Rotational Invariance Relationships Research Articles

Detection of bladder cancer with feature fusion, transfer learning and CapsNets

This paper confronts two approaches to classify bladder lesions shown in white light cystoscopy images when using small datasets: the classical one, where handcrafted-based features feed pattern recognition systems and the modern deep learning-based (DL) approach. In between, there are alternative DL models that had not received wide attention from the scientific community, even though they can be more appropriate for small datasets such as the human brain motivated capsule neural networks (CapsNets). However, CapsNets have not yet matured hence presenting lower performances than the most classic DL models. These models require higher computational resources, more computational skills from the physician and are more prone to overfitting, making them sometimes prohibitive in the routine of clinical practice. This paper shows that carefully handcrafted features used with more robust models can reach similar performances to the conventional DL-based models and deep CapsNets, making them more useful for clinical applications. Concerning feature extraction, it is proposed a new feature fusion approach for Ta and T1 bladder tumor detection by using decision fusion from multiple classifiers in a scheme known as stacking of classifiers. Three Neural Networks perform classification on three different feature sets, namely: Covariance of Color Histogram of Oriented Gradients, proposed in the ambit of this paper; Local Binary Patterns and Wavelet Coefficients taken from lower scales. Data diversity is ensured by a fourth Neural Network, which is used for decision fusion by combining the outputs of the ensemble elements to produce the classifier output. Both Feed Forward Neural Networks and Radial Basis Functions are used in the experiments. Contrarily, DL-based models extract automatically the best features at the cost of requiring huge amounts of training data, which in turn can be alleviated by using the Transfer Learning (TL) strategy. In this paper VGG16 and ResNet-34 pretrained in ImageNet were used for TL, slightly outperforming the proposed ensemble. CapsNets may overcome CNNs given their ability to deal with objects rotational invariance and spatial relationships. Therefore, they can be trained from scratch in applications using small amounts of data, which was beneficial for the current case, improving accuracy from 94.6% to 96.9%.

Direction-of-Arrival Estimation for 2D Coherently Distributed Sources with Nested Array Based on Matrix Reconstruction

This paper has made proposition of a nested array and an estimation algorithm for direction-of-arrival (DOA) of two-dimensional (2D) coherently distributed (CD) sources. According to the difference coarray concept, double parallel hole-free virtual uniform linear arrays are generated by virtue of vectorization operation on cross-correlation matrices of subarrays. Sensor coordinates of virtual arrays are derived. Rational invariance relationships of virtual arrays are derived. According to the rotational invariance relationships, matrices satisfying rotation invariance are constructed by extracting and regrouping the receive vectors of the virtual arrays, and then an estimation of signal parameters via rotational invariance techniques- (ESPRIT-) like framework on matrix reconstruction is deduced. Optimal configuration of the nested array as well as computational complexity are analyzed. Without pair matching, the proposed method can resolve more sources than the sensor number. Simulation outcomes indicate that the proposed method tends to have a better performance as compared to the traditional uniform arrays that have similar number of sensors.

A unified robust framework for multi-view feature extraction with L2,1-norm constraint

Multi-view feature extraction methods mainly focus on exploiting the consistency and complementary information between multi-view samples, and most of the current methods apply the F-norm or L2-norm as the metric, which are sensitive to the outliers or noises. In this paper, based on L2,1-norm, we propose a unified robust feature extraction framework, which includes four special multi-view feature extraction methods, and extends the state-of-art methods to a more generalized form. The proposed methods are less sensitive to outliers or noises. An efficient iterative algorithm is designed to solve L2,1-norm based methods. Comprehensive analyses, such as convergence analysis, rotational invariance analysis and relationship between our methods and previous F-norm based methods illustrate the effectiveness of our proposed methods. Experiments on two artificial datasets and six real datasets demonstrate that the proposed L2,1-norm based methods have better performance than the related methods.

Efficient tensor decomposition method for noncircular source in colocated coprime MIMO radar**Project supported by the National Natural Science Foundation of China (Grant Nos. 61701507, 61890542, and 61890540).

