Approximate Rotational Invariance Research Articles

Topological Phase Transitions in Multicomponent Superconductors.

We study the phase transition between a trivial and a time-reversal-invariant topological superconductor in a single-band system. By analyzing the interplay of symmetry, topology, and energetics, we show that for a generic normal state band structure, the phase transition occurs via extended intermediate phases in which even- and odd-parity pairing components coexist. For inversion-symmetric systems, the coexistence phase spontaneously breaks time-reversal symmetry. For noncentrosymmetric superconductors, the low-temperature intermediate phase is time-reversal breaking, while the high-temperature phase preserves time-reversal symmetry and has topologically protected line nodes. Furthermore, with approximate rotational invariance, the system has an emergent U(1)×U(1) symmetry, and novel topological defects, such as half vortex lines binding Majorana fermions, can exist. We analytically solve for the dispersion of the Majorana fermion and show that it exhibits small and large velocities at low and high energies. Relevance of our theory to superconducting pyrochlore oxide Cd_{2}Re_{2}O_{7} and half-Heusler materials is discussed.

Two-Dimensional DOA Estimation for Coherently Distributed Sources with Symmetric Properties in Crossed Arrays.

In this paper, a novel algorithm is proposed for the two-dimensional (2D) central direction-of-arrival (DOA) estimation of coherently distributed (CD) sources. Specifically, we focus on a centro-symmetric crossed array consisting of two uniform linear arrays (ULAs). Unlike the conventional low-complexity methods using the one-order Taylor series approximation to obtain the approximate rotational invariance relation, we first prove the symmetric property of angular signal distributed weight vectors of the CD source for an arbitrary centrosymmetric array, and then use this property to establish two generalized rotational invariance relations inside the array manifolds in the two ULAs. Making use of such relations, the central elevation and azimuth DOAs are obtained by employing a polynomial-root-based search-free approach, respectively. Finally, simple parameter matching is accomplished by searching for the minimums of the cost function of the estimated 2D angular parameters. When compared with the existing low-complexity methods, the proposed algorithm can greatly improve estimation accuracy without significant increment in computation complexity. Moreover, it performs independently of the deterministic angular distributed function. Simulation results are presented to illustrate the performance of the proposed algorithm.

Shadow detection and removal for moving objects using Daubechies complex wavelet transform

Shadow detection and removal is a challenging problem for several computer vision applications because shadow always makes object misclassified. A number of shadow detection and removal algorithms have been reported, and some of these algorithms require manual calibration in terms of some hypothesis and predefined specific parameters whereas others do not require manual intervention, but fail to give accurate result in various lighting and environmental conditions. This paper introduces a novel method for shadow detection and removal with Daubechies complex wavelet domain. Daubechies complex wavelet transform has been used in the proposed algorithm due to its strong edge detection, approximate shift-invariance as well as approximate rotation invariance properties. For shadow detection, we have proposed a new threshold in the form of coefficient of variation of wavelet coefficients. This threshold is automatically determined and does not require any manual calibration and training. Results of shadow detection and removal from moving objects after applying the proposed method are compared with the those of other state-of-the-art methods in terms of visual performance and number of quantitative performance evaluation parameters. The proposed method is found to perform better than other state-of-the-art methods.

Joint Angle Estimation and Signal Reconstruction for Coherently Distributed Sources in Massive MIMO Systems Based on 2-D Unitary ESPRIT

We consider the challenging problem of joint angle estimation and signal reconstruction for coherently distributed (CD) sources in massive multiple-input–multiple-output (MIMO) systems employing uniform rectangular arrays. A simplified method inspired by the two-dimensional (2-D) unitary estimating signal parameters via rotational invariance technique (ESPRIT) is proposed to estimate both the central angle and the angular spread without the need for a spectrum peak search and covariance matrix matching process. We first approximate the 2-D generalized steering vector expressed as a Schur-Hadamard product by a pair of one-dimensional generalized steering vectors. Then, we obtain two approximate rotational invariance relationships with respect to the central angles of the CD sources using a linear approximation of the individual generalized steering vectors of the azimuth and elevation subarrays. With the aid of this approximate decomposition, a new unitary ESPRIT-inspired algorithm is conceived to automatically pair the 2-D central angle estimations and a novel method capable of bypassing the high-complexity search process is proposed for angular spread estimation. Furthermore, the closed-form approximate Cramer-Rao lower bounds are derived for the estimators of both the central angles and the angular spreads. The complexity of the proposed estimator is also analyzed. Additionally, the orthogonality of the generalized steering vectors is proved, which enables us to propose a low-complexity method to reconstruct the CD signal matrix by replacing the inversion operator with the conjugate transpose operator. The simulation results demonstrate the efficiency of our proposed approach.

