Multivariate public key cryptosystem (MPKC) is one of the major post quantum cryptosystems (PQC), and the National Institute of Standards and Technology (NIST) recently selected four MPKCs as candidates of their PQC. The security of MPKC depends on the hardness of solving systems of algebraic equations over finite fields. In particular, the multivariate quadratic (MQ) problem is that of solving such a system consisting of quadratic polynomials and is regarded as an important research subject in cryptography. In the Fukuoka MQ challenge project, the hardness of the MQ problem is discussed, and algorithms for solving the MQ problem and the computational results obtained by these algorithms are reported. Algorithms for computing Gröbner basis are used as the main tools for solving the MQ problem. For example, the F4 algorithm and M4GB algorithm have succeeded in solving many instances of the MQ problem provided by the project. In this paper, based on the F4-style algorithm, we present an efficient algorithm to solve the MQ problems with dense polynomials generated in the Fukuoka MQ challenge project. We experimentally show that our algorithm requires less computational time and memory for these MQ problems than the F4 algorithm and M4GB algorithm. We succeeded in solving Type II and III problems of Fukuoka MQ challenge using our algorithm when the number of variables was 37 in both problems.

The impedance expansion method (IEM), which has been previously proposed by the authors, is a circuit-modeling technique for electrically-very-small devices. This paper provides a new idea on the principle of undesired radiation in wireless power transfer systems by employing IEM. In particular, it is shown that the undesired radiation is due to equivalent infinitesimal dipoles and loops of the currents on the coils.

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.

In this paper, we introduce a new method to remove random-valued impulse noise in an image. Random-valued impulse noise replaces the pixel value at a random position by a random value. Due to the randomness of the noisy pixel values, it is difficult to detect them by comparison with neighboring pixels, which is used in many conventional methods. Then we improve the recent noise detector which uses a non-local search of similar structure. Next we propose a new noise removal algorithm by sparse representation using DCT basis. Furthermore, the sparse representation can remove impulse noise by using the neighboring similar image patch. This method has much more superior noise removal performance than conventional methods at images. We confirm the effectiveness of the proposed method quantitatively and qualitatively.

In this paper, the problem of channel estimation in orthogonal frequency-division multiplexing systems over fast time-varying channel is investigated by using a Basis Expansion Model (BEM). Regarding the effects of the Gibbs phenomenon in the BEM, we propose a new method to alleviate it and reduce the modeling error. Theoretical analysis and detail comparison results show that the proposed BEM method can provide improved modeling error compared with other BEMs such as CE-BEM and GCE-BEM. In addition, instead of using the frequency-domain Kronecker delta structure, a new clustered pilot structure is proposed to enhance the estimation performance further. The new clustered pilot structure can effectively reduce the inter-carrier interference especially in the case of high Doppler spreads.

We propose a novel improved characteristic basis function method (IP-CBFM) for accurately analysing the radar cross section (RCS). This new IP-CBFM incorporates the effect of higher-order multiple scattering and has major influences in analyzing monostatic RCS (MRCS) of single incidence and bistatic RCS (BRCS) problems. We calculated the RCS of two scatterers and could confirm that the proposed IP-CBFM provided higher accuracy than the conventional method while significantly reducing the number of CBF.

We propose subquadratic space complexity multipliers for any finite field $mathbb{F}_{q^n}$ over the base field $mathbb{F}_q$ using the Dickson basis, where q is a prime power. It is shown that a field multiplication in $mathbb{F}_{q^n}$ based on the Dickson basis results in computations of Toeplitz matrix vector products (TMVPs). Therefore, an efficient computation of a TMVP yields an efficient multiplier. In order to derive efficient $mathbb{F}_{q^n}$ multipliers, we develop computational schemes for a TMVP over $mathbb{F}_{q}$. As a result, the $mathbb{F}_{2^n}$ multipliers, as special cases of the proposed $mathbb{F}_{q^n}$ multipliers, have lower time complexities as well as space complexities compared with existing results. For example, in the case that n is a power of 3, the proposed $mathbb{F}_{2^n}$ multiplier for an irreducible Dickson trinomial has about 14% reduced space complexity and lower time complexity compared with the best known results.

