Quantum color image scaling based on bilinear interpolation

As a part of quantum image processing, quantum image scaling is a significant technology for the development of quantum computation. At present, most of the quantum image scaling schemes are based on grayscale images, with relatively little processing for color images. This paper proposes a quantum color image scaling scheme based on bilinear interpolation, which realizes the 2^(n_(1)) × 2^(n_(2)) quantum color image scaling. Firstly, the improved novel quantum representation of color digital images(INCQI) is employed to represent a 2^(n_(1)) × 2^(n_(2)) quantum color image, and the bilinear interpolation method for calculating pixel values of the interpolated image is presented. Then the quantum color image scaling-up and scaling-down circuits are designed by utilizing a series of quantum modules, and the complexity of the circuits is analyzed.Finally, the experimental simulation results of MATLAB based on the classical computer are given. The ultimate results demonstrate that the complexities of the scaling-up and scaling-down schemes are quadratic and linear, respectively, which are much lower than the cubic function and exponential function of other bilinear interpolation schemes.

A theoretical study of the multigrid three-dimensional variational data assimilation scheme using a simple bilinear interpolation algorithm

In order to solve the so-called ＂bull-eye＂ problem caused by using a simple bilinear interpolation as an observational mapping operator in the cost function in the multigrid three-dimensional variational （3DVAR） data assimilation scheme, a smoothing term, equivalent to a penalty term, is introduced into the cost function to serve as a means of troubleshooting. A theoretical analysis is first performed to figure out what on earth results in the issue of ＂bull-eye＂, and then the meaning of such smoothing term is elucidated and the uniqueness of solution of the multigrid 3DVAR with the smoothing term added is discussed through the theoretical deduction for one-dimensional （1D） case, and two idealized data assimilation experiments （one- and two-dimensional （2D） cases）. By exploring the relationship between the smoothing term and the recursive filter theoretically and practically, it is revealed why satisfied analysis results can be achieved by using such proposed solution for the issue of the multigrid 3DVAR.

Improved absorbing boundary condition based on linear interpolation for ADI-FDTD method

With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.

An osculatory rational interpolation method of model reduction in linear system

A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation. On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear systems. Some numerical examples were given to explain the result in this paper.

LINEAR SYSTEMS AND LINEAR INTERPOLATION I

The linear interpolation of linear system on a family of linear systems is introduced and discussed. Some results and examples on singly generated systems on a finite dimensional vector space are given.

Tri-linear interpolation-based cerebral white matter fiber imaging

Diffusion tensor imaging is a unique method to visualize white matter fibers three-dimensionally, non-invasively and in vivo, and therefore it is an important tool for observing and researching neural regeneration. Different diffusion tensor imaging-based fiber tracking methods have been already investigated, but making the computing faster, fiber tracking longer and smoother and the details shown clearer are needed to be improved for clinical applications. This study proposed a new fiber tracking strategy based on tri-linear interpolation. We selected a patient with acute infarction of the right basal ganglia and designed experiments based on either the tri-linear interpolation algorithm or tensorline algorithm. Fiber tracking in the same regions of interest （genu of the corpus callosum） was performed separately. The validity of the tri-linear interpolation algorithm was verified by quan- titative analysis, and its feasibility in clinical diagnosis was confirmed by the contrast between tracking results and the disease condition of the patient as well as the actual brain anatomy. Statis- tical results showed that the maximum length and average length of the white matter fibers tracked by the tri-linear interpolation algorithm were significantly longer. The tracking images of the fibers indicated that this method can obtain smoother tracked fibers, more obvious orientation and clearer details. Tracking fiber abnormalities are in good agreement with the actual condition of patients, and tracking displayed fibers that passed though the corpus callosum, which was consistent with the anatomical structures of the brain. Therefore, the tri-linear interpolation algorithm can achieve a clear, anatomically correct and reliable tracking result.

Analysis and Comparison of Time Replica and Time Linear Interpolation for Pilot Aided Channel Estimation in OFDM Systems

This paper analyzes and compares two time interpolators, i.e., time replica and time linear interpolator, for pilot aided channel estimation in orthogonal frequency division multiplexing (OFDM) systems. The mean square error (MSE) of two interpolators is theoretically derived for the general case. The equally spaced pilot arrangement is proposed as a special platform for these two time interpolators. Based on this proposed platform, the MSE of two time interpolators at the virtual pilot tones is derived analytically;moreover, the MSE of per channel estimator at the entire OFDM symbol based on per time interpolator is also derived. The effectiveness of the theoretical analysis is demonstrated by numerical simulation in both the time-invariant frequency-selective channel and the time varying frequency-selective channel.

