Rotational invariants constructed by the products of three spherical harmonic polynomials

The rotational invariants constructed by the products of three spherical harmonic polynomials are expressed generally as homogeneous polynomials with respect to the three coordinate vectors in the compact form, where the coefficients are calculated explicitly in this paper.

Two-dimensional regularized inversion of AMT data based on rotation invariant of Central impedance tensor

Considering the uncertainty of the electrical axis for two-dimensional audo-magnetotelluric(AMT) data processing, an AMT inversion method with the Central impedance tensor was presented. First, we present a calculation expression of the Central impedance tensor in AMT, which can be considered as the arithmetic mean of TE-polarization mode and TM-polarization mode in the twodimensional geo-electrical model. Second, a least-squares iterative inversion algorithm is established, based on a smoothnessconstrained model, and an improved L-curve method is adopted to determine the best regularization parameters. We then test the above inversion method with synthetic data and field data. The test results show that this two-dimensional AMT inversion scheme for the responses of Central impedance is effective and can reconstruct reasonable two-dimensional subsurface resistivity structures. We conclude that the Central impedance tensor is a useful tool for two-dimensional inversion of AMT data.

A Secure Rotation Invariant LBP Feature Computation in Cloud Environment

In the era of big data,outsourcing massive data to a remote cloud server is a promising approach.Outsourcing storage and computation services can reduce storage costs and computational burdens.However,public cloud storage brings about new privacy and security concerns since the cloud servers can be shared by multiple users.Privacy-preserving feature extraction techniques are an effective solution to this issue.Because the Rotation Invariant Local Binary Pattern(RILBP)has been widely used in various image processing fields,we propose a new privacy-preserving outsourcing computation of RILBP over encrypted images in this paper(called PPRILBP).To protect image content,original images are encrypted using block scrambling,pixel circular shift,and pixel diffusion when uploaded to the cloud server.It is proved that RILBP features remain unchanged before and after encryption.Moreover,the server can directly extract RILBP features from encrypted images.Analyses and experiments confirm that the proposed scheme is secure and effective,and outperforms previous secure LBP feature computing methods.

Temporal-spatial subspaces modern combination method for 2D-DOA estimation in MIMO radar

A 2D-direction of arrival estimation (DOAE) for multi input and multi-output (MIMO) radar using improved multiple temporal-spatial subspaces in estimating signal parameters via rotational invariance techniques method (TS-ESPRIT) is introduced. In order to realize the improved TS-ESPRIT, the proposed algorithm divides the planar array into multiple uniform sub-planar arrays with common reference point to get a unified phase shifts measurement point for all sub-arrays. The TS-ESPRIT is applied to each sub-array separately, and in the same time with the others to realize the parallelly temporal and spatial processing, so that it reduces the non-linearity effect of model and decreases the computational time. Then, the time difference of arrival (TDOA) technique is applied to combine the multiple sub-arrays in order to form the improved TS-ESPRIT. It is found that the proposed method achieves high accuracy at a low signal to noise ratio (SNR) with low computational complexity, leading to enhancement of the estimators performance.

Low-complexity method for DOA estimation based on ESPRIT

A low-complexity method for direction of arrival（DOA） estimation based on estimation signal parameters via rotational invariance technique（ESPRIT） is proposed.Instead of using the cross-correlation vectors in multistage Wiener filter（MSWF）,the orthogonal residual vectors obtained in conjugate gradient（CG） method span the signal subspace used by ESPRIT.The computational complexity of the proposed method is significantly reduced,since the signal subspace estimation mainly needs two matrixvector complex multiplications at the iteration of data level.Furthermore,the prior training data are not needed in the proposed method.To overcome performance degradation at low signal to noise ratio（SNR）,the expanded signal subspace spanned by more basis vectors is used and simultaneously renders ESPRIT yield redundant DOAs,which can be excluded by performing ESPRIT once more using the unexpanded signal subspace.Compared with the traditional ESPRIT methods by MSWF and eigenvalue decomposition（EVD）,numerical results demonstrate the satisfactory performance of the proposed method.