This paper describes a novel statistical bandwidth extension (BWE) technique based on a Gaussian mixture model (GMM) and a sub-band basis spectrum model (SBM), in which each dimensional component represents a specific acoustic space in the frequency domain. The proposed method can achieve the BWE from speech data with an arbitrary frequency bandwidth whereas the conventional methods perform the conversion from fixed narrow-band data. In the proposed method, we train a GMM with SBM parameters extracted from full-band spectra in advance. According to the bandwidth of input signal, the trained GMM is reconstructed to the GMM of the joint probability density between low-band SBM and high-band SBM components. Then high-band SBM components are estimated from low-band SBM components of the input signal based on the reconstructed GMM. Finally, BWE is achieved by adding the spectra decoded from estimated high-band SBM components to the ones of the input signal. To construct the full-band signal from the narrow-band one, we apply this method to log-amplitude spectra and aperiodic components. Objective and subjective evaluation results show that the proposed method extends the bandwidth of speech data robustly for the log-amplitude spectra. Experimental results also indicate that the aperiodic component extracted from the upsampled narrow-band signal realizes the same performance as the restored and the full-band aperiodic components in the proposed method.

A projective Reed-Muller (PRM) code, obtained by modifying a Reed-Muller code with respect to a projective space, is a doubly extended Reed-Solomon code when the dimension of the related projective space is equal to 1. The minimum distance and the dual code of a PRM code are known, and some decoding examples have been presented for low-dimensional projective spaces. In this study, we construct a decoding algorithm for all PRM codes by dividing a projective space into a union of affine spaces. In addition, we determine the computational complexity and the number of correctable errors of our algorithm. Finally, we compare the codeword error rate of our algorithm with that of the minimum distance decoding.

The characteristic basis function method using improved primary characteristic basis functions (IP-CBFM) has been proposed as a technique for high-precision analysis of monostatic radar cross section (RCS) of a scattering field in a specific coordinate plane. IP-CBFM is a method which reduces the number of CBF necessary to express a current distribution by combining secondary CBF calculated for each block of the scatterer with the primary CBF to form a single improved primary CBF (IP-CBF). When the proposed technique was evaluated by calculating the monostatic RCS of a perfect electric conductor plate and cylinder, it was found that solutions corresponding well with analysis results from conventional CBFM can be obtained from small-scale matrix equations.

Satellite-borne or aircraft-borne synthetic aperture radar (SAR) is useful for high resolution imaging analysis for terrain surface monitoring or surveillance, particularly in optically harsh environments. For surveillance application, there are various approaches for automatic target recognition (ATR) of SAR images aiming at monitoring unidentified ships or aircraft. In addition, various types of analyses for full polarimetric data have been developed recently because it can provide significant information to identify structure of targets, such as vegetation, urban, sea surface areas. ATR generally consists of two processes, one is target feature extraction including target area determination, and the other is classification. In this paper, we propose novel methods for these two processes that suit full polarimetric exploitation. As the target area extraction method, we introduce a peak signal-to noise ratio (PSNR) based synthesis with full polarimetric SAR images. As the classification method, the circular polarization basis conversion is adopted to improve the robustness especially to variation of target rotation angles. Experiments on a 1/100 scale model of X-band SAR, demonstrate that our proposed method significantly improves the accuracy of target area extraction and classification, even in noisy or target rotating situations.

Nonnegative matrix factorization (NMF) is an unsupervised technique to represent nonnegative data as linear combinations of nonnegative bases, which has shown impressive performance for source separation. However, its source separation performance degrades when one signal can also be described well with the bases for the interfering source signals. In this paper, we propose a discriminative NMF (DNMF) algorithm which exploits the reconstruction error for the interfering signals as well as the target signal based on target bases. The objective function for training the bases is constructed so as to yield high reconstruction error for the interfering source signals while guaranteeing low reconstruction error for the target source signals. Experiments show that the proposed method outperformed the standard NMF and another DNMF method in terms of both the perceptual evaluation of speech quality score and signal-to-distortion ratio in various noisy environments.

A field multiplication in the extended binary field is often expressed using Toeplitz matrix-vector products (TMVPs), whose matrices have special properties such as symmetric or triangular. We show that such TMVPs can be efficiently implemented by taking advantage of some properties of matrices. This yields an efficient multiplier when a field multiplication involves such TMVPs. For example, we propose an efficient multiplier based on the Dickson basis which requires the reduced number of XOR gates by an average of 34% compared with previously known results.

