Image Reconstruction from Multiscale Singular Points Based on the Dual-Tree Complex Wavelet Transform

The representation of an image with several multiscale singular points has been the main concern in image processing. Based on the dual-tree complex wavelet transform (DT-CWT), a new image reconstruction (IR) algorithm from multiscale singular points is proposed. First, the image was transformed by DT-CWT, which provided multiresolution wavelet analysis. Then, accurate multiscale singular points for IR were detected in the DT-CWT domain due to the shift invariance and directional selectivity properties of DT-CWT. Finally, the images were reconstructed from the phases and magnitudes of the multiscale singular points by alternating orthogonal projections between the CT-DWT space and its affine space. Theoretical analysis and experimental results show that the proposed IR algorithm is feasible, efficient, and offers a certain degree of denoising. Furthermore, the proposed IR algorithm outperforms other classical IR algorithms in terms of performance metrics such as peak signal-to-noise ratio, mean squared error, and structural similarity.

Automatic Diagnosis of Epileptic Seizures in EEG Signals Using Fractal Dimension Features and Convolutional Autoencoder Method

This paper proposes a new method for epileptic seizure detection in electroencephalography (EEG) signals using nonlinear features based on fractal dimension (FD) and a deep learning (DL) model. Firstly, Bonn and Freiburg datasets were used to perform experiments. The Bonn dataset consists of binary and multi-class classification problems, and the Freiburg dataset consists of two-class EEG classification problems. In the preprocessing step, all datasets were prepossessed using a Butterworth band pass filter with 0.5–60 Hz cut-off frequency. Then, the EEG signals of the datasets were segmented into different time windows. In this section, dual-tree complex wavelet transform (DT-CWT) was used to decompose the EEG signals into the different sub-bands. In the following section, in order to feature extraction, various FD techniques were used, including Higuchi (HFD), Katz (KFD), Petrosian (PFD), Hurst exponent (HE), detrended fluctuation analysis (DFA), Sevcik, box counting (BC), multiresolution box-counting (MBC), Margaos-Sun (MSFD), multifractal DFA (MF-DFA), and recurrence quantification analysis (RQA). In the next step, the minimum redundancy maximum relevance (mRMR) technique was used for feature selection. Finally, the k-nearest neighbors (KNN), support vector machine (SVM), and convolutional autoencoder (CNN-AE) were used for the classification step. In the classification step, the K-fold cross-validation with k = 10 was employed to demonstrate the effectiveness of the classifier methods. The experiment results show that the proposed CNN-AE method achieved an accuracy of 99.736% and 99.176% for the Bonn and Freiburg datasets, respectively.

Analyzing Vibration Mechanism of Angular Contact Ball Bearing with Compound Faults on Inner and Outer Rings

This paper investigates a method to dynamically model compound faults on the inner and outer rings of an angular contact ball bearing as well as their effects on its dynamic behavior. Gupta’s dynamic modeling method is used to consider changes in the deformation and direction of the contact load when the ball passes through the damaged area and to develop a dynamic model of compound faults in the angular contact ball bearing. The step-changing fourth-order Runge–Kutta method is used to solve the dynamic compound fault model. The time-domain signal of vibration responses in the case of a single fault in the inner and outer rings exhibited a certain periodicity, and the frequency of faults in the envelope spectrum was clear. By comparison, the periodicity of compound faults was not clear. The signals of compound faults were decomposed by the dual-tree complex wavelet transform to identify their characteristic frequency. Errors occurred between the characteristic frequency of the theoretical fault and its simulated value. They increased with the rotational speed and decreased with an increase in axial load, whereas the influence of radial load on them was minor. For compound faults on the inner and outer rings of an angular contact ball bearing, this study provides a modeling method that can describe changes in the deformation and direction of the contact load when the ball passes through the damaged area of the inner and outer rings. The work here can provide an important foundation for fault identification in angular contact ball bearings.

