Undecimated Dual Tree Complex Wavelet Transform Research Articles

UDTCWT-PHFMs Domain Statistical Image Watermarking Using Vector BW-Type R Distribution

For any image watermarking algorithm, how to achieve the trade-off among robustness, imperceptibility, and watermark capacity is a challenging problem because of their mutually constrained relationship. In this paper, we design a statistical-based image watermarking system to solve the trade-off problem. In embedding process, consider the imperceptibility and the robustness, we inventively combine the undecimated dual tree complex Wavelet transform (UDTCWT) and the polar harmonic Fourier moments (PHFMs) to obtain the UDTCWT-PHFMs magnitudes as the watermark carriers, and we embed watermark signals in multiplicative manner. In modeling phase, by analyzing the statistical property and the multiple correlations of the UDTCWT-PHFMs magnitudes, we bound the magnitudes of different directions into the vector groups, and then we model them with the vector Roy type bivariate Weibull (BW-Type R) distribution so that we can capture accurately the marginal characteristics, the inter-scale dependencies, and the inter-orientation dependencies at the same time. Moreover, we obtain the model parameters with the double looped maximum likelihood estimation (double-looped MLE). Benefit from the reliable modeling result, we finally derive a novel specific image watermark decoder to blindly extract the hidden watermarks. Extensive experiment results declare the designed statistical image watermarking system achieves the better balance among imperceptibility, robustness, and payload.

Bidirectional RNN based early prediction of CVDs using ECG Signals for Type 2 diabetic patients

The ECG signal is important for early diagnosis of heart abnormalities. Type 2 Diabetic individuals’ ECG signals provide pertinent data about their hearts and are one of the most important diagnostic techniques used by doctors to identify cardiovascular diseases. The suggested study uses feature extraction and Bi-RNN based classification to analyse ECG signals of Type 2 patients. To reduce noise from the ECG signal, a hybrid preprocessing filter made up of a Median and Savitzky-Golay filter. Undecimated dual tree complex wavelet transform (UDTCWT) along with Detrended fluctuation (DA) analysis and empirical orthogonal function (EOF) analysis are then used to extract features. These features are classified with Bidirectional RNN. The proposed method was tested on the MIT-BIH, Physionet and DICARDIA databases, and the findings show that it achieves an average accuracy of 97.6% when compared to conventional techniques.

Bidirectional Recurrent Neural Network Based Early Prediction of Cardiovascular Diseases using Electrocardiogram Signals for Type 2 Diabetic Patients

Introduction: The electrocardiogram (ECG) signal is important for early diagnosis of heart abnormalities. Type 2 diabetic individuals’ ECG signals provide pertinent data about their heart and are one of the most important diagnostic techniques used by doctors to identify Cardiovascular Disease (CVD). Bidirectional Recurrent Neural Network (RNN) classifies the features linked to normal and abnormal stage ECG signal. Aim: To analyse ECG signals of type 2 diabetic patients for early prediction of CVDs using feature extraction and bidirectional RNN based classification. Materials and Methods: This was a secondary data-based modelling study at Shri Ramasamy Memorial University Sikkim, India from December 2020 to January 2022. Different noises were removed by hybrid preprocessing filter made up of a Median and Savitzky-Golay filter. Undecimated Dual Tree Complex Wavelet Transform (UDTCWT) along with Detrended fluctuation (DA) analysis and Empirical Orthogonal Function (EOF) analysis were then used to extract features. These features were classified with Bidirectional RNN. Results: The proposed method was tested on the MIT-BIH, Physionet and DICARDIA databases, and the findings showed that it achieves an average accuracy of 97.6% when compared to the conventional techniques. Conclusion: The proposed method proves to be the most effective way for detecting anomalies in ECG signals in both the early and pathological stages. This method is also effective to diagnose the early intervention of cardiovascular symptoms.

