A fast algorithm for optimal linear interpolation

1993 ◽  
Vol 41 (9) ◽  
pp. 2934-2937 ◽  
Author(s):  
M.R.K. Khansari ◽  
A. Leon-Garcia
Keyword(s):  
Fast Algorithm ◽  
Linear Interpolation ◽  
Optimal Linear

scholarly journals Optimal linear interpolation in linear predictive vocoders

1975 ◽  
Vol 57 (S1) ◽  
pp. S34-S34
Author(s):  
R. Viswanathan ◽  
John Makhoul ◽  
William Russell
Keyword(s):  
Linear Interpolation ◽  
Optimal Linear

Sensitivity Analysis and Multiobjective Optimization for LES Numerical Parameters

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
J.-C. Jouhaud ◽  
P. Sagaut ◽  
B. Enaux ◽  
J. Laurenceau
Keyword(s):  
Large Eddy Simulation ◽  
Surrogate Model ◽  
Low Cost ◽  
Linear Interpolation ◽  
Industrial Applications ◽  
Small Subset ◽  
Eddy Simulation ◽  
Subgrid Model ◽  
Large Eddy ◽  
Optimal Linear

Accuracy and reliability of large-eddy simulation data in a really complex industrial geometry are invesigated. An original methodology based on a response surface for LES data is introduced. This surrogate model for the full LES problem is built using the Kriging technique, which enables a low-cost optimal linear interpolation of a restricted set of large-eddy simulation (LES) solutions. Therefore, it can be used in most realistic industrial applications. Using this surrogate model, it is shown that (i) optimal sets of simulation parameters (subgrid model constant and artificial viscosity parameter in the present case) can be found; (ii) optimal values, as expected, depend on the cost functional to be minimized. Here, a realistic approach, which takes into account experimental data sparseness, is introduced. It is observed that minimization of the error evaluated using a too small subset of reference data may yield a global deterioration of the results.

scholarly journals A method for optimal linear super-resolution image restoration

2021 ◽  
Vol 5 (45) ◽  
pp. 692-701
Author(s):  
A.I. Maksimov ◽  
V.V. Sergeyev
Keyword(s):  
General Scheme ◽  
Super Resolution ◽  
Linear Interpolation ◽  
Reconstruction Error ◽  
Observation Model ◽  
Refinement Method ◽  
Optimal Linear ◽  
Recovery Error ◽  
Image Pixels ◽  
Significant Superiority

In this paper, we propose a super-resolution (pixel grid refinement) method for digital images. It is based on the linear filtering of a zero-padded discrete signal. We introduce a continuous-discrete observation model to create a reconstruction system. The proposed observation model is typical of real-world imaging systems - an initially continuous signal first undergoes linear (dynamic) distortions and then is subjected to sampling and the effect of additive noise. The proposed method is optimal in the sense of mean square recovery error minimization. In the theoretical part of the article, a general scheme of the linear super-resolution of the signal is presented and expressions for the impulse and frequency responses of the optimal reconstruction system are derived. An expression for the error of such restoration is also derived. For the sake of brevity, the entire description is presented for one-dimensional signals, but the obtained results can easily be generalized for the case of two-dimensional images. The experimental section of the paper is devoted to the analysis of the super-resolution reconstruction error depending on the parameters of the observation model. The significant superiority of the proposed method in terms of the reconstruction error is demonstrated in comparison with linear interpolation, which is usually used to refine the grid of image pixels.

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