An effective method via tensor decomposition is proposed to deal with the joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation of noncircular sources in colocated coprime MIMO radar. By decomposing the transmitter and receiver into two sparse subarrays, noncircular property of source can be used to construct new extended received signal model for two sparse subarrays. The new received model can double the virtual array aperture due to the elliptic covariance of imping sources is nonzero. To further exploit the multidimensional structure of the noncircular received model, we stack the subarray output and its conjugation according to mode-1 unfolding and mode-2 unfolding of a third-order tensor, respectively. Thus, the corresponding extended tensor model consisted of noncircular information for DOA and DOD can be obtained. Then, the higher-order singular value decomposition technique is utilized to estimate the accurate signal subspace and angular parameter can be automatically paired via the rotational invariance relationship. Specifically, the ambiguous angle can be eliminated and the true targets can be achieved with the aid of the coprime property. Furthermore, a closed-form expression for the deterministic CRB under the NC sources scenario is also derived. Simulation results verify the superiority of the proposed estimator.

DOA Estimation of Two-Dimensional Coherently Distributed Sources Based on Spatial Smoothing of Uniform Rectangular Arrays

Aiming at the direction-of-arrival (DOA) estimation of two-dimensional (2D) coherently distributed (CD) sources which are coherent with each other, we explore the propagator method based on spatial smoothing of a uniform rectangular array (URA). The rotational invariance relationships with respect to the nominal azimuth and nominal elevation are obtained under the small angular spreads assumption. A propagator operator is constructed through spatial smoothing of sample covariance matrices firstly. Then, combination of propagator and identical matrix is divided according to rotational operators, and the nominal angles can be obtained through eigendecomposition lastly. Realizing angle matching automatically, the proposed method can estimate multiple DOAs of 2D coherent CD sources without spectral peak searching and prior knowledge of deterministic angular signal distribution function. Simulations are conducted to verify the effectiveness of the proposed method.

A 2D Nested Array Based DOA Estimator for Incoherently Distributed Sources via Sparse Representation Utilizing L1-Norm

Nested arrays are sparse arrays composed of subarrays with nonuniform sensor spacing. Compared with traditional uniform arrays, nested arrays have more degree of freedoms (DOFs) and larger apertures. In this paper, a nested array has been proposed as well as a direction-of-arrival (DOA) estimation method for two-dimensional (2D) incoherently distributed (ID) sources. A virtual array is firstly obtained through vectorization of the cross-correlation matrix of subarrays. Sensor positions of the virtual array and the optimal configuration of the nested array are derived next. Then rotational invariance relationship for generalized steering matrix of the virtual array with respect to nominal azimuth is deduced. According to the rotational invariance relationship, sparse representation model under l1-norm constraint is established, which is resolved by transferring the objective function to second-order cone constraints and combining a estimation residual error constraint for receive vector of the virtual array. Simulations are conducted to investigate the effectiveness of the proposed method in underdetermined situation and examine different experiment factors including SNR, snapshots, and angular spreads as well as sensor number of subarrays. Results show that the proposed method has better performance than uniform parallel arrays with the same number of sensors.

On Spatial Smoothing for DOA Estimation of 2D Coherently Distributed Sources with Double Parallel Linear Arrays

Considering coherently-distributed (CD) sources are correlated with each other, a two-dimensional (2D) coherent CD source model is proposed according to the characteristics of an underwater acoustic channel. Under the assumption of small angular spreads, rotational invariance relationships within and between subarrays of double parallel linear arrays are derived. As the covariance matrix of spatial smoothing obtained from receive vectors expressed by rotational invariance relationships is proven to be full rank, decoherence of the 2D coherent CD source is proposed by spatial smoothing of the double parallel linear arrays. A propagator method base on spatial smoothing (SS-PM) and estimation of signal parameters via rotational invariance techniques (ESPRIT) base on spatial smoothing (SS-ESPRIT) method established by covariance matrix of spatial smoothing are proposed. The proposed methods do not require peak-searching, angles matching and information of deterministic angular signal distribution function. Simulations are conducted to verify the effectiveness of the proposed methods.