Fingerprint singular points extraction based on orientation tensor field and Laurent series

Singular point(SP)extraction is a key component in automatic fingerprint identification system(AFIS).A new method was proposed for fingerprint singular points extraction,based on orientation tensor field and Laurent series.First,fingerprint orientation flow field was obtained,using the gradient of fingerprint image.With these gradients,fingerprint orientation tensor field was calculated.Then,candidate SPs were detected by the cross-correlation energy in multi-scale Gaussian space.The energy was calculated between fingerprint orientation tensor field and Laurent polynomial model.As a global descriptor,the Laurent polynomial coefficients were allowed for rotational invariance.Furthermore,a support vector machine(SVM)classifier was trained to remove spurious SPs,using cross-correlation coefficient as a feature vector.Finally,experiments were performed on Singular Point Detection Competition 2010(SPD2010)database.Compared to the winner algorithm of SPD2010 which has best accuracy of 31.90%,the accuracy of proposed algorithm is 45.34%.The results show that the proposed method outperforms the state-of-the-art detection algorithms by large margin,and the detection is invariant to rotational transformations.

High Resolution Multipath Time Delay Estimation Based on FLOCCS-ESPRIT

The non-Gaussian α-stable distribution is introduced to model impulsive noise. Based on the theory of fractional lower order statistics (FLOS), the fractional lower order cross-covariance (FLOCC) sequence for two received signals is obtained and the fractional lower order cross-covariance spectrum (FLOCCS) can be approached by taking a Fourier transform for the FLOCC sequence. When the FLOCCS is treated as a sequence in the time domain, the problem of multipath time delay estimation (TDE) may be converted into one on multi-frequencies estimation or directions of arrival estimation. Accordingly, the high resolution multipath TDE can be realized with the ESPRIT technology. This idea on multipath TDE is referred to as FLOCCS-ESPRIT in this paper. Computer simulations show that this method has good performance both in a Gaussian noise and in an impulsive noise environment.

Frequency domain polarization weighted ESPRIT method for bearing angle

The signal to noise ratio （SNR） of seismic waves is usually very low after long distance transmission. For this condition, to improve the bearing estimation capability in the low SNR, a frequency domain polarization weighted ESPRIT method using a single vector device is proposed. The frequency domain polari- zation parameters extracted from the signals are used to design the weighted function which is applied to the received signals. The bearing angle and the target frequency are estimated through ESPRIT using the weighted signals. The simulation and experiment results show that the presented method can obtain accurate estimation values under the low SNR with little prior information.

MULTI-INVARIANCE ESPRIT-LIKE ALGORITHMS FOR COHERENT DOA ESTIMATION

Estimation of Signal Parameters via Rotational Invariance Technique(ESPRIT) algorithm can estimate Direction-Of-Arrival(DOA) of coherent signal,but its performance can not reach full satisfaction.We reconstruct the received signal to form data model with multi-invariance property,and multi-invariance ESPRIT algorithm for coherent DOA estimation is proposed in this paper.The proposed algorithm can resolve the DOAs of coherent signals and performs better in DOA estimation than that of ESPRIT-like algorithm.Meanwhile,it identifies more DOAs than ESPRIT-like algorithm.The simulation results demonstrate its validity.

Low-Complexity DOA Estimation of Noncircular Signals for Coprime Sensor Arrays

This paper presents a low?complexity method for the direction?of?arrival(DOA)estimation of noncircular signals for coprime sensor arrays.The noncircular property is exploited to improve the performance of DOA estimation.To reduce the computational complexity,the rotational invariance propagator method(RIPM)is included in the algorithm.First,the extended array output is reconstructed by combining the array output and its conjugated counterpart.Then,the RIPM is utilized to obtain two sets of DOA estimates for two subarrays.Finally,the true DOAs are estimated by combining the consistent results of the two subarrays.This illustrates the potential gain that both noncircularity and coprime arrays provide when considered together.The proposed algorithm has a lower computational complexity and a better DOA estimation performance than the standard estimation of signal parameters by the rotational invariance technique and Capon algorithm.Numerical simulation results illustrate the effectiveness and superiority of the proposed algorithm.

