts are made to explore the effects of the amplified information of wavelet transformation, the displaying of hidden information and its opposite process. Based on the model of the influence of information hiding on carrier properties, this paper establishes a general mathematical model for extracting hidden information and a positive transfer function and a reverse transfer function oriented to the set of “the influence of information hiding on carrier properties”. After the information is marked, analyzed and extracted, the hidden information can be restored, with satisfactory results for information recognition and analysis. As a result, it is possible to extract electronic evidence of hidden data rapidly.

Non-destructive testing is developing in the direction of automatization and intelligentization, but there still exists some difficulty in analyzing quantitatively the signal of magnetic flux leakage. The Mallat quick algorithm of wavelet transformation is described simply. As an advanced digital signal processing method, wavelet transformation can be used to compress data and separate the signal and the noise in the magnetic flux leakage inspection. So introducing wavelet transformation into the magnetic flux leakage inspection provides high feasibility for the quantitative analysis of the test signals.

Based on the composite model of wavelet transformation and neural networks, the method of image definition recognition has stronger ability in image edge character extraction, nonlinear process, self-adapted study and pattern recognition. In the paper two-dimension (2D) discrete wavelet transformation is used to extract image signal character, and 7 wavelet components and 16 statistical values obtained from the statistical process of original image are treated as the image characteristic values for the follow-up recognition and analysis. The 5 layer model of BP neural networks is constructed to perform image definition recognition. A fastest descent method with an additional momentum item of variable step length is adopted to adjust network weights. The designed neural networks first train the training set composed by 75 images and then perform experimental verification for the testing set composed by 102 images. The results showed that this is a very effective identifying method with a high recognition rate.

Human detection algorithm based on Support Vector Machines and system realization were system-matically discussed. We extract local shape mutation feature of the targets through wavelet transformation of the static image, and combine the gait feature of the dynamic frame. We also use a better learning and generalization of two-layer support vector machines in a small sample conditions. Our approach has real-time, high accuracy and wide range of application.

Non-destructive testing is developing in the direction of automatization and intelligentization, but there still exists some difficulty in analyzing quantitatively the signal of magnetic flux leakage. The Mallat quick algorithm of wavelet transformation is described simply. As an advanced digital signal processing method, wavelet transformation can be used to compress data and separate the signal and the noise in the magnetic flux leakage inspection. So introducing wavelet transformation into the magnetic flux leakage inspection provides high feasibility for the quantitative analysis of the test signals.

Scrambling and gray-level spreading are two methods of image scrambling, whose aim is both to make the scrambled image unrecognizable. In this paper, two scrambling and spreading algorithms are proposed which are wavelet-based scrambling, spreading algorithm and local area single point spreading algorithm. These algorithms change not only the points' position but also the gray value. The experimental results show that these algorithms have good scrambling effect and security, as well as strong anti-attack ability.

Complex noise is not only distributed in high-frequency band, but also in low-frequency band in the application of engineering. To solve this problem, an integrated denoising method is proposed in this paper. This algorithm employed a denoising method based on singular value decomposition to eliminate the weak low-frequency noise and partial highfrequency noise in signals, and then got the preliminary de-noised signals. Later a wavelet transform denoising method was used to remove the high-frequency band noise which is in the preliminary de-noised signals effectively, and get the final de-noised signals. The proposed method for noise reduction was simulated in MATLAB, which demonstrated that it is suitable for depressing the noise that magnitude is not very weak in the whole frequency band. Furthermore, the SNR of this integrated denoising method is higher than other algorithms possessing the single denoising structure.

Identifying and mining outlier data is very important data analysis. Anomalies may result from disrupted or contaminated process, or conform to some rare but real situations. Applying outlier data mining in data analysis of tracking ships significantly enhances analysis and diagnose capabilities. This paper proposes a wavelet-analysis-based method after comparing outlier data mining methods. Wavelet multi-scale analysis and wavelet local analysis are applied to study the identification of outlier data. This method takes into account the noise suppressing and conserves local anomalies. It significantly enhances detection of outlier data.