Fractional Fourier Entropy Research Articles

Fractional Fourier Transform-Based Tensor RX for Hyperspectral Anomaly Detection

Anomaly targets in a hyperspectral image (HSI) are often multi-pixel, rather than single-pixel, objects. Therefore, algorithms using a test point vector may ignore the spatial characteristics of the test point. In addition, hyperspectral anomaly detection (AD) algorithms usually use original spectral signatures. In a fractional Fourier transform (FrFT), the signals in the fractional Fourier domain (FrFD) possess complementary characteristics of both the original reflectance spectrum and its Fourier transform. In this paper, a tensor RX (TRX) algorithm based on FrFT (FrFT-TRX) is proposed for hyperspectral AD. First, the fractional order of FrFT is selected by fractional Fourier entropy (FrFE) maximization. Then, the HSI is transformed into the FrFD by FrFT. Next, TRX is employed in the FrFD. Finally, according to the optimal spatial dimensions of the target and background tensors, the optimal AD result is achieved by adjusting the fractional order. TRX employs a test point tensor, making better use of the spatial characteristics of the test point. TRX in the FrFD exploits the complementary advantages of the intermediate domain to increase discrimination between the target and background. Six existing algorithms are used for comparison in order to verify the AD performance of the proposed FrFT-TRX over five real HSIs. The experimental results demonstrate the superiority of the proposed algorithm.

SECONDARY PULMONARY TUBERCULOSIS RECOGNITION BY ROTATION ANGLE VECTOR GRID-BASED FRACTIONAL FOURIER ENTROPY

Aim: Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis bacteria. This study plans to build a novel deep learning-based model for the accurate recognition of tuberculosis. Methods: We propose a novel model — rotation angle vector grid-based fractional Fourier entropy and deep stacked sparse autoencoder (RAVG-FrFE–DSSAE) — which uses RAVG-FrFE as a feature extractor and harnesses DSSAE as the classifier. Moreover, an 18-way MDA is introduced on the training set to avoid overfitting. Results: Experimental results of 10 runs of 10-fold CV showcase that this proposed RAVG-FrFE–DSSAE algorithm yields a reasonable performance including of 93.68[Formula: see text]±[Formula: see text]1.11% sensitivity, 94.38[Formula: see text]±[Formula: see text]1.11% specificity, 94.35[Formula: see text]±[Formula: see text]1.04% precision, 94.03[Formula: see text]±[Formula: see text]0.69% accuracy, 94.01[Formula: see text]±[Formula: see text]0.70% [Formula: see text]-score, 88.07[Formula: see text]±[Formula: see text]1.38% MCC, 94.01[Formula: see text]±[Formula: see text]0.70% FMI, and 0.9725 AUC, respectively. Conclusions: Our result outperforms the eight state-of-the-art approaches. Besides, the result shows the effectiveness of the 18-way MDA.

DSSAE: Deep Stacked Sparse Autoencoder Analytical Model for COVID-19 Diagnosis by Fractional Fourier Entropy

( Aim ) COVID-19 has caused more than 2.28 million deaths till 4/Feb/2021 while it is still spreading across the world. This study proposed a novel artificial intelligence model to diagnose COVID-19 based on chest CT images. ( Methods ) First, the two-dimensional fractional Fourier entropy was used to extract features. Second, a custom deep stacked sparse autoencoder (DSSAE) model was created to serve as the classifier. Third, an improved multiple-way data augmentation was proposed to resist overfitting. ( Results ) Our DSSAE model obtains a micro-averaged F1 score of 92.32% in handling a four-class problem (COVID-19, community-acquired pneumonia, secondary pulmonary tuberculosis, and healthy control). ( Conclusion ) Our method outperforms 10 state-of-the-art approaches.

Gingivitis detection by Fractional Fourier Entropy and Particle Swarm Optimization

INTRODUCTION: we propose a detection model of gingivitis based on feature extraction based on particle swarm optimization neural network with fractional Fourier entropy. OBJECTIVES: For the sake of reduce the diagnostic burden of doctors' frequent and high concentration. METHODS: Prim

Fruit category classification by fractional Fourier entropy with rotation angle vector grid and stacked sparse autoencoder

AbstractAimFruit category classification is important in factory packing and transportation, price prediction, dietary intake, and so forth.MethodsThis study proposed a novel artificial intelligence system to classify fruit categories. First, 2D fractional Fourier entropy with rotation angle vector grid was used to extract features from fruit images. Afterwards, a five‐layer stacked sparse autoencoder was used as the classifier.ResultsTen runs on the test set showed our method achieved a micro‐averaged F1 score of 95.08% for an 18‐category fruit dataset.ConclusionOur method gives better micro‐averaged F1 score than 10 state‐of‐the‐art approaches.