Fast BSC-based algorithm for near-field signal localization via uniform circular array

In this paper,we propose a beam space coversion(BSC)-based approach to achieve a single near-field signal local-ization under uniform circular array(UCA).By employing the centro-symmetric geometry of UCA,we apply BSC to extract the two-dimensional(2-D)angles of near-field signal in the Van-dermonde form,which allows for azimuth and elevation angle estimation by utilizing the improved estimation of signal para-meters via rotational invariance techniques(ESPRIT)algorithm.By substituting the calculated 2-D angles into the direction vec-tor of near-field signal,the range parameter can be conse-quently obtained by the 1-D multiple signal classification(MU-SIC)method.Simulations demonstrate that the proposed al-gorithm can achieve a single near-field signal localization,which can provide satisfactory performance and reduce computational complexity.

Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems

We show that violation of the variance based local sum uncertainty relation(LSUR)for angular momentum operators of a bipartite system,proposed by Hofmann and Takeuchi[Phys.Rev.A 68032103(2003)],reflects entanglement in the equal bipartitions of an N-qubit symmetric state with even qubits.We establish the one-to-one connection with the violation of LSUR with negativity of covariance matrix[Phys.Lett.A 364203(2007)]of the two-qubit reduced system of a permutation symmetric N-qubit state.

Symbols detection for frequency-selective V-BLAST OFDM systems

As the combining form of the orthogonal frequency-division multiplexing (OFDM) technique and the vertical Bell Labs layered space-time (V-BLAST) architecture, the V-BLAST OFDM system can better meet the demand of next-generation (NextG) broadband mobile wireless multimedia communications. The symbols detection problem of the V-BLAST OFDM system is investigated under the frequency-selective fading environment. The joint space-frequency demultiplexing operation is proposed in the V-BLAST OFDM system. Successively, one novel half-rate rotational invariance joint space-frequency coding scheme for the V-BLAST OFDM system is proposed. By elegantly exploiting the above rotational invariance property, we derive one direct symbols detection scheme without knowing channels state information (CSI) for the frequency-selective V-BLAST OFDM system. Extensive simulation results demonstrate the validity of the novel half-rate rotational invariance joint space-frequency coding scheme and the performance of the direct symbols detection scheme.

Application of PRO-ESPRIT algorithm in identification of surface acoustic wave identification-tags

The surface acoustic wave （SAW） identification （ID）-tags have great potential for application in radio frequency identification （RFID） due to their characteristics of wireless sensing and passive operation. In the measurements based on the frequency domain sampling （FDS）, to expand the range of detection and allow the system work in harsh environments, it is necessary to enhance the identification capability at low SNR. In addition, to identify the tags in real time, it is important to reduce identification time. Therefore, estimation of signal parameters based on the Procrustes rotations via the rotational invariance technique （PRO-ESPRIT） is adopted. Experimental results show that good identification capability is achieved with a relatively faster measurement speed.

A Local Binary Pattern-Based Method for Color and Multicomponent Texture Analysis

Local Binary Patterns (LBPs) have been highly used in texture classification for their robustness, their ease of implementation and their low computational cost. Initially designed to deal with gray level images, several methods based on them in the literature have been proposed for images having more than one spectral band. To achieve it, whether assumption using color information or combining spectral band two by two was done. Those methods use micro structures as texture features. In this paper, our goal was to design texture features which are relevant to color and multicomponent texture analysis without any assumption. Based on methods designed for gray scale images, we find the combination of micro and macro structures efficient for multispectral texture analysis. The experimentations were carried out on color images from Outex databases and multicomponent images from red blood cells captured using a multispectral microscope equipped with 13 LEDs ranging from 375 nm to 940 nm. In all achieved experimentations, our proposal presents the best classification scores compared to common multicomponent LBP methods. 99.81%, 100.00%, 99.07% and 97.67% are maximum scores obtained with our strategy respectively applied to images subject to rotation, blur, illumination variation and the multicomponent ones.

Content-Based Image Retrieval with Feature Extraction and Rotation Invariance

Over recent years, Convolutional Neural Networks (CNN) has improved performance on practically every image-based task, including Content-Based Image Retrieval (CBIR). Nevertheless, since features of CNN have altered orientation, training a CBIR system to detect and correct the angle is complex. While it is possible to construct rotation-invariant features by hand, retrieval accuracy will be low because hand engineering only creates low-level features, while deep learning methods build high-level and low-level features simultaneously. This paper presents a novel approach that combines a deep learning orientation angle detection model with the CBIR feature extraction model to correct the rotation angle of any image. This offers a unique construction of a rotation-invariant CBIR system that handles the CNN features that are not rotation invariant. This research also proposes a further study on how a rotation-invariant deep CBIR can recover images from the dataset in real-time. The final results of this system show significant improvement as compared to a default CNN feature extraction model without the OAD.