Incorporating approximate rotational invariance into two‐dimensional S‐transform

The discrete two-dimensional (2D) S-transform (ST-2D) is a space-frequency representation that provides the local spectrum at each pixel in an image. The inherent localisation properties of the ST-2D make it a preferred candidate for space-frequency analysis. However, the ST-2D is sensitive to the image rotation. This limits its use in many image processing applications such as texture analysis. This study describes the rotational sensitivity of the ST-2D, and explains how this limits its application. To overcome these problems, a novel rotationally invariant S-transform (RIST) is formulated, and its rotational invariance is investigated. The RIST can provide approximate rotational invariance for magnitudes and complex values over a wide range of rotation angles, but with a trade-off of higher computation time. The RIST may be useful for many medical, scientific and industrial applications.

Low-Complexity Estimation of the Nominal Azimuth and Elevation for Incoherently Distributed Sources

This paper develops a new technique for estimating the two-dimensional direction-of-arrivals (DOAs) of incoherently distributed (ID) sources, which can estimate effectively the nominal azimuth and nominal elevation of multiple ID sources at the cost of less computational complexity. Using a pair of parallel uniform linear arrays (ULAs), a new approach for 2D DOA estimation of multiple ID sources is proposed. The proposed method firstly estimates the nominal elevation by the modified TLS-ESPRIT method, which is based on the approximate rotational invariance property with respect to the nominal elevation between two closely parallel ULAs. And then with the help of the nominal elevation estimates, the nominal azimuth is estimated by one-dimensional searching. Without multi-dimensional searching, the proposed method has significantly reduced the computational cost compared with the existing methods. Simulation results indicate that the proposed method can exhibit a good performance and be applied to the multisource scenario where different sources may have different angular distribution shapes.

Fast DOA estimation of incoherently distributed sources by novel propagator

A low-complexity algorithm is presented for the estimation of the nominal direction-of-arrivals (DOAs) of incoherently distributed (ID) sources. The presented algorithm estimates the nominal DOAs of ID sources by a novel propagator method which makes use of the approximate rotational invariance relationship between two closely spaced identical uniform linear arrays. Without any search and the eigendecomposition of the sample covariance matrix, our algorithm can provide lower computational complexity than other known methods. In addition, it can be applied to the multisource scenario with different angular distribution shapes. Simulation results prove the effectiveness of the presented algorithm.

Simplified Estimation of 2D DOA for Coherently Distributed Sources

In mobile communications, local scattering in the vicinity of the mobile results in angular spreading as seen from a base station antenna array. In this paper, we consider the problem of estimating the two-dimensional (azimuth and elevation) direction-of-arrival (DOA) parameters of spatially distributed sources. Based on double parallel uniform linear arrays (ULAs), a simplified method without spectrum-peak searching is proposed for the 2D DOA estimation of multiple coherently distributed (CD) sources. The proposed method firstly obtains two approximate rotational invariance relations with respect to the nominal DOAs of CD sources by using one-order Taylor approximation to the generalized steering vectors (GSVs) of two pairs of shifted subarrays. And then a new ESPRIT-based method is utilized to estimate the nominal azimuth DOA and nominal elevation DOA. In addition, a simple parameter matching approach is also given. Compared with the conventional methods, our method has significantly reduced the computational cost and can sustain the estimation performance within a tolerable level. Moreover, our method is a blind estimator without any prior knowledge about angular distribution shape. Numerical examples illustrate the performance of the method.

Rotation invariant iris feature extraction using Gaussian Markov random fields with non-separable wavelet

Rotation invariance is important for an iris recognition system since changes of head orientation and binocular vergence may cause eye rotation. The conventional methods of iris recognition cannot achieve true rotation invariance. They only achieve approximate rotation invariance by rotating the feature vector before matching or unwrapping the iris ring at different initial angles. In these methods, the complexity of the method is increased, and when the rotation scale is beyond the certain scope, the error rates of these methods may substantially increase. In order to solve this problem, a new rotation invariant approach for iris feature extraction based on the non-separable wavelet is proposed in this paper. Firstly, a bank of non-separable orthogonal wavelet filters is used to capture characteristics of the iris. Secondly, a method of Markov random fields is used to capture rotation invariant iris feature. Finally, two-class kernel Fisher classifiers are adopted for classification. Experimental results on public iris databases show that the proposed approach has a low error rate and achieves true rotation invariance.

Convergence rate and locality of improved overlap fermions

We construct new Ginsparg–Wilson fermions for QCD by inserting an approximately chiral Dirac operator—which involves ingredients of a perfect action—into the overlap formula. This accelerates the convergence of the overlap Dirac operator by a factor of 5 compared to the standard construction, which inserts the Wilson fermion as a point of departure. Taking into account the effort for treating the improved fermion, we are left with an total computational overhead of about a factor 3. This remaining factor is likely to be compensated by other virtues; here we show that the level of locality is clearly improved, so that the exponent of the correlation decay is doubled. We also show that approximate rotation invariance is drastically improved, but a careful scaling test has to be postponed.