Texture image segmentation using Vonn mixtures-based hidden Markov tree model and relative phase

Texture segmentation is a frequently occurring and challenging problem in many computer vision and pattern recognition applications. The importance of phase information for texture analysis has been earlier established for many image processing. Undecimated dual tree complex wavelet transform (UDTCWT) is a new image decomposition. It not only provides exact translational invariance and rich directional selectivity, but also offers perfect consistent relative phase relationships across scales. In this paper, we propose a novel texture image segmentation framework using Vonn mixtures-based hidden Markov trees (HMT) and UDTCWT domain relative phase. Firstly, we analyze the robustness and marginal distribution of UDTCWT relative phases, and various strong dependencies between UDTCWT relative phases. Then, we propose a new HMT statistical model in UDTCWT domain, namely Vonn mixtures-based HMT, by describing the UDTCWT relative phases statistical distribution with Vonn mixtures (VM), which can capture both the subband marginal distributions and the strong dependencies across scales of the UDTCWT relative phases. Finally, we develop a texture image segmentation framework using the Vonn mixtures-based HMT model of UDTCWT domain relative phases, in which expectation–maximization (EM) parameter estimation, Bayesian multiscale raw segmentation, and context based multiscale fusion are used. Comparing to the state-of-the-art techniques, the proposed method can not only produce high-quality segmentation results in a more efficient way, but also keep a lot of boundary details in the segmentation results.

Image denoising in undecimated dual-tree complex wavelet domain using multivariate t-distribution

Denoising of natural images is a basic problem in image processing. The present paper proposes a new algorithm for image denoising based on the maximum a-posteriori (MAP) estimator in undecimated dual-tree complex wavelet transform. The undecimated dual-tree complex wavelet transform (UDT-CWT), along with the directional selectivity of the dual-tree complex wavelet transform (DT-CWT), offers exact translational invariance property through removing the down-sampling of filter outputs together with the up-sampling of the complex filter pairs of DT-CWT. These properties are very important in image denoising. The performance of the MAP estimator depends strongly on the probability of noise-free wavelet coefficients. In our proposed denoising method, multivariate t-distribution is applied as the prior probability of noise-free coefficients. The t-distribution can accurately model the statistics of wavelet coefficients, which have peaky and heavy-tailed characteristics. On the other hand, the multivariate model makes it possible to take into account the dependencies of wavelet coefficients and their neighbors. Also, in our work, the necessary parameters of the multivariate distribution will be estimated in a locally-adaptive way to improve the denoising results via using the correlations among the amplitudes of neighbor coefficients. Simulation results delineate that the proposed algorithm outperforms state-of-the-art denoising algorithms in the literature.

Blind Image Watermark Decoder in UDTCWT Domain Using Weibull Mixtures-Based Vector HMT

As one promising solution, digital watermarking has been proposed to resolve image copyright protection and content authentication, and has been applied successfully in many fields. Owing to their excellent description capability and invariance property, statistical models have become a popular tool for the image watermarking resulting in favorable trade-offs among imperceptibility, robustness and data payload. By modeling the robust undecimated dual tree complex Wavelet transform (UDTCWT) coefficient magnitudes with the Weibull mixtures based vector hidden Markov trees (HMT) and employing maximum likelihood (ML) test criterion, we propose a new image watermarking approach in UDTCWT domain in this paper. Our image watermarking approach consists of two parts, namely, embedding and extracting. In the embedding process, we compute the robust UDTCWT coefficient magnitudes with UDTCWT domain real/imaginary parts, and insert the digital watermark into the significant UDTCWT coefficient magnitude subband. In the extracting phase, robust UDTCWT coefficient magnitudes are firstly modeled by employing the Weibull mixture-based vector HMT, where the statistical properties of UDTCWT magnitudes are captured accurately. Then the expectation/conditional maximization (ECM) approach is introduced to estimate the statistical model parameters. Finally, an image watermark decoder for multiplicative watermarking is developed using the Weibull mixtures based vector HMT and ML test. The experiments show that the proposed method not only improves the imperceptibility, but also increases the robustness performance and outperforms state-of-the-art methods on a set of standard test images.