Shifted Linear Interpolation Filter

Linear interpolation has been adapted in many signal and image processing applications due to its simple implementation and low computational cost. In standard linear interpolation the kernel is the second order B-spline. In this work we show that the interpolation error can be remarkably diminished by using the time-shifted B-spline as an interpolation kernel. We verify by experimental tests that the optimal shift is. In VLSI and microprocessor circuits the shifted linear interpolation (SLI) algorithm can be effectively implemented by the z-transform filter. The interpolation error of the SLI filter is comparable to the more elaborate higher order cubic convolution interpolation.

A Linear Interpolation-Based Algorithm for Path Planning and Replanning on Girds

Field D* algorithm is widely used in mobile robot navigation since it can plan and replan any-angle paths through non-uniform cost grids. However, it still suffers from inefficiency and sub-optimality. In this article, a new linear interpolation-based planning and replanning algorithm, Update-Reducing Field D*, is proposed. It employs different approaches during initial planning and replanning respectively in order to reduce the number of updates of the rhs-values of vertices. Experiments have shown that Update-Reducing Field D* runs faster than Field D* and returns smoother and lower-cost paths.

Realization of orientation interpolation of 6-axis articulated robot using quaternion

In general, the orientation interpolation of industrial robots has been done based on Euler angle system which can result in singular point （so-called Gimbal Lock）. However, quaternion interpolation has the advantage of natural （specifically smooth） orientation interpolation without Gimbal Lock. This work presents the application of quatemion interpolation, specifically Spherical Linear IntERPolation （SLERP）, to the orientation control of the 6-axis articulated robot （RS2） using LabVIEW and RecurDyn. For the comparison of SLERP with linear Euler interpolation in the view of smooth movement （profile） of joint angles （torques）, the two methods are dynamically simulated on RS2 by using both LabVIEW and RecurDyn. Finally, our original work, specifically the implementation of SLERP and linear Euler interpolation on the actual robot, i.e. RS2, is done using LabVIEW motion control tool kit. The SLERP orientation control is shown to be effective in terms of smooth joint motion and torque when compared to a conventional （linear） Euler interpolation.

Static output feedback control for discrete-time fuzzy bilinear system

The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.

A modified time domain interpolation method for LS channel estimation in OFDM systems

A modified time domain interpolation method is proposed for orthogonal frequency division multiplexing(OFDM)systems to address the problem that time domain interpolation in the least square(LS)channel estimation method based on comb-type pilots cannot choose the pilot spacing flexibly.Firstly,the estimated channel frequency response(CFR)at pilot positions in the frequency domain is obtained by LS channel estimation based on comb-type pilots,and the estimated channel impulse response(CIR)in the time domain is obtained by linear interpolation and inverse fast Fourier transform(IFFT).Secondly,the error of the estimated CIR obtained by linear interpolation is analyzed by theoretical deduction,and a method for correcting it is proposed.Finally,an estimated CFR at all subcarrier positions in the frequency domain is obtained by performing zero padding in the time domain and fast Fourier transform(FFT)on the modified CIR.The simulation results suggest that the proposed method gives similar performance to time domain interpolation,yet it does not need to meet the condition of time domain interpolation that the number of subcarriers must be an integral multiple of pilot spacing to use it.The proposed method allows for flexible pilot spacing,reducing the number of pilots and the consumption of subcarriers used for channel estimation.

A comparison of piecewise cubic Hermite interpolating polynomials,cubic splines and piecewise linear functions for the approximation of projectile aerodynamics

Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.

Seismic ray-tracing calculation based on parabolic travel-time interpolation

A new seismic ray-tracing method is put forward based on parabolic travel-time interpolation(PTI) method, which is more accurate than the linear travel-time interpolation (LTI) method. Both PTI method and LTI method are used to compute seismic travel-time and ray-path in a 2-D grid cell model. Firstly, some basic concepts are introduced. The calculations of travel-time and ray-path are carried out only at cell boundaries. So, the ray-path is always straight in the same cells with uniform velocity. Two steps are applied in PTI and LTI method, step 1 computes travel-time and step 2 traces ray-path. Then, the derivation of LTI formulas is described. Because of the presence of refraction wave in shot cell, the formula aiming at shot cell is also derived. Finally, PTI method is presented. The calculation of PTI method is more complex than that of LTI method, but the error is limited. The results of numerical model show that PTI method can trace ray-path more accurately and efficiently than LTI method does.