This letter studies the problem of cooperative spectrum sensing in wideband cognitive radio networks. Based on the basis expansion model (BEM), the problem of estimation of power spectral density (PSD) is transformed to estimation of BEM coefficients. The sparsity both in frequency domain and space domain is used to construct a sparse estimation structure. The theory of L1/2 regularization is used to solve the compressed sensing problem. Simulation results demonstrate the effectiveness of the proposed method.

This paper represents an illumination modeling method for lighting control which can model the illumination distribution inside office buildings. The algorithm uses data from the illumination sensors to train Radial Basis Function Neural Networks (RBFNN) which can be used to calculate 1) the illuminance contribution from each luminaire to different positions in the office 2) the natural illuminance distribution inside the office. This method can be used to provide detailed illumination contribution from both artificial and natural light sources for lighting control algorithms by using small amount of sensors. Simulations with DIALux are made to prove the feasibility and accuracy of the modeling method.

The higher-order characteristic basis function method (HO-CBFM) is clearly formulated. HO-CBFM provides results accurately even if a block division is arbitrary. The HO-CBFM combined with a volume integral equation (VIE) is used in the analysis of various antennas in the vicinity of a dielectric object. The results of the numerical analysis show that the HO-CBFM can reduce the CPU time while still achieving the desired accuracy.

This paper presents a graph-based approach to designing arithmetic circuits over Galois fields (GFs) using normal basis representations. The proposed method is based on a graph-based circuit description called Galois-field Arithmetic Circuit Graph (GF-ACG). First, we extend GF-ACG representation to describe GFs defined by normal basis in addition to polynomial basis. We then apply the extended design method to Massey-Omura parallel multipliers which are well known as typical multipliers based on normal basis. We present the formal description of the multipliers in a hierarchical manner and show that the verification time can be greatly reduced in comparison with those of the conventional techniques. In addition, we design GF exponentiation circuits consisting of the Massey-Omura parallel multipliers and an inversion circuit over composite field GF(((22)2)2) in order to demonstrate the advantages of normal-basis circuits over polynomial-basis ones.

This paper presents an application of the constained interpolation profile basis set (CIP-BS) method to electromagnetic fields analyses. Electromagnetic fields can be expanded in terms of multi-dimensional CIP basis functions, and the Galerkin method can then be applied to obtain a system of linear equations. In the present study, we focus on a two-dimensional problem with TMz polarization. In order to examine the precision of the CIP-BS method, TE202 resonant mode in a rectangular cavity is analyzed. The numerical results show that CIP-BS method has better performance than the finite-difference time-domain (FDTD) method when the time step is small. Then an absorbing boundary condition based on the perfectly matched layer (PML) is formulated, and the absorption performance is demonstrated. Finally, the propagation in an inhomogeneous medium is computed by using the proposed method, and it is observed that in the CIP-BS method, smooth variation of material constants is effectively formulated without additional computational costs, and that accurate results are obtained in comparison with the FDTD method even if the permittivity is high.

We propose a composite DCT basis line test signal to evaluate the video quality of a DTV encoder. The proposed composite test signal contains a frame index, a calibration square wave, and 7-field basis signals. The results show that the proposed method may be useful for an in-service video quality verifier, using an ordinary oscilloscope instead of special equipment.

We propose an accurate and scalable solution to the perspective-n-point problem, referred to as ASPnP. Our main idea is to estimate the orientation and position parameters by directly minimizing a properly defined algebraic error. By using a novel quaternion representation of the rotation, our solution is immune to any parametrization degeneracy. To obtain the global optimum, we use the Grobner basis technique to solve the polynomial system derived from the first-order optimality condition. The main advantages of our proposed solution lie in accuracy and scalability. Extensive experiment results, with both synthetic and real data, demonstrate that our proposed solution has better accuracy than the state-of-the-art noniterative solutions. More importantly, by exploiting vectorization operations, the computational cost of our ASPnP solution is almost constant, independent of the number of point correspondences n in the wide range from 4 to 1000. In our experiment settings, the ASPnP solution takes about 4 milliseconds, thus best suited for real-time applications with a drastically varying number of 3D-to-2D point correspondences.