This letter deals with the joint direction of arrival and direction of departure estimation problem for overloaded target in bistatic multiple-input multiple-output radar system. In order to achieve the purpose of effective estimation, the presented Khatri-Rao (KR) MUSIC estimator with the ability to handle overloaded targets mainly combines the subspace characteristics of the target reflected wave signal and the KR product based on the array response. This letter also presents a computationally efficient KR noise subspace projection matrix estimation technique to reduce the computational load due to perform high-dimensional singular value decomposition. Finally, the effectiveness of the proposed method is verified by computer simulation.

There are two types of elliptic curves, ordinary elliptic curves and supersingular elliptic curves. In 2012, Sutherland proposed an efficient and almost deterministic algorithm for determining whether a given curve is ordinary or supersingular. Sutherland's algorithm is based on sequences of isogenies started from the input curve, and computation of each isogeny requires square root computations, which is the dominant cost of the algorithm. In this paper, we reduce this dominant cost of Sutherland's algorithm to approximately a half of the original. In contrast to Sutherland's algorithm using j-invariants and modular polynomials, our proposed algorithm is based on Legendre form of elliptic curves, which simplifies the expression of each isogeny. Moreover, by carefully selecting the type of isogenies to be computed, we succeeded in gathering square root computations at two consecutive steps of Sutherland's algorithm into just a single fourth root computation (with experimentally almost the same cost as a single square root computation). The results of our experiments using Magma are supporting our argument; for cases of characteristic p of 768-bit to 1024-bit lengths, our proposed algorithm for characteristic p≡1 (mod 4) runs in about 61.5% of the time and for characteristic p≡3 (mod 4) also runs in about 54.9% of the time compared to Sutherland's algorithm.

This paper proposes multi-input physical layer network coding (multi-input PLNC) for high speed wireless communication in two-dimensional wireless multihop networks. In the proposed PLNC, all the terminals send their packets simultaneously for the neighboring relays to maximize the network throughput in the first slot, and all the relays also do the same to the neighboring terminals in the second slot. Those simultaneous signal transmissions cause multiple signals to be received at the relays and the terminals. Signal reception in the multi-input PLNC uses multichannel filtering to mitigate the difficulties caused by the multiple signal reception, which enables the two-input PLNC to be applied. In addition, a non-linear precoding is proposed to reduce the computational complexity of the signal detection at the relays and the terminals. The proposed multi-input PLNC makes all the terminals exchange their packets with the neighboring terminals in only two time slots. The performance of the proposed multi-input PLNC is confirmed by computer simulation. The proposed multi-input physical layer network coding achieves much higher network throughput than conventional techniques in a two-dimensional multihop wireless network with 7 terminals. The proposed multi-input physical layer network coding attains superior transmission performance in wireless hexagonal multihop networks, as long as more than 6 antennas are placed on the terminals and the relays.

Millimeter wave (mmWave) massive Multiple-Input Multiple-Output (MIMO) systems generally adopt hybrid precoding combining digital and analog precoder as an alternative to full digital precoding to reduce RF chains and energy consumption. In order to balance the relationship between spectral efficiency, energy efficiency and hardware complexity, the hybrid-connected system structure should be adopted, and then the solution process of hybrid precoding can be simplified by decomposing the total achievable rate into several sub-rates. However, the singular value decomposition (SVD) incurs high complexity in calculating the optimal unconstrained hybrid precoder for each sub-rate. Therefore, this paper proposes PAST, a low complexity hybrid precoding algorithm based on projection approximate subspace tracking. The optimal unconstrained hybrid precoder of each sub-rate is estimated with the PAST algorithm, which avoids the high complexity process of calculating the left and right singular vectors and singular value matrix by SVD. Simulations demonstrate that PAST matches the spectral efficiency of SVD-based hybrid precoding in full-connected (FC), hybrid-connected (HC) and sub-connected (SC) system structure. Moreover, the superiority of PAST over SVD-based hybrid precoding in terms of complexity and increases with the number of transmitting antennas.

