SpectrumDeconvolution: Improvement of the resolution in spectra, decomposition of...
In Peaks: Peaks

Description Usage Arguments Details Value Author(s) References

View source: R/zzz.R

This function is used to strip-off known instrumental function from source spectrum. It is achieved by deconvolution of source spectrum according to response spectrum using Gold or Richardson-Lucy algorithms. Both methods provides less osccillating solutions than Fourier or VanCittert algorithms.

1 2	SpectrumDeconvolution(y,response,iterations=10,repetitions=1, boost=1.0,method=c("Gold","RL"))

`y`	numeric vector of source spectrum
`response`	vector of response spectrum. Its length shold be less or equal the length of `y`
`iterations`	number of iterations (parameter L in the Gold deconvolution algorithm) between boosting operations
`repetitions`	number of repetitions of boosting operations. It must be greater or equal to one. So the total number of iterations is `repetitions*iterations`
`boost`	boosting coefficient/exponent. Applies only if `repetitions` is greater than one. Recommended range [1..2].
`method`	method selected for deconvolution. Either Gold or Richardson-Lucy

Both methods search iteratively for solution of deconvolution problem

y(i)=∑_{j=1}^{n}h(i-j)x(j)+e(i)

in the form

x^{(k)}(i)=M^{(k)}(i)x^{(k-1)}(i)

For Gold method:

M^{(k)}(i)=\frac{x^{(k-1)}(i)}{∑_{j=1}^{n}h(i-j)x^{(k-1)}(j)}

For Richardson-Lucy:

M^{(k)}(i)=∑_{l=0}^{n}h(i-l)\frac{x^{(k-1)}(l)}{∑_{j=1}^{n}h(l-j) x^{(k-1)}(j)}

Boosting is the exponentiation of iterated value with boosting coefficient/exponent. It is generally improve stability.

Numeric vector of the same length as y with deconvoluted spectrum.

Miroslav Morhác

Abreu M.C. et al., A four-dimensional deconvolution method to correct NA38 experimental data, NIM A 405 (1998) 139.

Lucy L.B., A.J. 79 (1974) 745.

Richardson W.H., J. Opt. Soc. Am. 62 (1972) 55.

Gold R., ANL-6984, Argonne National Laboratories, Argonne Ill, 1964.

Coote G.E., Iterative smoothing and deconvolution of one- and two-dimensional elemental distribution data, NIM B 130 (1997) 118.

M. Morhác, J. Kliman, V. Matousek, M. Veselský, I. Turzo.: Efficient one- and two-dimensional Gold deconvolution and its application to gamma-ray spectra decomposition. NIM, A401 (1997) 385-408.

Morhác M., Matousek V., Kliman J., Efficient algorithm of multidimensional deconvolution and its application to nuclear data processing, Digital Signal Processing 13 (2003) 144.

Peaks documentation built on May 29, 2017, 8:29 p.m.