Image Representation Method Based on Complex Wavelet Transform and Phase Congruency, with Automatic Threshold Selection

Image representation is an active area of research with increasing applications in military and defense. Image representation aims at representing an image with lesser number of coefficients than the actual image, without affecting the image quality. It is the first step in image compression. Once the image is represented by using some set of coefficients, it is further encoded using various compression algorithms. This paper proposes an adaptive method for image representation, which uses Complex Wavelet transform and the concept of phase congruency, where the number of coefficients used for image representation depends on the information content in the input image. The efficiency of the proposed method has been assessed by comparing the number of coefficients used to represent the image using the proposed method with that used when Complex Wavelet transform is used for image representation. The resultant image quality is determined by computing the PSNR values and Normalized Cross Correlation. Experiments carried out show highly promising results, in terms of the reduction in the number of coefficients used for image representation and the quality of the resultant image.

DEPSO With DTCWT Algorithm for Multimodal Medical Image Fusion

In this paper, the authors propose an algorithm of hybrid particle swarm with differential evolution (DE) operator, termed DEPSO, with the help of a multi-resolution transform named dual tree complex wavelet transform (DTCWT) to solve the problem of multimodal medical image fusion. This hybridizing approach aims to combine algorithms in a judicious manner, where the resulting algorithm will contain the positive features of these different algorithms. This new algorithm decomposes the source images into high-frequency and low-frequency coefficients by the DTCWT, then adopts the absolute maximum method to fuse high-frequency coefficients; the low-frequency coefficients are fused by a weighted average method while the weights are estimated and enhanced by an optimization method to gain optimal results. The authors demonstrate by the experiments that this algorithm, besides its simplicity, provides a robust and efficient way to fuse multimodal medical images compared to existing wavelet transform-based image fusion algorithms.

Lifting dual tree complex wavelets transform

We describe the lifting dual tree complex wavelet transform (LDTCWT), a type of lifting wavelets remodeling that produce complex coefficients by employing a dual tree of lifting wavelets filters to get its real part and imaginary part. Permits the remodel to produce approximate shift invariance, directionally selective filters and reduces the computation time (properties lacking within the classical wavelets transform). We describe a way to estimate the accuracy of this approximation and style appropriate filters to attain this. These benefits are often exploited among applications like denoising, segmentation, image fusion and compression. The results of applications shrinkage denoising demonstrate objective and subjective enhancements over the dual tree complex wavelet transform (DTCWT). The results of the shrinkage denoising example application indicate empirical and subjective enhancements over the DTCWT. The new transform with the DTCWT provide a trade-off between denoising computational competence of performance, and memory necessities. We tend to use the PSNR (peak signal to noise ratio) alongside the structural similarity index measure (SSIM) and the SSIM map to estimate denoised image quality.

Image Focus Enhancement Using Focusing Filter and DT-CWT Based Image Fusion

Combining multi-model images of the same scene that have different focus distances can produce clearer and sharper images with a larger depth of field. Most available image fusion algorithms are superior in results. However, they did not take into account the focus of the image. In this paper a fusion method is proposed to increase the focus of the fused image and to achieve highest quality image using the suggested focusing filter and Dual Tree-Complex Wavelet Transform. The focusing filter consist of a combination of two filters, which are Wiener filter and a sharpening filter. This filter is used before the fusion operation using Dual Tree-Complex Wavelet Transform. The common fusion rules, which are the average-fusion rule and maximum-fusion rule, were used to obtain the fused image. In the experiment, using the focus operators, the performance of the proposed fusion algorithm was compared with the existing algorithms. The results showed that the proposed method is better than these fusion methods in terms of the focus and quality.

A Novel Zero Watermarking Based on DT-CWT and Quaternion for HDR Image

This paper presents a high dynamic range (HDR) image zero watermarking method based on dual tree complex wavelet transform (DT-CWT) and quaternion. In order to be against tone mapping (TM), DT-CWT is used to transform the three RGB color channels of the HDR image for obtaining the low-pass sub-bands, respectively, since DT-CWT can extract the contour of the HDR image and the contour change of the HDR image is small after TM. The HDR image provides a wide dynamic range, and thus, three-color channel correlations are higher than inner-relationships and the quaternion is used to consider three color channels as a whole to be transformed. Quaternion fast Fourier transform (QFFT) and quaternion singular value decomposition (QSVD) are utilized to decompose the HDR image for obtaining robust features, which is fused with a binary watermark to generate a zero watermark for copyright protection. Furthermore, the binary watermark is scrambled for the security by using the Arnold transform. Experimental results denote that the proposed zero-watermarking method is robust to TM and other image processing attacks, and can protect the HDR image efficiently.