scholarly journals Numerical differentiation from a viewpoint of regularization theory

2006 ◽  
Vol 75 (256) ◽  
pp. 1853-1870 ◽  
Author(s):  
Shuai Lu ◽  
Sergei V. Pereverzev
Keyword(s):  
Numerical Differentiation ◽  
Regularization Theory

Resolution Enhancement of Composite Spectra with Fractal Noise in Derivative Spectrometry

2000 ◽  
Vol 54 (5) ◽  
pp. 721-730 ◽  
Author(s):  
S. S. Kharintsev ◽  
D. I. Kamalova ◽  
M. Kh. Salakhov
Keyword(s):  
A Priori ◽  
Resolution Enhancement ◽  
Numerical Differentiation ◽  
A Priori Information ◽  
Experimental Ir ◽  
Composite Spectra ◽  
Self Similar ◽  
Priori Information ◽  
Fractal Noise ◽  
Derivative Spectrometry

The problem of improving the resolution of composite spectra with statistically self-similar (fractal) noise is considered within the framework of derivative spectrometry. An algorithm of the numerical differentiation of an arbitrary (including fractional) order of spectra is produced by the statistical regularization method taking into account a priori information on statistical properties of the fractal noise. Fractal noise is analyzed in terms of the statistical Hurst method. The efficiency and expedience of this algorithm are exemplified by treating simulated and experimental IR spectra.

Computational vision and regularization theory

Nature ◽  
1985 ◽  
Vol 317 (6035) ◽  
pp. 314-319 ◽  
Author(s):  
Tomaso Poggio ◽  
Vincent Torre ◽  
Christof Koch
Keyword(s):  
Regularization Theory ◽  
Computational Vision
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