One-dimensional Linear Interpolation Research Articles

An Improved Hybrid Cartesian/Immersed Boundary Method for Flow Simulation with Moving Boundaries

To simulate flow problems with moving fluid-solid interfaces, a boundary treatment technique based on a hybrid Cartesian/immersed boundary method is presented. In the vicinity of the immersed boundary, a forcing term is added into the governing flow equations to modify the discretization scheme for the viscous term during its spatial discretization. Addition of such a term enforces desired boundary condition on the immersed boundary. A one-dimensional linear interpolation scheme is used to obtained required information for the modified discretization scheme when dealing with a moving boundary. The present method is essentially second-order accurate and can obtain results that are in good agreement with benchmark references when simulating the flow induced by the in-line oscillation of a circular cylinder.

Channel Estimation Based on Statistical Frames and Confidence Level in OFDM Systems

Channel estimation is an important module for improving the performance of the orthogonal frequency division multiplexing (OFDM) system. The pilot-based least square (LS) algorithm can improve the channel estimation accuracy and the symbol error rate (SER) performance of the communication system. In pilot-based channel estimation, a certain number of pilots are inserted at fixed intervals between OFDM symbols to estimate the initial channel information, and channel estimation results can be obtained by one-dimensional linear interpolation. The minimum mean square error (MMSE) and linear minimum mean square error (LMMSE) algorithms involve the inverse operation of the channel matrix. If the number of subcarriers increases, the dimension of the matrix becomes large. Therefore, the inverse operation is more complex. To overcome the disadvantages of the conventional channel estimation methods, this paper proposes a novel OFDM channel estimation method based on statistical frames and the confidence level. The noise variance in the estimated channel impulse response (CIR) can be largely reduced under statistical frames and the confidence level; therefore, it reduces the computational complexity and improves the accuracy of channel estimation. Simulation results verify the effectiveness of the proposed channel estimation method based on the confidence level in time-varying dynamic wireless channels.

Assessment of metal artifact reduction methods in pelvic CT.

Metal artifact reduction (MAR) produces images with improved quality potentially leading to confident and reliable clinical diagnosis and therapy planning. In this work, the authors evaluate the performance of five MAR techniques for the assessment of computed tomography images of patients with hip prostheses. Five MAR algorithms were evaluated using simulation and clinical studies. The algorithms included one-dimensional linear interpolation (LI) of the corrupted projection bins in the sinogram, two-dimensional interpolation (2D), a normalized metal artifact reduction (NMAR) technique, a metal deletion technique, and a maximum a posteriori completion (MAPC) approach. The algorithms were applied to ten simulated datasets as well as 30 clinical studies of patients with metallic hip implants. Qualitative evaluations were performed by two blinded experienced radiologists who ranked overall artifact severity and pelvic organ recognition for each algorithm by assigning scores from zero to five (zero indicating totally obscured organs with no structures identifiable and five indicating recognition with high confidence). Simulation studies revealed that 2D, NMAR, and MAPC techniques performed almost equally well in all regions. LI falls behind the other approaches in terms of reducing dark streaking artifacts as well as preserving unaffected regions (p < 0.05). Visual assessment of clinical datasets revealed the superiority of NMAR and MAPC in the evaluated pelvic organs and in terms of overall image quality. Overall, all methods, except LI, performed equally well in artifact-free regions. Considering both clinical and simulation studies, 2D, NMAR, and MAPC seem to outperform the other techniques.

Using One-Dimensional Linear Interpolation Method to Check Over-Fitting in Neural Network with Multi-Dimensional Inputs

Neural networks are widely used to learn and predict the correlation between input and output. However, in the process of learning, the excessive reduction of errors may influence the validity of prediction, this phenomenon is called over-fitting. In order to address this problem, this study sequenced the input data into one-dimensional data for the neural network structure of multi-dimensional inputs, and used visual graphics to observe whether there is over-fitting. This method is called one-dimensional linear interpolation method. The result of example validation proved that the proposed method can provide specific graphical information effectively, and determine whether there is over-fitting.

