Jihong Pei

An analysis of THz-TDS signals using geometric algebra

THz-TDS signals can be represented as vectors in a high dimensional vector space, which are hyper-complex numbers in geometric algebra (GA). Using the language of GA, the properties of these vectors are theoretically analyzed and demonstrate the projective character of THz-TDS signals. The tangential distance of vectors is used to measure the difference of the corresponding THz-TDS signals. A novel imensionality reduction method via the projective split is presented, by which vectors of THz-TDS signals can be linear mapped from a high dimensional space into a lower dimensional space. The projective split is recursively employed and linear maps the vector space of high dimension into a sequence of sub-spaces step by step. Experiments demonstrate the feasibility and accuracy of our method.

Optimal wavelet analysis for THz-TDS pulse signals

A THz time-domain spectroscopy (THz-TDS) pulse signal is a temporal response of THz reference pulse. Although the field of THz-TDS signal processing and analysis techniques is relatively unexplored, work has been reported in this field. One of those is wavelet analysis approach of terahertz signals. It has been shown that the wavelet transform is an efficient representation of THz pulses due to their pulse-like nature. Unlike Fourier analysis, which only uses infinite sinusoids as the basis functions, in wavelet analysis, there are a large number of wavelet bases for different applications, and each of these wavelet bases exhibits different properties. In this paper, the problem that how to select an appropriate wavelet basis for representation and analysis of THz-TDS signals is discussed by lots of comparing experiments. Three criterions, which are wavelet basis efficiency index (WBEI), pulse spectral relative entropy (PSRE) and pulse spectral cumulative error (PSCE), are presented to determine a preferable mother wavelet for a given THz-TDS reference pulse.

THz-TDS Signal Analysis and Substance Identification

The terahertz time-domain spectroscopy (THz-TDS) imaging system can obtain high-dimensional signals of the substance fingerprint information. It is necessary to process properly to use some signal processing techniques especially for high dimensional signals. As a mathematical description language, geometric algebra (GA) provides not only a powerful algebraic framework for the multi-dimensional vector analysis and computing, but also a unified measurement and geometrical description for different geometric models. On the basis of the GA theories, a new signal analysis method of the THz-TDS is presented. Based on the characteristics of THz-TDS signals, signals are mapped into vectors in the high-dimensional real vector space. The vectors are represented with hyper-complex numbers. We can analyze the vectors using theories of GA. Based on the physical mechanism of the THz-TDS signal analysis, geometric distribution properties and algebraic relationships of THz-TDS signals are deduced. It is demonstrated that every complex refractive index of the sample relates to a unique 2-blade B2, all vectors corresponding to the samples of the same substance are collinear and belong to the intrinsic 2-blade of the substance. In projective interpretation, the 2-blade B2 represents a fixed line and all vectors related to the same substance are along that line. Accordingly, a novel substance identification method based on the relative THz-TDS is presented. In the method, two THz-TDS signals through the samples of the same substance but different thickness are measured. The intrinsic 2-blade B2 of the substance is then determined by the outer product of these two corresponding vectors. Using the conformal split by the fixed bivector B2, each vector corresponding to THz-TDS signals in the vector space Vn can be linearly splitted into vectors in vector spaces V2 and Vn−2. Since that 2-dimensional subspace V2 is the support of B2, the subspace is also a label for substances. So substances of samples can be identified on the magnitudes of projection vectors in that subspace. This method can contribute to the accurate classification and identification, and facilitate the feature extraction. Finally, experiments are presented and show that the substance identification method is feasible and effective.

A Clifford Algebra analysis method of THz-TDS images

A novel Clifford Algebra analysis method of terahertz time domain spectroscopy (THz-TDS) images is presented, which is based on the physical basis of the THz-TDS transmission system. Pixels in THz-TDS images, as well as the complex refractive indexes of materials in THz band, can be expressed as vectors in a high-dimensional space, or hyper-complex numbers in the Clifford algebra. Based on that the magnitude and phase of the transfer function of the THz-TDS system are primarily governed by the materialpsilas intrinsic complex refractive index and its thickness, two functions are given to construct hyper-complex numbers in Clifford algebra, and then several properties of data distributions in the THz-TDS signal vector space are discussed with Clifford algebra analysis. Finally, experiments are given to show the potential of the proposed method.

THz-TDS signal analysis and substance identification via the conformal split

A terahertz time-domain spectroscopy (THz-TDS) imaging system can obtain high-dimensional signals with substance fingerprint information. By introducing geometric algebra, a novel signal analysis approach to THz-TDS signals is developed based on an optical physical mechanism. Using this approach, signals are represented with vectors in the high-dimensional real vector space. Geometric distribution properties and algebraic relationships of THz-TDS signals are deduced. It is proved that every complex refractive index of substances relates to a unique 2-blade, the vectors corresponding to the samples of the same substance are collinear and belong to the intrinsic 2-blade of the substance. When decomposed through the conformal split with respect to a 2-blade, THz-TDS signals of high dimensionality can be related to vectors in a 2-dimensional subspace. Based on the conformal split properties we deduced, two criteria for substance identification on the basis of THz-TDS signals are proposed. Accordingly, a novel substance identification method via the conformal split is presented. In the method, the 2-blade related to each “known” substance is calculated with two vectors corresponding to THz-TDS signals measured from samples of the substance but with different thicknesses. Using the conformal split with respect to those 2-blades, an identified vector corresponding to a THz-TDS signal is linearly related to the vector in a 2-dimensional subspace. The substance of a sample can be identified using criteria on the projected vectors in the subspaces. This method can contribute to accurate classification and identification. Finally, two experiments are presented that show the feasibility and accuracy of this method.

