Tikhonov-Miller regularization with a denoisy and deconvolved signal as model of solution for improvement of depth resolution in SIMS analysis

Abstract

In this paper the improvement by deconvolution of the depth resolution in Secondary Ion Masse Spectrometry (SIMS) analysis is studied. Indeed, a new Tikhonov-Miller deconvolution method, where a priori model of solution is included. The latter is a denoisy and pre-deconvolved signal obtained firstly by the application of wavelet shrinkage algorithm and after, by the introduction of the obtained denoisy signal in an iterative deconvolution algorithm. The results of the proposed algorithm are compared to those of Tikhonov-Miller regularization where the model of solution is a raw signal. Finally, based on the obtained results the advantages and limitations of the proposed method as well as suggestions for future work are presented and discussed.

Multi-Scale Deconvolution of Mass Spectrometry Signals

“…For this reason, it is important to remove noise components from the signal (the model of solution). The idea is to introduce a denoisy and deconvoluted signal as model of solution in Barakat's approach, which constitutes our first contribution in this field (Boulakroune, 2008). The first proposed deconvolution scheme is constructed by the following steps:…”

Improvement of Depth Resolution in Secondary Ion Mass Spectrometry Analysis Using Multiresolution Deconvolution

“…Thus, the results must be regularized. [15][16][17][18][19][20][21][22][23][24][25][26][27] To this end, the solution is superimposed with certain limitations by introducing some additional limitative operators, whose shape is chosen depending on the formalism used for the solution of the ill-posed problem, into a goal function; usually the goal function is the mismatch between the convoluted solution and the initial data. 3) Indeed, different forms of limitative operator have been used.…”

“…Depth profiling in SIMS analysis is mathematically described by the convolution integral which is governed by the depth resolution function (DRF), hðzÞ. If the integral over hðzÞ is normalized to unity, then the measured (convolved) signal is given by the well-known convolution integral [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] yðzÞ ¼…”