MRF-Based Multispectral Image Fusion Using an Adaptive Approach Based on Edge-Guided Interpolation

In interpretation of remote sensing images, it is possible that some images which are supplied by different sensors become incomprehensible. For better visual perception of these images, it is essential to operate series of pre-processing and elementary corrections and then operate a series of main processing steps for more precise analysis on the images. There are several approaches for processing which are depended on the type of remote sensing images. The discussed approach in this article, i.e. image fusion, is the use of natural colors of an optical image for adding color to a grayscale satellite image which gives us the ability for better observation of the HR image of OLI sensor of Landsat-8. This process with emphasis on details of fusion technique has previously been performed;however, we are going to apply the concept of the interpolation process. In fact, we see many important software tools such as ENVI and ERDAS as the most famous remote sensing image processing tools have only classical interpolation techniques (such as bi-linear (BL) and bi-cubic/cubic convolution (CC)). Therefore, ENVI- and ERDAS-based researches in image fusion area and even other fusion researches often don’t use new and better interpolators and are mainly concentrated on the fusion algorithm’s details for achieving a better quality, so we only focus on the interpolation impact on fusion quality in Landsat-8 multispectral images. The important feature of this approach is to use a statistical, adaptive, and edge-guided interpolation method for improving the color quality in the images in practice. Numerical simulations show selecting the suitable interpolation techniques in MRF-based images creates better quality than the classical interpolators.

BILINEAR FORMS AND LINEAR CODES

Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding process and the decoding procedure of RS codes are simplified via circulant matrices. Finally, the results show that the correspondence between bilinear forms and linear codes is not unique.

High accuracy NURBS interpolation for five-axis machine of table-rotating/spindle-tilting type

In this paper, the definition of NURBS curve and a speed-controlled interpolation in which the feed rate is automatically adjusted in order to meet the specified chord error limit were discussed. Besides those, a definition of linear interpolation error of post-processed data was proposed, which should be paid more attention to because it will not only reduce quality of the surface but also may cause interference and other unexpected trouble. In order to control the error, a robust algorithm was proposed, which successfully met a desired error limit through interpolating some essential CL data. The excellence of the proposed algorithm, in terms of its reliability and self-adaptiveness, has been proved by simulation results.

A Virtual Walk along Street Based on View Interpolation

Image morphing is a powerful tool for visual effect. In this paper, a view interpolation algorithm is proposed to simulate a virtual walk along a street from start position to end position. To simulate a virtual walking view needs to create new appearing scene in the vision-vanishing point and disappearing scene beyond the scope of view. To attain these two aims we use two enhanced position parameters to match pixels of source images and target images. One enhanced position parameter is the angular coordinates of pixels. Another enhanced position parameter is the distances from pixels to the vision-vanishing point. According to the parameter values, pixels beyond the scope of view can be ＂moved＂ out in linear interpolation. Result demonstrates the validity of the algorithm. Another advantage of this algorithm is that the enhanced position parameters are based on real locations and walking distances, so it is also an approach to online virtual tour by satellite maps of virtual globe applications such as Google Earth.

Feedback Linearization Optimal Control Approach for Bilinear Systems in CSTR Chemical Reactor

This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a pseudo linear system model through the coordinate transformation. Then based on the theory of linear quadratic optimal control, the optimal controller is designed by solving the Riccati equation and introducing state feedback with state prediction. At last, the simulation results in CSTR Chemical reactor show the effectiveness of the method.

Optimal Control for Time-Delay Bilinear Systems with Sinusoidal Disturbances

This paper considers the optimal control problem for time-delay bilinear systems affected by sinusoidal disturbances with known frequency and measurable amplitude and phase. Firstly, using the differential homeomorphism, a time-delay bilinear system affected by sinusoidal disturbances is changed to a time-delay pseudo linear system through the coordinate transformation. Then the system with time-delay in control variable is transformed to a linear controllable system without delay using model transformation. At last based on the theory of linear quadratic optimal control, an optimal control law which is used to eliminate the influence of the disturbances is derived from a Riccati equation and Matrix equations. The simulation results show the effectiveness of the method.