Radial Hahn Moment Invariants for 2D and 3D Image Recognition

Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional（2D and 3D） image not only in pattern recognition, image vision, but also in image processing and applications engineering. Yet, there is still a major difficulty in 3D rotation invariants. In this paper, we propose new sets of invariants for 2D and 3D rotation, scaling and translation based on orthogonal radial Hahn moments. We also present theoretical mathematics to derive them. Thus, this paper introduces in the first case new 2D radial Hahn moments based on polar representation of an object by one-dimensional orthogonal discrete Hahn polynomials, and a circular function. In the second case, we present new 3D radial Hahn moments using a spherical representation of volumetric image by one-dimensional orthogonal discrete Hahn polynomials and a spherical function. Further 2D and 3D invariants are derived from the proposed 2D and 3D radial Hahn moments respectively, which appear as the third case. In order to test the proposed approach, we have resolved three issues： the image reconstruction, the invariance of rotation, scaling and translation, and the pattern recognition. The result of experiments show that the Hahn moments have done better than the Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges quickly to the original image using 2D and 3D radial Hahn moments, and the test images are clearly recognized from a set of images that are available in COIL-20 database for 2D image, and Princeton shape benchmark（PSB） database for 3D image.

Rotation Scaling and Translation Invariants of 3D Radial Shifted Legendre Moments

This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments： a 3D substituted radial shifted Legendre moments （3DSRSLMs） and a 3D weighted radial one （3DWRSLMs）. Both are centered on two types of polynomials. In the first case, a new 3D ra- dial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendremoments （3DSRSLMs/3DWRSLMs） are introduced using a spherical representation of volumetric image. 3D invariants as derived from the sug- gested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three is- sues. To confirm the proposed approach, we have resolved three issues： rotation, scaling and translation invariants. The result of experi- ments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Sim- ultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark （PSB） database for 3D image.

RB-SLAM:visual SLAM based on rotated BEBLID feature point description

The extraction and description of image features are very important for visual simultaneous localization and mapping(V-SLAM).A rotated boosted efficient binary local image descriptor(BEBLID)SLAM(RB-SLAM)algorithm based on improved oriented fast and rotated brief(ORB)feature description is proposed in this paper,which can solve the problems of low localization accuracy and time efficiency of the current ORB-SLAM3 algorithm.Firstly,it uses the BEBLID to replace the feature point description algorithm of the original ORB to enhance the expressiveness and description efficiency of the image.Secondly,it adds rotational invariance to the BEBLID using the orientation information of the feature points.It also selects the rotationally stable bits in the BEBLID to further enhance the rotational invariance of the BEBLID.Finally,it retrains the binary visual dictionary based on the BEBLID to reduce the cumulative error of V-SLAM and improve the loading speed of the visual dictionary.Experiments show that the dictionary loading efficiency is improved by more than 10 times.The RB-SLAM algorithm improves the trajectory accuracy by 24.75%on the TUM dataset and 26.25%on the EuRoC dataset compared to the ORB-SLAM3 algorithm.

Early Analogue Modeling Experiments and Related Studies to Today's Problems of Geo-electromagnetic Exploration

As I learned it from extensive geo-electromagnetic analogue modeling experiments, some specific nonconventional interpretation parameters, in certain conditions, give more detailed information about the geometry of subsurface resistivity inhomogeneities than the routinely used parameters. In this article, I show several examples, and I present how these early results influenced our later research. An enhanced geometric sensitivity may be due to special array geometry （as we call it ＂null array＂）, or it may be due to a narrow and very special frequency range （i.e., the so-called ＂keyhole＂ range）. Nonconventional but physically based interpretation parameters （like the Poynting vector） or higher order invariants of resistivity or impedance tensors may also give useful additional information about the shape of subsurface bodies. One should be very careful in their application because a large part of these nontraditional approaches are strongly constrained by measuring errors and geological noise.