Zero-shot learning (ZSL) aims to classify images of unseen classes by learning relationship between visual and semantic features. Existing works have been improving recognition accuracy from various approaches, but they employ computationally intensive algorithms that require iterative optimization. In this work, we revisit the primary approach of the pattern recognition, ı.e., nearest neighbor classifiers, to solve the ZSL task by an extremely simple and fast way, called SimpleZSL. Our algorithm consists of the following three simple techniques: (1) just averaging feature vectors to obtain visual prototypes of seen classes, (2) calculating a pseudo-inverse matrix via singular value decomposition to generate visual features of unseen classes, and (3) inferring unseen classes by a nearest neighbor classifier in which cosine similarity is used to measure distance between feature vectors. Through the experiments on common datasets, the proposed method achieves good recognition accuracy with drastically small computational costs. The execution time of the proposed method on a single CPU is more than 100 times faster than those of the GPU implementations of the existing methods with comparable accuracies.

In this Letter, we propose a blind and robust multiple watermarking scheme using Contourlet transform and singular value decomposition (SVD). The host image is first decomposed by Contourlet transform. Singular values of Contourlet coefficient blocks are adopted to embed watermark information, and a fast calculation method is proposed to avoid the heavy computation of SVD. The watermark is embedded in both low and high frequency Contourlet coefficients to increase the robustness against various attacks. Moreover, the proposed scheme intrinsically exploits the characteristics of human visual system and thus can ensure the invisibility of the watermark. Simulation results show that the proposed scheme outperforms other related methods in terms of both robustness and execution time.

The test of homogeneity for normal mixtures has been used in various fields, but its theoretical understanding is limited because the parameter set for the null hypothesis corresponds to singular points in the parameter space. In this paper, we shed a light on this issue from a new perspective, variational Bayes, and offer a theory for testing homogeneity based on it. Conventional theory has not reveal the stochastic behavior of the variational free energy, which is necessary for constructing a hypothesis test, has remained unknown. We clarify it for the first time and construct a new test base on it. Numerical experiments show the validity of our results.

At ASIACRYPT 2018, Castryck, Lange, Martindale, Panny and Renes proposed CSIDH, which is a key-exchange protocol based on isogenies between elliptic curves, and a candidate for post-quantum cryptography. However, the implementation by Castryck et al. is not constant-time. Specifically, a part of the secret key could be recovered by the side-channel attacks. Recently, Meyer, Campos, and Reith proposed a constant-time implementation of CSIDH by introducing dummy isogenies and taking secret exponents only from intervals of non-negative integers. Their non-negative intervals make the calculation cost of their implementation of CSIDH twice that of the worst case of the standard (variable-time) implementation of CSIDH. In this paper, we propose a more efficient constant-time algorithm that takes secret exponents from intervals symmetric with respect to the zero. For using these intervals, we need to keep two torsion points on an elliptic curve and calculation for these points. We evaluate the costs of our implementation and that of Meyer et al. in terms of the number of operations on a finite prime field. Our evaluation shows that our constant-time implementation of CSIDH reduces the calculation cost by 28% compared with the implementation by Mayer et al. We also implemented our algorithm by extending the implementation in C of Meyer et al. (originally from Castryck et al.). Then our implementation achieved 152 million clock cycles, which is about 29% faster than that of Meyer et al. and confirms the above reduction ratio in our cost evaluation.

Fast computation of singular value decomposition (SVD) is of great interest in various machine learning tasks. Recently, SVD methods based on randomized linear algebra have shown significant speedup in this regime. For processing large-scale data, computing systems with accelerators like GPUs have become the mainstream approach. In those systems, access to the input data dominates the overall process time; therefore, it is needed to design an out-of-core algorithm to dispatch the computation into accelerators. This paper proposes an accurate two-pass randomized SVD, named block randomized SVD (BRSVD), designed for matrices with a slow-decay singular spectrum that is often observed in image data. BRSVD fully utilizes the power of modern computing system architectures and efficiently processes large-scale data in a parallel and out-of-core fashion. Our experiments show that BRSVD effectively moves the performance bottleneck from data transfer to computation, so that outperforms existing randomized SVD methods in terms of speed with retaining similar accuracy.

