Coding Prony’s method in MATLAB and applying it to biomedical signal filtering
Abstract Background The response of many biomedical systems can be modelled using a linear combination of damped exponential functions. The approximation parameters, based on equally spaced samples, can be obtained using Prony’s method and its variants (e.g. the matrix pencil method). This paper pro...
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| Format: | Article |
| Language: | English |
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BMC
2018-11-01
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| Series: | BMC Bioinformatics |
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| Online Access: | http://link.springer.com/article/10.1186/s12859-018-2473-y |
| _version_ | 1818927151202697216 |
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| author | A. Fernández Rodríguez L. de Santiago Rodrigo E. López Guillén J. M. Rodríguez Ascariz J. M. Miguel Jiménez Luciano Boquete |
| author_facet | A. Fernández Rodríguez L. de Santiago Rodrigo E. López Guillén J. M. Rodríguez Ascariz J. M. Miguel Jiménez Luciano Boquete |
| author_sort | A. Fernández Rodríguez |
| collection | DOAJ |
| description | Abstract Background The response of many biomedical systems can be modelled using a linear combination of damped exponential functions. The approximation parameters, based on equally spaced samples, can be obtained using Prony’s method and its variants (e.g. the matrix pencil method). This paper provides a tutorial on the main polynomial Prony and matrix pencil methods and their implementation in MATLAB and analyses how they perform with synthetic and multifocal visual-evoked potential (mfVEP) signals. This paper briefly describes the theoretical basis of four polynomial Prony approximation methods: classic, least squares (LS), total least squares (TLS) and matrix pencil method (MPM). In each of these cases, implementation uses general MATLAB functions. The features of the various options are tested by approximating a set of synthetic mathematical functions and evaluating filtering performance in the Prony domain when applied to mfVEP signals to improve diagnosis of patients with multiple sclerosis (MS). Results The code implemented does not achieve 100%-correct signal approximation and, of the methods tested, LS and MPM perform best. When filtering mfVEP records in the Prony domain, the value of the area under the receiver-operating-characteristic (ROC) curve is 0.7055 compared with 0.6538 obtained with the usual filtering method used for this type of signal (discrete Fourier transform low-pass filter with a cut-off frequency of 35 Hz). Conclusions This paper reviews Prony’s method in relation to signal filtering and approximation, provides the MATLAB code needed to implement the classic, LS, TLS and MPM methods, and tests their performance in biomedical signal filtering and function approximation. It emphasizes the importance of improving the computational methods used to implement the various methods described above. |
| first_indexed | 2024-12-20T03:08:27Z |
| format | Article |
| id | doaj.art-47f3597ed2734b75a12c033a315b11e2 |
| institution | Directory Open Access Journal |
| issn | 1471-2105 |
| language | English |
| last_indexed | 2024-12-20T03:08:27Z |
| publishDate | 2018-11-01 |
| publisher | BMC |
| record_format | Article |
| series | BMC Bioinformatics |
| spelling | doaj.art-47f3597ed2734b75a12c033a315b11e22022-12-21T19:55:31ZengBMCBMC Bioinformatics1471-21052018-11-0119111410.1186/s12859-018-2473-yCoding Prony’s method in MATLAB and applying it to biomedical signal filteringA. Fernández Rodríguez0L. de Santiago Rodrigo1E. López Guillén2J. M. Rodríguez Ascariz3J. M. Miguel Jiménez4Luciano Boquete5Grupo de Ingeniería Biomédica, Departamento de Electrónica, Universidad de AlcaláGrupo de Ingeniería Biomédica, Departamento de Electrónica, Universidad de AlcaláGrupo de Ingeniería Biomédica, Departamento de Electrónica, Universidad de AlcaláGrupo de Ingeniería Biomédica, Departamento de Electrónica, Universidad de AlcaláGrupo de Ingeniería Biomédica, Departamento de Electrónica, Universidad de AlcaláGrupo de Ingeniería Biomédica, Departamento de Electrónica, Universidad de AlcaláAbstract Background The response of many biomedical systems can be modelled using a linear combination of damped exponential functions. The approximation parameters, based on equally spaced samples, can be obtained using Prony’s method and its variants (e.g. the matrix pencil method). This paper provides a tutorial on the main polynomial Prony and matrix pencil methods and their implementation in MATLAB and analyses how they perform with synthetic and multifocal visual-evoked potential (mfVEP) signals. This paper briefly describes the theoretical basis of four polynomial Prony approximation methods: classic, least squares (LS), total least squares (TLS) and matrix pencil method (MPM). In each of these cases, implementation uses general MATLAB functions. The features of the various options are tested by approximating a set of synthetic mathematical functions and evaluating filtering performance in the Prony domain when applied to mfVEP signals to improve diagnosis of patients with multiple sclerosis (MS). Results The code implemented does not achieve 100%-correct signal approximation and, of the methods tested, LS and MPM perform best. When filtering mfVEP records in the Prony domain, the value of the area under the receiver-operating-characteristic (ROC) curve is 0.7055 compared with 0.6538 obtained with the usual filtering method used for this type of signal (discrete Fourier transform low-pass filter with a cut-off frequency of 35 Hz). Conclusions This paper reviews Prony’s method in relation to signal filtering and approximation, provides the MATLAB code needed to implement the classic, LS, TLS and MPM methods, and tests their performance in biomedical signal filtering and function approximation. It emphasizes the importance of improving the computational methods used to implement the various methods described above.http://link.springer.com/article/10.1186/s12859-018-2473-yProny’s methodMatrix pencilLeast squaresTotal least squaresMultifocal evoked visual potentialsMultiple sclerosis |
| spellingShingle | A. Fernández Rodríguez L. de Santiago Rodrigo E. López Guillén J. M. Rodríguez Ascariz J. M. Miguel Jiménez Luciano Boquete Coding Prony’s method in MATLAB and applying it to biomedical signal filtering BMC Bioinformatics Prony’s method Matrix pencil Least squares Total least squares Multifocal evoked visual potentials Multiple sclerosis |
| title | Coding Prony’s method in MATLAB and applying it to biomedical signal filtering |
| title_full | Coding Prony’s method in MATLAB and applying it to biomedical signal filtering |
| title_fullStr | Coding Prony’s method in MATLAB and applying it to biomedical signal filtering |
| title_full_unstemmed | Coding Prony’s method in MATLAB and applying it to biomedical signal filtering |
| title_short | Coding Prony’s method in MATLAB and applying it to biomedical signal filtering |
| title_sort | coding prony s method in matlab and applying it to biomedical signal filtering |
| topic | Prony’s method Matrix pencil Least squares Total least squares Multifocal evoked visual potentials Multiple sclerosis |
| url | http://link.springer.com/article/10.1186/s12859-018-2473-y |
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