Lanczos interpolation

The most successful strategy for approximating the Liouville-von Neumann propagator is to interpolate the operator with polynomial operators. To this end, Newton and Faber polynomials have been suggested to globally approximate the propagator,126,127,225,232-234 as in Eq. [95]. For short-time propagation, short-iterative Arnoldi,235 dual Lanczos,236 and Chebyshev... 

Lanczos C (1938) Trigonometric Interpolation of Empirical and Analytical Functions. J Math Phys 17 123-199... 

Numerical methods include those based on finite difference calculus. They are ideally suited for tabulated experimental data such as one finds in thermodynamic tables. They also include methods of solving simultaneous linear equations, curve fitting, numerical solution of ordinary and partial differential equations and matrix operations. In this appendix, numerical interpolation, integration, and differentiation are considered. Information about the other topics is available in monographs by Hornbeck [2] and Lanczos [3]. 

Region Adaptive, Unsharp Masking Based Lanczos-3 Interpolation for 2-D Up-Sampling Crisp-Rule Versus Fuzzy-Rule Based Approach... 

Keywords Image and video processing Unsharp masking Lanczos-3 interpolation Variance Up-sampling Fuzzy logic... 

Region Adaptive, Unsharp Masking Based Lanczos-3 Interpolation... 

Lanczos is a spatial domain interpolation technique which is implemented by multiplying a sine function with a sine window which is scaled to be wider and truncated to zero outside of the main lobe. In case of Lanczos-3 interpolation, the main lobe of the sine function along with the two subsequent side lobes on either side is used as a sine window. The Lanczos window is a product of sine functions sin c x) with the scaled... 

For a two dimensional function such as an image g2(x, y), an interpolated value at an arbitrary point (xo, yo) using Lanczos-3 interpolation is given by ... 

Fig. 3 Block diagram of the proposed fuzzy weighted, region adaptive unsharp masking based Lanczos-3 interpolation technique...

The sharpened sub-sampled sequence is then finally up-sampled using Lanczos-3 interpolation technique to generate the high resolution video sequence. The Lanczos-3 interpolation technique is discussed in detail in Sect. 2.3. 

Bicubic, Lanczos-3, proposed-1 and proposed-2 interpolation techniques at 4 1 and 16 1 compression ratios respectively. The bold values signify the maximum PSNR (dB) gain among all the methods. Experimental results reveal, at 4 1 compression ratio the proposed technique shows the average PSNR improvement up to 0.48 dB than DCT and an improvement up to 1.6 dB than the popular Bicubic interpolation technique particularly in the case of football sequence. Similarly the proposed... 

Fig. 10 Subjective performance of the 20th frame of the akiyo sequence at 4 1 compression ratio using different interpolation techniques a Origintil, b Bicubic, c Lanczos-3, d DCT, e Crisp-rule based Lanczos-3 (Proposed-1), f Fuzzy-rule based Lanczos-3 (Proposed-2)...

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