Homotopy algorithm provides a very powerful approach to select the best regularization term for the l1-norm minimization problem, but it is lack of provision for handling singularities. The singularity problem might be frequently encountered in practical implementations if the measurement matrix contains duplicate columns, approximate columns or columns with linear dependent in kernel space. The existing method for handling Homotopy singularities introduces a high-dimensional random ridge term into the measurement matrix, which has at least two shortcomings: 1) it is very difficult to choose a proper ridge term that applies to several different measurement matrices; and 2) the high-dimensional ridge term may accumulatively degrade the recovery performance for large-scale applications. To get around these shortcomings, a modified ridge-adding method is proposed to deal with the singularity problem, which introduces a low-dimensional random ridge vector into the l1-norm minimization problem directly. Our method provides a much simpler implementation, and it can alleviate the degradation caused by the ridge term because the dimension of ridge term in the proposed method is much smaller than the original one. Moreover, the proposed method can be further extended to handle the SVMpath initialization singularities. Theoretical analysis and experimental results validate the performance of the proposed method.

In order to solve the problem in Automatic Identification System (AIS) that the signal in the target slot cannot be correctly received due to partial overlap of signals in adjacent time slots, the paper introduces a new criterion: maximum expected signal power (MESP) and proposes a novel beamforming algorithm based on generalized singular value decomposition (GSVD) and orthogonal projection. The algorithm employs GSVD to estimate the signal subspace, and adopts orthogonal projection to project the received signal onto the orthogonal subspace of the non-target signal. Then, beamforming technique is used to maximize the output power of the target signal on the basis of MESP. Theoretical analysis and simulation results show the effectiveness of the proposed algorithm.

Multiuser massive multi-input multi-output (MU massive MIMO) is considered as a promising technology for the fifth generation (5G) of the wireless communication system. In this paper, we propose a low-complexity joint antenna and user selection scheme with block diagonalization (BD) precoding for MU massive MIMO downlink channel in the time division duplex (TDD) system. The base station (BS) is equipped with a large-scale transmit antenna array while each user is using the single receive antenna in the system. To reduce the hardware cost, BS will be implemented by limited number of radio frequency (RF) chains and BS must activate some selected transmit antennas in the BS side for data transmitting and some users' receive antennas in user side for data receiving. To achieve the reduction in the computation complexity in the antenna and user selection while maintaining the same or higher sum-rate in the system, the proposed scheme relies on three complexity reduction key factors. The first key factor is that finding the average channel gains for the transmit antenna in the BS side and the receive antenna in the user side to select the best channel gain antennas and users. The second key factor called the complexity control factor ξ(Xi) for the antenna set and the user set limitation is used to control the complexity of the brute force search. The third one is that using the assumption of the point-to-point deterministic MIMO channel model to avoid the singular value decomposition (SVD) computation in the brute force search. We show that the proposed scheme offers enormous reduction in the computation complexity while ensuring the acceptable performance in terms of total system sum-rate compared with optimal and other conventional schemes.

Compressed sensing theory provides a new approach to acquire data as a sampling technique and makes sure that a sparse signal can be reconstructed from few measurements. The construction of compressed sensing matrices is a main problem in compressed sensing theory (CS). In this paper, the deterministic constructions of compressed sensing matrices based on affine singular linear space over finite fields are presented and a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. By choosing appropriate parameters, our sparse compressed sensing matrices are superior to the DeVore's matrices. Then we use a new formulation of support recovery to recover the support sets of signals with sparsity no more than k on account of binary compressed sensing matrices satisfying disjunct and inclusive properties.

This paper presents an efficient acceleration algorithm for Lloyd-type k-means clustering, which is suitable to a large-scale and high-dimensional data set with potentially numerous classes. The algorithm employs a novel projection-based filter (PRJ) to avoid unnecessary distance calculations, resulting in high-speed performance keeping the same results as a standard Lloyd's algorithm. The PRJ exploits a summable lower bound on a squared distance defined in a lower-dimensional space to which data points are projected. The summable lower bound can make the bound tighter dynamically by incremental addition of components in the lower-dimensional space within each iteration although the existing lower bounds used in other acceleration algorithms work only once as a fixed filter. Experimental results on large-scale and high-dimensional real image data sets demonstrate that the proposed algorithm works at high speed and with low memory consumption when large k values are given, compared with the state-of-the-art algorithms.

