Table of Links Abstract and 1. Introduction 2. Preliminaries and 2.1. Blind deconvolution 2.2. Quadratic neural networks 3. Methodology 3.1. Time domain quadratic convolutional filter 3.2. Superiority of cyclic features extraction by QCNN 3.3. Frequency domain linear filter with envelope spectrum objective function 3.4. Integral optimization with uncertainty-aware weighing scheme 4. Computational experiments 4.1. Experimental configurations 4.2. Case study 1: PU dataset 4.3. Case study 2: JNU dataset 4.4. Case study 3: HIT dataset 5. Computational experiments 5.1. Comparison of BD methods 5.2. Classification results on various noise conditions 5.3. Employing ClassBD to deep learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.5. Feature extraction ability of quadratic and conventional networks 5.6. Comparison of ClassBD filters 6. Conclusions Appendix and References 3. Methodology The proposed framework, as illustrated in Figure 1, primarily consists of two BD filters, namely a time domain quadratic convolutional filter and a frequency domain linear filter. These filters serve as a plug-and-play denoising module, and they are designed to perform the same function as conventional BD methods to ensure that the output is in the same dimension as the input. The time domain filter is characterized by two symmetric quadratic convolutional neural network (QCNN) layers. A 16-channel QCNN is employed to filter the input signal (1 × 2048), and an inverse QCNN layer is used to fuse the 16 channels into one for recovering the input signal.


The frequency domain filter, on the other hand, starts with the fast Fourier transform (FFT) with an emphasis on highlighting the discrete frequency components. Subsequently, a linear neural layer filters the frequency domain of the signals, and the inverse FFT (IFFT) is conducted to recover the time domain signal. Moreover, an objective function in the envelope spectrum (ES) is designed for optimization. Authors:
(1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China;
(3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China;
(4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Preliminaries and 2.1. Blind deconvolution 2. Preliminaries and 2.1. Blind deconvolution 2.2. Quadratic neural networks 2.2. Quadratic neural networks 3. Methodology 3. Methodology 3.1. Time domain quadratic convolutional filter 3.1. Time domain quadratic convolutional filter 3.2. Superiority of cyclic features extraction by QCNN 3.2. Superiority of cyclic features extraction by QCNN 3.3. Frequency domain linear filter with envelope spectrum objective function 3.3. Frequency domain linear filter with envelope spectrum objective function 3.4. Integral optimization with uncertainty-aware weighing scheme 3.4. Integral optimization with uncertainty-aware weighing scheme 4. Computational experiments 4.1. Experimental configurations 4.1. Experimental configurations 4.2. Case study 1: PU dataset 4.2. Case study 1: PU dataset 4.3. Case study 2: JNU dataset 4.3. Case study 2: JNU dataset 4.4. Case study 3: HIT dataset 4.4. Case study 3: HIT dataset 5. Computational experiments 5.1. Comparison of BD methods 5.1. Comparison of BD methods 5.2. Classification results on various noise conditions 5.2. Classification results on various noise conditions 5.3. Employing ClassBD to deep learning classifiers 5.3. Employing ClassBD to deep learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.5. Feature extraction ability of quadratic and conventional networks 5.5. Feature extraction ability of quadratic and conventional networks 5.6. Comparison of ClassBD filters 5.6. Comparison of ClassBD filters 6. Conclusions 6. Conclusions Appendix and References Appendix and References 3. Methodology The proposed framework, as illustrated in Figure 1, primarily consists of two BD filters, namely a time domain quadratic convolutional filter and a frequency domain linear filter. These filters serve as a plug-and-play denoising module, and they are designed to perform the same function as conventional BD methods to ensure that the output is in the same dimension as the input. The time domain filter is characterized by two symmetric quadratic convolutional neural network (QCNN) layers. A 16-channel QCNN is employed to filter the input signal (1 × 2048), and an inverse QCNN layer is used to fuse the 16 channels into one for recovering the input signal. The frequency domain filter, on the other hand, starts with the fast Fourier transform (FFT) with an emphasis on highlighting the discrete frequency components. Subsequently, a linear neural layer filters the frequency domain of the signals, and the inverse FFT (IFFT) is conducted to recover the time domain signal. Moreover, an objective function in the envelope spectrum (ES) is designed for optimization. The time domain filter is characterized by two symmetric quadratic convolutional neural network (QCNN) layers. A 16-channel QCNN is employed to filter the input signal (1 × 2048), and an inverse QCNN layer is used to fuse the 16 channels into one for recovering the input signal. The time domain filter is characterized by two symmetric quadratic convolutional neural network (QCNN) layers. A 16-channel QCNN is employed to filter the input signal (1 × 2048), and an inverse QCNN layer is used to fuse the 16 channels into one for recovering the input signal. The frequency domain filter, on the other hand, starts with the fast Fourier transform (FFT) with an emphasis on highlighting the discrete frequency components. Subsequently, a linear neural layer filters the frequency domain of the signals, and the inverse FFT (IFFT) is conducted to recover the time domain signal. Moreover, an objective function in the envelope spectrum (ES) is designed for optimization. The frequency domain filter, on the other hand, starts with the fast Fourier transform (FFT) with an emphasis on highlighting the discrete frequency components. Subsequently, a linear neural layer filters the frequency domain of the signals, and the inverse FFT (IFFT) is conducted to recover the time domain signal. Moreover, an objective function in the envelope spectrum (ES) is designed for optimization. Authors: (1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China; (3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China; (4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. Authors: Authors: (1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China; (3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China; (4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv

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