A fully 3D approach for metal artifact reduction in computed tomography

In computed tomography imaging metal objects in the region of interest introduce inconsistencies during data acquisition. Reconstructing these data leads to an image in spatial domain including star-shaped or stripe-like artifacts. In order to enhance the quality of the resulting image the influence of the metal objects can be reduced. Here, a metal artifact reduction (MAR) approach is proposed that is based on a recomputation of the inconsistent projection data using a fully three-dimensional Fourier-based interpolation. The success of the projection space restoration depends sensitively on a sensible continuation of neighboring structures into the recomputed area. Fortunately, structural information of the entire data is inherently included in the Fourier space of the data. This can be used for a reasonable recomputation of the inconsistent projection data. The key step of the proposed MAR strategy is the recomputation of the inconsistent projection data based on an interpolation using nonequispaced fast Fourier transforms (NFFT). The NFFT interpolation can be applied in arbitrary dimension. The approach overcomes the problem of adequate neighborhood definitions on irregular grids, since this is inherently given through the usage of higher dimensional Fourier transforms. Here, applications up to the third interpolation dimension are presented and validated. Furthermore, prior knowledge may be included by an appropriate damping of the transform during the interpolation step. This MAR method is applicable on each angular view of a detector row, on two-dimensional projection data as well as on three-dimensional projection data, e.g., a set of sequential acquisitions at different spatial positions, projection data of a spiral acquisition, or cone-beam projection data. Results of the novel MAR scheme based on one-, two-, and three-dimensional NFFT interpolations are presented. All results are compared in projection data space and spatial domain with the well-known one-dimensional linear interpolation strategy. In conclusion, it is recommended to include as much spatial information into the recomputation step as possible. This is realized by increasing the dimension of the NFFT. The resulting image quality can be enhanced considerably.

Fractionally Spaced Frequency Equalization Method for Orthogonal Frequency Division Multiplexing (OFDM) Jointing with Modified Pilot Sequences

In order to obtain accurate and high-speed data transmission, the orthogonal frequency division multiplexing(OFDM) technology is introduced and it is a kind of a multi-carriers modulation technology with high efficiency in the use of frequency band and characteristics of strong anti-interference ability. The fractionally spaced OFDM frequency domain equalization algorithm based on modified pilot sequences is proposed. In this proposed algorithm, one-dimensional linear interpolation method is used to estimate the frequency domain response of all subcarriers by part of the subcarriers’ frequency domain response with reducing the number of transmitted pilot sequences, and received signals are oversampled to acquire more detailed channel information. The computer simulations in underwater acoustic channel show that the performance of proposed method outperforms the single-carrier system and traditional OFDM system.

Optimal Design of a Complex High-Rise Building Based on Cost-Effectiveness Criterion

In this paper, an optimal design process for high-rise building structures is presented based on cost-effectiveness criterion. Then, an optimal design of a complex high-rise building based on cost-effectiveness criterion is carried out by using the design process. A minimum life cycle cost and corresponding elastic inter story drift considering initial cost and damage cost as two separate objective functions are obtained by using genetic algorithm. Finally, fitting curves of life cycle cost, initial cost, damage cost and corresponding performance indexes are interpolated by using one-dimensional linear interpolation considering elastic inter story drift ratio as control performance indexes. And lots of life cycle cost designs and corresponding performance indexes of the separated objective function are given. The results show that the optimal design process is practical and optimal results are diverse, and can be chosen flexibly by owners.

A new scan conversion algorithm for ultrasound compound scanning.

An improved scan conversion algorithm for ultrasound compound scanning is proposed. In this algorithm, the input data in the spatial domain is sampled by the concentric square raster sampling (CSRS) method, and the display pixel data are filled by one-dimensional linear interpolation. The reconstruction error of the proposed algorithm is much smaller than that of other algorithms, because only one-dimensional, rather than two-dimensional, interpolation is involved. This algorithm greatly simplifies implementation of a real-time digital scan converter (DSC) for spatial compounding of ultrasound images.

A new scan conversion algorithm for ultrasound compound scanning

An improved scan conversion algorithm for ultrasound compound scanning is proposed. In this algorithm, the input data in the spatial domain is sampled by the concentric square raster sampling (CSRS) method, and the display pixel data are filled by one-dimensional linear interpolation. The reconstruction error of the proposed algorithm is much smaller than that of other algorithms, because only one-dimensional, rather than two-dimensional, interpolation is involved. This algorithm greatly simplifies implementation of a real-time digital scan converter (DSC) for spatial compounding of ultrasound images.