Moore-Penrose Pseudo-inverse Matrix Research Articles

Optimal Linear Glauber Model

Contrary to the actual nonlinear Glauber model (NLGM), the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate ($w_j$) in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear $w_j$ are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau (TDGL) equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

Algorithm for improving SNR using high voltage and differential Manchester code for capacitive touch screen panel

An algorithm for a capacitive touch screen panel that can make the sum of the signal into `0' for the use of high voltage is presented. The differential Manchester code is combined with the Walsh-Hadamard code to generate an input coded signal. Owing to the property of the differential Manchester code, the Moore-Penrose pseudoinverse matrix is employed to decode-mutual capacitance from the received signal. As only the variation between the un-touch and touch condition is detected at the receiver, a high-voltage input coded signal is used. Unlike a normal touch system, the decoded sensing capacitance in the proposed algorithm does not have an absolute value. Positive decoded capacitance is the un-touch condition and negative decoded capacitance is the touch condition. The simulated signal-to-noise ratio (SNR) of the proposed algorithm is 27.9 dB, which is 8.26 dB higher than SNR in not return to zero (NRZ).

Automatic building detection based on Purposive FastICA (PFICA) algorithm using monocular high resolution Google Earth images

This paper proposes an improved FastICA model named as Purposive FastICA (PFICA) with initializing by a simple color space transformation and a novel masking approach to automatically detect buildings from high resolution Google Earth imagery. ICA and FastICA algorithms are defined as Blind Source Separation (BSS) techniques for unmixing source signals using the reference data sets. In order to overcome the limitations of the ICA and FastICA algorithms and make them purposeful, we developed a novel method involving three main steps: 1-Improving the FastICA algorithm using Moore–Penrose pseudo inverse matrix model, 2-Automated seeding of the PFICA algorithm based on LUV color space and proposed simple rules to split image into three regions; shadow+vegetation, baresoil+roads and buildings, respectively, 3-Masking out the final building detection results from PFICA outputs utilizing the K-means clustering algorithm with two number of clusters and conducting simple morphological operations to remove noises. Evaluation of the results illustrates that buildings detected from dense and suburban districts with divers characteristics and color combinations using our proposed method have 88.6% and 85.5% overall pixel-based and object-based precision performances, respectively.

Characterization method for a multispectral high-dynamic-range imaging system

An accurate characterization method for a multispectral high-dynamic-range (HDR) imaging system is proposed by combining multispectral and HDR imaging technologies. The multispectral HDR imaging system, which can acquire the visible spectrum at many wavelength bands, can provide an accurate color reproduction and physical radiance information of real objects. An HDR camera is used to capture an HDR image without multiple exposures and a liquid crystal tunable filter (LCTF) is used to generate multispectral images. Due to its several limitations in the multispectral HDR imaging system, a carefully designed and an innovative characterization algorithm is presented by considering a logarithmic camera response of the HDR camera and different spectral transmittance of the LCTF. The proposed method efficiently and accurately recovers the full spectrum from the multispectral HDR images using a transformation matrix and provides device-independent color information (e.g., CIEXYZ and CIELAB). The transformation matrix is estimated by training the estimated sensor responses from a multispectral HDR imaging system and the reflectance measurements from a spectroradiometer using Moore–Penrose pseudoinverse matrix.

Efficient detection scheme in MIMO-OFDM for high speed wireless home network system

This paper proposes a MIMO-OFDM scheme reducing the computational complexity and providing comparable performance to QRD-M detection scheme in IEEE 802.11n. The proposed scheme checks the channel condition per subcarrier and then selects either ordered DFE scheme or adaptive QRD-M detection scheme according to that information. The post-detection SNR which judges channel condition depends on Moore-Penrose pseudo-inverse matrix G. The proposed scheme selects the ordered DFE detection scheme in case of good channel condition and the adaptive QRD-M detection scheme in case of bad channel condition per subcarrier. The adaptive QRDM detection scheme selects the number of variable survival symbols M in accordance with the channel condition at each layer. Compared with the conventional QRD-M (M=16) detection scheme, the proposed detection scheme reduces the computational complexity about 67 percents and achieves similar performance.

화학반응식 균형과 안정성을 위한 새로운 유사 역행렬법

이 논문에 화학반응식 균형을 맞추기 위한 새로운 유사 역행렬법이 기술되었다. 여기에 제공된 방법은 Moore-Penrose 유사 역행렬을 사용한 Diophantin 행렬식의 해에 기초를 둔다. 방법은 전형적인 여러 화학반응식에 시험적용되었고 폭넓은 균형연구에서 모든 반응식에 매우 성공적이었다. 이 방법은 아무 제한없이 성공적으로 적용되고, 또한 새로운 화학반응식의 타당성에 대한 검증력도 있고, 만일 새식이 타당하다면 화학식 균형을 이룰 것이다. 여기서 다루어진 화학반응식들은 소수산화수를 지닌 원자를 포함하고 있다. 또한, 화학반응식의 확장된 행렬의 안정성에 대한 화학반응식의 안정성의 필요충분조건을 이 연구에 소개하였다. this work is given a new pseudoniverse matrix method for balancing chemical equations. Here offered method is founded on virtue of the solution of a Diophantine matrix equation by using of a Moore-Penrose pseudoinverse matrix. The method has been tested on several typical chemical equations and found to be very successful for the all equations in our extensive balancing research. This method, which works successfully without any limitations, also has the capability to determine the feasibility of a new chemical reaction, and if it is feasible, then it will balance the equation. Chemical equations treated here possess atoms with fractional oxidation numbers. Also, in the present work are introduced necessary and sufficient criteria for stability of chemical equations over stability of their extended matrices.

Resistor mesh model of a spherical head: Part 1: Applications to scalp potential interpolation

A resistor mesh model (RMM) has been implemented to describe the electrical properties of the head and the configuration of the intracerebral current sources by simulation of forward and inverse problems in electroencephalogram/event related potential (EEG/ERP) studies. For this study, the RMM representing the three basic tissues of the human head (brain, skull and scalp) was superimposed on a spherical volume mimicking the head volume: it included 43 102 resistances and 14 123 nodes. The validation was performed with reference to the analytical model by consideration of a set of four dipoles close to the cortex. Using the RMM and the chosen dipoles, four distinct families of interpolation technique (nearest neighbour, polynomial, splines and lead fields) were tested and compared so that the scalp potentials could be recovered from the electrode potentials. The 3D spline interpolation and the inverse forward technique (IFT) gave the best results. The IFT is very easy to use when the lead-field matrix between scalp electrodes and cortex nodes has been calculated. By simple application of the Moore-Penrose pseudo inverse matrix to the electrode cap potentials, a set of current sources on the cortex is obtained. Then, the forward problem using these cortex sources renders all the scalp potentials.

Optimally regularized inverse of singular value decomposition and application to signal extrapolation

The singular value decomposition (SVD) is an excellent tool to attain reliable and stable least squares parameters estimation in ill-conditioned cases, by discarding small singular values adequately. However, large singular values and small singular values do not always separate neatly. In the present paper, we introduce multiple regularization parameters to modify the Moore-Penrose pseudo-inverse matrix for the purpose of stabilization of ill-posed least squares problems. Optimal values of the regularization parameters can be determined so as to minimize an estimated mean squares error (EMSE) criterion calculated by using only accessible signal data. Thus, the proposed scheme can successfully give threshold conditions whether smaller singular values should be adopted or discarded. The relationship with the optimal truncation of the singular values is also investigated analytically. Effectiveness of the proposed method is discussed in applications to optimal extrapolation of band-limited signals.