This paper proposes a novel access technique that enables uplink multiuser multiple input multiple output (MU-MIMO) access with small overhead in distributed wireless networks. The proposed access technique introduces a probe packet that is sent to all terminals to judge whether they have the right to transmit their signals or not. The probe packet guarantees high quality MU-MIMO signal transmission when a minimum mean square error (MMSE) filter is applied at the access point, which results in high frequency utilization efficiency. Computer simulation reveals that the proposed access achieves more than twice of the capacity obtained by the traditional carrier sense multiple access/collision avoidance (CSMA/CA) with a single user MIMO, when the access point with 5 antennas is surrounded by the terminals with 2 antennas.

This paper proposes an image denoising method using singular value decomposition (SVD) with block-rotation-based operations in wavelet domain. First, we decompose a noisy image to some sub-blocks, and use the single-level discrete 2-D wavelet transform to decompose each sub-block into the low-frequency image part and the high-frequency parts. Then, we use SVD and rotation-based SVD with the rank-1 approximation to filter the noise of the different high-frequency parts, and get the denoised sub-blocks. Finally, we reconstruct the sub-block from the low-frequency part and the filtered the high-frequency parts by the inverse wavelet transform, and reorganize each denoised sub-blocks to obtain the final denoised image. Experiments show the effectiveness of this method, compared with relevant methods.

A method is proposed for improving the accuracy of the characteristic basis function method (CBFM) using the multilevel approach. With this technique, CBFs taking into account multiple scattering calculated for each block (IP-CBFs; improved primary CBFs) are applied to CBFM using a multilevel approach. By using IP-CBFs, the interaction between blocks is taken into account, and thus it is possible to reduce the number of CBFs while maintaining accuracy, even if the multilevel approach is used. The radar cross section (RCS) of a cube, a cavity, and a dielectric sphere were analyzed using the proposed CBFs, and as a result it was found that accuracy is improved over the conventional method, despite no major change in the number of CBFs.

The Retinex theory assumes that large intensity changes correspond to reflectance edges, while smoothly-varying regions are due to shading. Some algorithms based on the theory adopt simple thresholding schemes and achieve adequate results for reflectance estimation. In this paper, we present a practical reflectance estimation technique for hyperspectral images. Our method is realized simply by thresholding singular values of a matrix calculated from scaled pixel values. In the method, we estimate the reflectance image by measuring spectral similarity between two adjacent pixels. We demonstrate that our thresholding scheme effectively estimates the reflectance and outperforms the Retinex-based thresholding. In particular, our methods can precisely distinguish edges caused by reflectance change and shadows.

This paper proposes a blind, inaudible, robust digital-audio watermarking scheme based on singular-spectrum analysis, which relates to watermarking techniques based on singular value decomposition. We decompose a host signal into its oscillatory components and modify amplitudes of some of those components with respect to a watermark bit and embedding rule. To improve the sound quality of a watermarked signal and still maintain robustness, differential evolution is introduced to find optimal parameters of the proposed scheme. Test results show that, although a trade-off between inaudibility and robustness still persists, the difference in sound quality between the original and the watermarked one is considerably smaller. This improved scheme is robust against many attacks, such as MP3 and MP4 compression, and band-pass filtering. However, there is a drawback, i.e., some music-dependent parameters need to be shared between embedding and extraction processes. To overcome this drawback, we propose a method for automatic parameter estimation. By incorporating the estimation method into the framework, those parameters need not to be shared, and the test results show that it can blindly decode watermark bits with an accuracy of 99.99%. This paper not only proposes a new technique and scheme but also discusses the singular value and its physical interpretation.

This paper proposes a novel image integral equation of the first type (IIE-1) for a TE plane wave scattering from periodic rough surfaces with perfect conductivity by means of the method of image Green's function. Since such an IIE-1 is valid for any incident wavenumbers including the critical wavenumbers, the analytical properties of the scattered wavefield can be generally and rigorously discussed. This paper firstly points out that the branch point singularity of the bare propagator inevitably appears on the incident wavenumber characteristics of the scattered wavefield and its related quantities just at the critical wavenumbers. By applying a quadrature method, the IIE-1 becomes a matrix equation to be numerically solved. For a periodic rough surface, several properties of the scattering are shown in figures as functions of the incident wavenumbers. It is then confirmed that the branch point singularity clearly appears in the numerical solution. Moreover, it is shown that the proposed IIE-1 gives a numerical solution satisfying sufficiently the optical theorem even for the critical wavenumbers.