A combined model based on stacked autoencoders and fractional Fourier entropy for hyperspectral anomaly detection

ABSTRACT Nowadays, some models based on deep learning (DL) show good performance for hyperspectral anomaly detection (AD). However, most of these models only use original spectral signatures and the ability of signal enhancement and noise suppression may not be satisfactory. The above problems may be solved by transforming to the intermediate domain between the original reflectance spectrum and its Fourier transform based on fractional Fourier entropy (FrFE). In this paper, a combined model based on stacked autoencoders (SAE) and FrFE (CSF) is proposed for hyperspectral AD. First, the optimal fractional Fourier domain (FrFD) of the difference between original hyperspectral imagery (HSI) and its SAE reconstruction is obtained based on FrFE and the sparsity of test points in the optimal FrFD is calculated. Then, the optimal FrFD of the low-dimension dataset acquired through SAE is obtained and spatial sparsity divergence index (SDI) of test points in the optimal FrFD is calculated. Finally, the sparsity and spatial SDI are combined for the final detection result. Experiments performed on four hyperspectral datasets demonstrate the effectiveness of the proposed CSF algorithm.

Gingivitis detection by fractional Fourier entropy with optimization of hidden neurons

Oral health care has always been a more expensive medical program than other types of treatment. Gingivitis is one of the oral problems that often be overlooked until the pain of gum is noticed by patients. When initial symptoms of gingivitis occur, people are more likely to ignore mild symptoms and choose not to treat them. Until they feel great pain, they have to go to the hospital for treatment, which is too late for doctors and patients. The complexity of operation will increase and may lead to serious life risks when the disease becomes worsen, therefore it is important for dentists to detect the underlying warning signs of gingivitis as soon as possible. In order to reduce the difficulty of artificial detection and improve the detection efficiency, we propose a new intelligent detection method for gingivitis. The key eigenvalue extraction of the gingivitis image in this approach is derived from the fractional Fourier entropy (FRFE) feature extraction method. This efficient eigenvector value is used for a standard genetic algorithm (SGA) classification together with an optimization of hidden neurons (OHN), which allows us to obtain a more efficient detection result than other gingivitis recognition systems.

Hyperspectral Anomaly Detection by Fractional Fourier Entropy

Anomaly detection is an important task in hyperspectral remote sensing. Most widely used detectors, such as Reed-Xiaoli (RX), have been developed only using original spectral signatures, which may lack the capability of signal enhancement and noise suppression. In this article, an effective alternative approach, fractional Fourier entropy (FrFE)-based hyperspectral anomaly detection method, is proposed. First, fractional Fourier transform (FrFT) is employed as preprocessing, which obtains features in an intermediate domain between the original reflectance spectrum and its Fourier transform with complementary strengths by space-frequency representations. It is desirable for noise removal so as to enhance the discrimination between anomalies and background. Furthermore, an FrFE-based step is developed to automatically determine an optimal fractional transform order. With a more flexible constraint, i.e., Shannon entropy uncertainty principle on FrFT, the proposed method can significantly distinguish signal from background and noise. Finally, the proposed FrFE-based anomaly detection method is implemented in the optimal fractional domain. Experimental results obtained on real hyperspectral datasets demonstrate that the proposed method is quite competitive.

Multiple Sclerosis Identification Based on Fractional Fourier Entropy and a Modified Jaya Algorithm.

Aim: Currently, identifying multiple sclerosis (MS) by human experts may come across the problem of “normal-appearing white matter”, which causes a low sensitivity. Methods: In this study, we presented a computer vision based approached to identify MS in an automatic way. This proposed method first extracted the fractional Fourier entropy map from a specified brain image. Afterwards, it sent the features to a multilayer perceptron trained by a proposed improved parameter-free Jaya algorithm. We used cost-sensitivity learning to handle the imbalanced data problem. Results: The 10 × 10-fold cross validation showed our method yielded a sensitivity of 97.40 ± 0.60%, a specificity of 97.39 ± 0.65%, and an accuracy of 97.39 ± 0.59%. Conclusions: We validated by experiments that the proposed improved Jaya performs better than plain Jaya algorithm and other latest bioinspired algorithms in terms of classification performance and training speed. In addition, our method is superior to four state-of-the-art MS identification approaches.

Preliminary study on angiosperm genus classification by weight decay and combination of most abundant color index with fractional Fourier entropy

In order to develop an efficient angiosperm-genus classification system, we first collected petal image of Hibiscus, Orchis, and Prunus, by digital camera, and remove the backgrounds by region-growing method. Next, we proposed a novel feature-extraction method, which combined most abundant color index (MACI) and introduced the fractional Fourier entropy (FRFE). Third, we submitted the 41 features to a single-hidden layer feedforward neural-network (SLFN), with weight decay (WD) to avoid overfitting. The 10 × 10-fold cross validation showed our method achieved an overall accuracy of 98.92%. Without weight decay, the overall accuracy decreased to 95.50%. Our experiments validated that optimal decay factor is 0.1, and optimal number of hidden neurons is 15. This proposed method is excellent. It performs better than six state-of-the-art approaches and AlexNet. The weight decay helps to enhance generalization of our classifier.

