A neural network approach for micro-PIXE data E. Rokita a, * , P.H.A. Mutsaers b , J.A. Quaedackers b , Z. Tabor a , M.J.A. de Voigt b a Institute of Physics, Jagiellonian University, Reymonta 4, PL-30059 Cracow, Poland b Eindhoven University of Technology, Cyclotron Laboratory, P.O. Box 513, 5600 MB Eindhoven, The Netherlands Abstract The application of the arti®cial neural network for the processing of one-dimensional micro-PIXE data is described. The network architecture, selection of the transfer function as well as the training and veri®cation operations are described in detail. The performed reconstructions con®rm that the neural network may be used for improvement of the resolution and for processing of low statistics data. The limitations of the neural network application for two-di- mensional images are discussed. Ó 1999 Elsevier Science B.V. All rights reserved. Keywords: Micro-PIXE; Image processing; Arti®cial neural networks 1. Introduction To solve many biomedical problems the deter- mination of one- (1D) or two-dimensional (2D) distributions of the trace (ppm level) element concentrations at a resolution of <1 lm is needed. Currently, a proton microprobe in proton induced X-ray emission (micro-PIXE) mode is useless for this purpose since the achievement of adequate beam current for elemental analysis at a micro- beam diameter below 1 lm is not possible. Theoretically, there are possibilities to improve the resolution of the micro-PIXE maps by means of digital image processing. The distribution of the concentration of the element (image ± I) is the convolution of the target distribution (object ± O) with the microbeam pro®le (B). In discrete form it may be written as I j; k X m X n Oj  m; k  nBm; n N j; k; 1 where N j; k is the noise matrix. The calculation of the object function (O) consists of two steps. The ®rst step comprises the determination of the microbeam pro®le (B) while the second step relies on the solution of Eq. (1). The procedure seems to be simple and well de®ned, however, the practical implementation must overcome three major obstacles. Firstly, the noise matrix is unknown. Therefore, an assumption has to be made to describe the noise characteristic. Secondly, to obtain the beam pro®le (B) an additional measurement of a known object is necessary, and thirdly, the calculations are based on the assumption that the microbeam pro®le Nuclear Instruments and Methods in Physics Research B 158 (1999) 159±164 www.elsevier.nl/locate/nimb * Corresponding author. Tel.: +48-12-6339376; fax: +48-12- 6338076; e-mail: ufrokita@cyf-kr.edu.pl 0168-583X/99/$ - see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 5 0 4 - 2