SpectrumDeconvolution: Improvement of the resolution in spectra, decomposition of multiplets

Description

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.

Usage

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

Arguments

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

Value

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

encoding

latin1

Details

Both methods search iteratively for solution of deconvolution problem $$y(i)=\sum_{j=1}^{n}h(i-j)x(j)+e(i)$$ in the form $$x^{(k)}(i)=M^{(k)}(i)x^{(k-1)}(i)$$

For Gold method:

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

For Richardson-Lucy: $$M^{(k)}(i)=\sum_{l=0}^{n}h(i-l)\frac{x^{(k-1)}(l)}{\sum_{j=1}^{n}h(l-j) x^{(k-1)}(j)}$$

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

References

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

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