SpectrumDeconvolution {Peaks} | R Documentation |
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.
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)=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.
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.