{"title":"Separation of Spectral Lines from a Broadband Background and Noise Filtering by Modified Tikhonov Regularization","authors":"I. A. Larkin, A. V. Vagov, V. I. Korepanov","doi":"10.3103/s8756699023060080","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We propose a technique for processing noisy spectral data that implements a mathematically based selection of sharp signal peaks on an unknown smooth background, for which there is no reliable theoretical model. The fundamental concept of the technique is to construct an optimizing functional that gives the most probable parameters of spectral lines. Unlike the Tikhonov regularization method, where a smooth unknown function is extracted from a noisy signal, we consider the problem of regularizing the superposition of a smooth background function with sharp peaks. The proposed approach provides an algorithm for processing experimental data that makes it possible to filter out random noise and determine both the peak parameters and the background function with good accuracy. Finding the optimal regularization parameters is based on a priori assumptions about the smoothness of the background function and the statistical properties of random noise.</p>","PeriodicalId":44919,"journal":{"name":"Optoelectronics Instrumentation and Data Processing","volume":"56 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optoelectronics Instrumentation and Data Processing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s8756699023060080","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We propose a technique for processing noisy spectral data that implements a mathematically based selection of sharp signal peaks on an unknown smooth background, for which there is no reliable theoretical model. The fundamental concept of the technique is to construct an optimizing functional that gives the most probable parameters of spectral lines. Unlike the Tikhonov regularization method, where a smooth unknown function is extracted from a noisy signal, we consider the problem of regularizing the superposition of a smooth background function with sharp peaks. The proposed approach provides an algorithm for processing experimental data that makes it possible to filter out random noise and determine both the peak parameters and the background function with good accuracy. Finding the optimal regularization parameters is based on a priori assumptions about the smoothness of the background function and the statistical properties of random noise.
期刊介绍：
The scope of Optoelectronics, Instrumentation and Data Processing encompasses, but is not restricted to, the following areas: analysis and synthesis of signals and images; artificial intelligence methods; automated measurement systems; physicotechnical foundations of micro- and optoelectronics; optical information technologies; systems and components; modelling in physicotechnical research; laser physics applications; computer networks and data transmission systems. The journal publishes original papers, reviews, and short communications in order to provide the widest possible coverage of latest research and development in its chosen field.
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