Texture Analysis Method Based on Fractional Fourier Entropy and Fitness-scaling Adaptive Genetic Algorithm for Detecting Left-sided and Right-sided Sensorineural Hearing Loss

Texture Analysis Method Based on Fractional Fourier Entropy and Fitness-scaling Adaptive Genetic Algorithm for Detecting Left-sided and Right-sided Sensorineural Hearing Loss

Smart detection on abnormal breasts in digital mammography based on contrast-limited adaptive histogram equalization and chaotic adaptive real-coded biogeography-based optimization

In this study, we proposed a smart detection method for abnormal breasts in digital mammography. Firstly, preprocessing was carried out to deaden noises, enhance images, and remove background and pectoral muscles. Secondly, fractional Fourier entropy was employed to extract global features. Thirdly, the Welch’s t-test was utilized to select important features. Fourthly, the multi-layer perceptron was used as the classifier. Finally, we proposed a novel chaotic adaptive real-coded biogeography-based optimization to train the classifier. We implemented 10-fold cross-validation for statistical analysis. The experimental results showed our method selected in total 23 distinguishing features, and yielded a sensitivity of 92.54%, a specificity of 92.50%, a precision of 92.50%, and an accuracy of 92.52%. This proposed system performs better than five state-of-the-art methods. It is effective in abnormal breast detection.

A Multilayer Perceptron Based Smart Pathological Brain Detection System by Fractional Fourier Entropy.

This work aims at developing a novel pathological brain detection system (PBDS) to assist neuroradiologists to interpret magnetic resonance (MR) brain images. We simplify this problem as recognizing pathological brains from healthy brains. First, 12 fractional Fourier entropy (FRFE) features were extracted from each brain image. Next, we submit those features to a multi-layer perceptron (MLP) classifier. Two improvements were proposed for MLP. One improvement is the pruning technique that determines the optimal hidden neuron number. We compared three pruning techniques: dynamic pruning (DP), Bayesian detection boundaries (BDB), and Kappa coefficient (KC). The other improvement is to use the adaptive real-coded biogeography-based optimization (ARCBBO) to train the biases and weights of MLP. The experiments showed that the proposed FRFE + KC-MLP + ARCBBO achieved an average accuracy of 99.53% based on 10 repetitions of K-fold cross validation, which was better than 11 recent PBDS methods.

Tea Category Identification Using a Novel Fractional Fourier Entropy and Jaya Algorithm

This work proposes a tea-category identification (TCI) system, which can automatically determine tea category from images captured by a 3 charge-coupled device (CCD) digital camera. Three-hundred tea images were acquired as the dataset. Apart from the 64 traditional color histogram features that were extracted, we also introduced a relatively new feature as fractional Fourier entropy (FRFE) and extracted 25 FRFE features from each tea image. Furthermore, the kernel principal component analysis (KPCA) was harnessed to reduce 64 + 25 = 89 features. The four reduced features were fed into a feedforward neural network (FNN). Its optimal weights were obtained by Jaya algorithm. The 10 × 10-fold stratified cross-validation (SCV) showed that our TCI system obtains an overall average sensitivity rate of 97.9%, which was higher than seven existing approaches. In addition, we used only four features less than or equal to state-of-the-art approaches. Our proposed system is efficient in terms of tea-category identification.

Pathological Brain Detection by a Novel Image Feature—Fractional Fourier Entropy

Aim: To detect pathological brain conditions early is a core procedure for patients so as to have enough time for treatment. Traditional manual detection is either cumbersome, or expensive, or time-consuming. We aim to offer a system that can automatically identify pathological brain images in this paper. Method: We propose a novel image feature, viz., Fractional Fourier Entropy (FRFE), which is based on the combination of Fractional Fourier Transform (FRFT) and Shannon entropy. Afterwards, the Welch’s t-test (WTT) and Mahalanobis distance (MD) were harnessed to select distinguishing features. Finally, we introduced an advanced classifier: twin support vector machine (TSVM). Results: A 10 × K-fold stratified cross validation test showed that this proposed “FRFE + WTT + TSVM” yielded an accuracy of 100.00%, 100.00%, and 99.57% on datasets that contained 66, 160, and 255 brain images, respectively. Conclusions: The proposed “FRFE + WTT + TSVM” method is superior to 20 state-of-the-art methods.