Hybrid SAR Speckle Reduction Using Complex Wavelet Shrinkage and Non-Local PCA-Based Filtering

In this paper, a new hybrid despeckling method, based on Undecimated Dual-Tree Complex Wavelet Transform (UDT-CWT) using maximum a posteriori (MAP) estimator and non-local Principal Component Analysis (PCA)-based filtering with local pixel grouping (LPG-PCA), was proposed. To achieve a heterogeneous-adaptive speckle reduction, SAR image is classified into three classes of point targets, details, or homogeneous areas. The despeckling is done for each pixel based on its class of information. Logarithm transform was applied to the SAR image to convert the multiplicative speckle into additive noise. Our proposed method contains two principal steps. In the first step, denoising was done in the complex wavelet domain via MAP estimator. After performing UDT-CWT, the noise-free complex wavelet coefficients of the log-transformed SAR image were modeled as a two-state Gaussian mixture model. Furthermore, the additive noise in the complex wavelet domain was considered as a zero-mean Gaussian distribution. In the second step, after applying inverse UDT-CWT, an iterative LPG-PCA method was used to smooth the homogeneous areas and enhance the details. The proposed method was compared with some state-of-the-art despeckling methods. The experimental results showed that the proposed method leads to a better speckle reduction in homogeneous areas while preserving details.

Image Enhancement through Denoising and Retrieval of Vegetation Parameters from Landsat8

This paper proposed the enhancement of Landsat8 imagery through an Un-decimated Dual-Tree Complex Wavelet Transform (UDT-CWT) based denoising method and modified homographic filter for edge preservation. This work has been extended by estimating several vegetation parameters like Normalized Difference of Vegetation Index (NDVI), Green Normalized Difference Vegetation Index (GNDVI), Modified Soil Adjusted Vegetation Index (MASVI), and Soil & Atmospherically Resistant Vegetation Index (SARVI). Once the estimation of these parameters was done, the effect of noise was verified. Wavelet decomposes the image into frequency subbands and de-noises each subband separately. These subbands help to increase the resolution. The general problem of the homomorphic filter is that it doesn’t enhance the Low-frequency components which also play a key role in estimating Vegetation Indices (VI).So it was modified to enhance the high-frequency components as well as low-frequency details. Monitoring of vegetation parameters using remote sensing is one of the prominent ways in the estimation of crop yield, Land Use Land Cover (LULC), Water resource management, Drought management, etc. The high-resolution image is more preferable than moderate resolution image to retrieve VI. Image denoising and enhancing the spatial resolution helps to retrieve the parameters well and accurate. The proposed algorithm was working on the images of Landsat8.

Denoising of images using principal component analysis and undecimated dual tree complex wavelet transform

Here, a method based on the combination of Undecimated Discrete Wavelet Transform (UDWT) and Dual Tree Complex Wavelet Transform (DTCWT) with PCA for denoising images corrupted by Gaussian noise is proposed. The blend of UDWT and DTCWT results in Undecimated Dual Tree Complex Wavelet Transform (UDTCWT) which is a one-to-one relationship between co-located complex coefficients in all sub-bands and offers improved lower scale sub-band localisation together with improved directional selectivity. But each wavelet coefficients and its parent are not aligned properly. The proposed method uses UDTCWT with PCA to obtain the compaction of signal energy in to a few principal components by spreading the noise over all the transformed coefficients. These coefficients allow removing the noise, with a suitable locally adaptive window shrinkage function. This denoising method is tested on standard test images. The results show that this method is better than existing methods in terms of PSNR.

Denoising of images using principal component analysis and undecimated dual tree complex wavelet transform

Here, a method based on the combination of Undecimated Discrete Wavelet Transform (UDWT) and Dual Tree Complex Wavelet Transform (DTCWT) with PCA for denoising images corrupted by Gaussian noise is proposed. The blend of UDWT and DTCWT results in Undecimated Dual Tree Complex Wavelet Transform (UDTCWT) which is a one-to-one relationship between co-located complex coefficients in all sub-bands and offers improved lower scale sub-band localisation together with improved directional selectivity. But each wavelet coefficients and its parent are not aligned properly. The proposed method uses UDTCWT with PCA to obtain the compaction of signal energy in to a few principal components by spreading the noise over all the transformed coefficients. These coefficients allow removing the noise, with a suitable locally adaptive window shrinkage function. This denoising method is tested on standard test images. The results show that this method is better than existing methods in terms of PSNR.

An Improved Infrared/Visible Fusion for Astronomical Images

An undecimated dual tree complex wavelet transform (UDTCWT) based fusion scheme for astronomical visible/IR images is developed. The UDTCWT reduces noise effects and improves object classification due to its inherited shift invariance property. Local standard deviation and distance transforms are used to extract useful information (especially small objects). Simulation results compared with the state-of-the-art fusion techniques illustrate the superiority of proposed scheme in terms of accuracy for most of the cases.