Hybrid Structure-Adaptive RBF-ELM Network Classifier

In this paper, a hybrid structure-adaptive radial basis function-extreme learning machine (HSARBF-ELM) network classifier is presented. HSARBF-ELM consists of a structure-adaptive radial basis function (SARBF) network and an extreme learning machine (ELM) network of cascade, where the output of the SARBF network hidden layer is used as the input layer of the ELM network. In the HSARBF-ELM network classifier, the SARBF network is utilized to achieve adaptively localizing kernel mapping of input vectors, after that step, the ELM network is utilized to implement global classification of mapping samples in the kernel space. HSARBF-ELM indicates the combination of localized kernel mapping learning and the global nonlinear classification, which combines the advantages of the SARBF network and the ELM network. The quantitative conditions for the separability enhancement and the corresponding theoretical explanation for the HSARBF-ELM network are given, which demonstrate that when input vectors go through the SARBF network, adaptively adjusting the RBF kernel parameters can boost the separability of the original sample space. Thus, the classification performance of the HSARBF-ELM network can be guaranteed theoretically. An appropriate learning algorithm for the HSARBF-ELM network is subsequently presented, which effectively combines the methods of density clustering with a potential function, center-oriented unidirectional repulsive force and the existing ELM algorithm, and the optimized complementary HSARBF-ELM network can be constructed. The experimental results show that the classification performance of the HSARBF-ELM network clearly outperforms the ELM network, and outperforms other classifiers on most classification problems.

A local adaptive threshold noise detection linear interpolation filter (LALIF) for stripe noise removal in infrared images

Stripe noise is usually introduced into infrared images during acquisition, which seriously deteriorates the image quality and affects the subsequent analysis of the image. In this paper, the spatial mathematic model and the comb-like impulse spectrum characteristics in Fourier domain of stripe noise are given. On this basis, a local adaptive threshold noise detection linear interpolation filter (LALIF) for stripe noise removal in infrared images is designed. In the filter method, the first, we crop the original image into two sub-images with optimal size to make the comb-like impulse spectrum characteristics of the stripe noise most prominent. The second, we use a local adaptive threshold to distinguish noise frequency points from the useful frequency points in the peak regions of the amplitude spectrum, and reassign the value of noise frequency points by linear interpolation. At last, we amalgamate the sub-images to obtain the stripe noise removal image. Experimental results indicate that the proposed method has a good performance in adaptability and stability for complex stripe noise removal in infrared images.

Ship detection based on surface fitting modeling for large range background of ocean images

For the seawater background interference problem in ship detection of high resolution remote sensing images, the characteristics of seawater background are analyzed deeply in this paper. And its found that there is consistent in local but continuous variation in large range. On the basis of above analysis, a Gauss variable surface seawater background model for high resolution remote sensing images is built, and the estimation of mean surface and variance surface are also given. Then, a novel ship detection method based on sea background statistical modeling is proposed for large range high resolution remote sensing images. The experimental results show the feasibility of our proposed method in sea background modeling and target detection for different kinds of high resolution remote sensing images. Compared with the other relative method, the proposed method has higher recall rate and lower missing rate.

A Structure-Adaptive Hybrid RBF-BP Classifier with an Optimized Learning Strategy

This paper presents a structure-adaptive hybrid RBF-BP (SAHRBF-BP) classifier with an optimized learning strategy. SAHRBF-BP is composed of a structure-adaptive RBF network and a BP network of cascade, where the number of RBF hidden nodes is adjusted adaptively according to the distribution of sample space, the adaptive RBF network is used for nonlinear kernel mapping and the BP network is used for nonlinear classification. The optimized learning strategy is as follows: firstly, a potential function is introduced into training sample space to adaptively determine the number of initial RBF hidden nodes and node parameters, and a form of heterogeneous samples repulsive force is designed to further optimize each generated RBF hidden node parameters, the optimized structure-adaptive RBF network is used for adaptively nonlinear mapping the sample space; then, according to the number of adaptively generated RBF hidden nodes, the number of subsequent BP input nodes can be determined, and the overall SAHRBF-BP classifier is built up; finally, different training sample sets are used to train the BP network parameters in SAHRBF-BP. Compared with other algorithms applied to different data sets, experiments show the superiority of SAHRBF-BP. Especially on most low dimensional and large number of data sets, the classification performance of SAHRBF-BP outperforms other training SLFNs algorithms.

A pre-radical basis function with deep back propagation neural network research

In the paper, the architecture of a pre-radical basis function(RBF) with deep back propagation(BP) neural network is proposed. The three-layer RBF network is altered into a two-layer RBF, the output of RBF hidden layer is processed and then connected with a multilayer perceptron network. Firstly, the input samples go through RBF hidden units and are pre-trained via unsupervised learning, after the data obtained are normalized, the supervised BP learning algorithm is used to achieve adjustments of the network weights, thus completing the training of the entire network. Experiments show that the improved architecture simplifies the selection of parameters in the former RBF network, while reducing dependence on the number of hidden layers and neurons in the BP network. Meanwhile, the improved architecture accelerates the convergence rate of BP network which can effectively avoid falling into the risk of local minimum, it also improves the classification accuracy.