Joint DOD and DOA Estimation for Coherently Distributed Sources in Bistatic MIMO Radar Based on Joint Diagonalization

In this paper, an efficient method via unitary joint diagonalization is proposed to deal with the coherently distributed sources in bistatic multiple-input multiple-output (MIMO) radar systems. In order to determine the direction of departure (DOD) and direction of arrival (DOA) of the coherently distributed source, a special array configuration is designed both for transmitter and receiver in bistatic MIMO radar system. Then, a new signal model can be obtained by utilizing the designed array characteristic and the rotational invariance relationship is constructed both for DOD and DOA. For the special rotational invariance relationship, the joint diagonalization technique is adopted to locate the coherently distributed sources and the angular parameters are automatically paired without multidimensional search process. The proposed joint diagonalization method can also determine the targets when multiple imping sources have the common DODs or DOAs. Finally, the approximate determined Cramer-Rao bound of the proposed estimator for the coherently distributed sources is also derived. And, additional numerical results are conducted to verify the effectiveness and superiority of the proposed method.

Direction finding for two-dimensional incoherently distributed sources with Hadamard shift invariance in non-uniform orthogonal arrays

This paper proposes a novel algorithm for Two-Dimensional (2D) central Direction-of-Arrival (DOA) estimation of incoherently distributed sources. In particular, an orthogonal array structure consisting of two Non-uniform Linear Arrays (NLAs) is considered. Based on first-order Taylor series approximation, the Generalized Array Manifold (GAM) model can first be established to separate the central DOAs from the original array manifold. Then, the Hadamard rotational invariance relationships inside the GAMs of two NLAs are identified. With the aid of such relationships, the central elevation and azimuth DOAs can be estimated through a search-free polynomial rooting method. Additionally, a simple parameter pairing of the estimated 2D angular parameters is also accomplished via the Hadamard rotational invariance relationship inside the GAM of the whole array. A secondary but important result is a derivation of closed-form expressions of the Cramer-Rao lower bound. The simulation results show that the proposed algorithm can achieve a remarkably higher precision at less complexity increment compared with the existing low-complexity methods, which benefits from the larger array aperture of the NLAs. Moreover, it requires no priori information about the angular distributed function.

Computational Efficient Two-Dimension DOA Estimation for Incoherently Distributed Noncircular Sources With Automatic Pairing

In this paper, the problem of two-dimensional (2-D) direction-of-arrival (DOA) estimation for incoherently distributed (ID) noncircular sources is addressed. A low-complexity estimator with automatic pairing in the three-parallel uniform linear arrays (ULAs) is proposed. First, the signal non-circularity is applied to establish an extended generalized array manifold (GAM) model based on one-order Taylor series approximation. Resorting to such model, the generalized rotational invariance relationships are identified among the extended GAM matrices of the three ULAs. Thereafter, a modified propagator method is utilized to estimate the central elevation and azimuth DOAs. Without any spectrum searching, estimation or eigenvalue decomposition of the sample covariance matrix, the proposed approach is capable of considerably reducing the calculation cost in comparison with the existing methods. In addition, it can automatically pair the estimated central azimuth and central elevation DOAs. We also derive the Cramer-Rao lower bound regarding the 2-D DOA estimation of the ID noncircular source and conduct the computational complexity analysis. Numerical results demonstrate that the proposed method achieves better estimation performance than the existing methods. Furthermore, it can be applied in the multi-source scenario where different sources may have different angular distribution shapes.

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.

A unitary ESPRIT scheme of joint angle estimation for MOTS MIMO radar.

The transmit array of multi-overlapped-transmit-subarray configured bistatic multiple-input multiple-output (MOTS MIMO) radar is partitioned into a number of overlapped subarrays, which is different from the traditional bistatic MIMO radar. In this paper, a new unitary ESPRIT scheme for joint estimation of the direction of departure (DOD) and the direction of arrival (DOA) for MOTS MIMO radar is proposed. In our method, each overlapped-transmit-subarray (OTS) with the identical effective aperture is regarded as a transmit element and the characteristics that the phase delays between the two OTSs is utilized. First, the measurements corresponding to all the OTSs are partitioned into two groups which have a rotational invariance relationship with each other. Then, the properties of centro-Hermitian matrices and real-valued rotational invariance factors are exploited to double the measurement samples and reduce computational complexity. Finally, the close-formed solution of automatically paired DOAs and DODs of targets is derived in a new manner. The proposed scheme provides increased estimation accuracy with the combination of inherent advantages of MOTS MIMO radar with unitary ESPRIT. Simulation results are presented to demonstrate the effectiveness and advantage of the proposed scheme.

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.