A typical way to compute a meaningful solution of a linear least squares problem involves the introduction of a filter factors array, whose aim is to avoid noise amplification due to the presence of small singular values. Beyond the classical direct regularization approaches, iterative gradient methods can be thought as filtering methods, due to their typical capability to recover the desired components of the true solution at the first iterations. For an iterative method, regularization is achieved by stopping the procedure before the noise introduces artifacts, making the iteration number playing the role of the regularization parameter. In this paper we want to investigate the filtering and regularizing effects of some first-order algorithms, showing in particular which benefits can be gained in recovering the filters of the true solution by means of a suitable scaling matrix.

A typical way to compute a meaningful solution of a linear least squares problem involves the introduction of a filter factors array, whose aim is to avoid noise amplification due to the presence of small singular values. Beyond the classical direct regularization approaches, iterative gradient methods can be thought as filtering methods, due to their typical capability to recover the desired components of the true solution at the first iterations. For an iterative method, regularization is achieved by stopping the procedure before the noise introduces artifacts, making the iteration number playing the role of the regularization parameter. In this paper we want to investigate the filtering and regularizing effects of some first-order algorithms, showing in particular which benefits can be gained in recovering the filters of the true solution by means of a suitable scaling matrix. © Published under licence by IOP Publishing Ltd.

Filter factor analysis of scaled gradient methods for linear least squares / Porta, F.; Cornelio, A.; Zanni, L.; Prato, M.. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6588. - STAMPA. - 464:1(2013), p. 012006. (Intervento presentato al convegno 3rd International Workshop on New Computational Methods for Inverse Problems, NCMIP 2013 tenutosi a Cachan, fra nel 22 maggio 2013) [10.1088/1742-6596/464/1/012006].

Filter factor analysis of scaled gradient methods for linear least squares

Porta F.;Cornelio A.;Zanni L.;Prato M.
2013

Abstract

A typical way to compute a meaningful solution of a linear least squares problem involves the introduction of a filter factors array, whose aim is to avoid noise amplification due to the presence of small singular values. Beyond the classical direct regularization approaches, iterative gradient methods can be thought as filtering methods, due to their typical capability to recover the desired components of the true solution at the first iterations. For an iterative method, regularization is achieved by stopping the procedure before the noise introduces artifacts, making the iteration number playing the role of the regularization parameter. In this paper we want to investigate the filtering and regularizing effects of some first-order algorithms, showing in particular which benefits can be gained in recovering the filters of the true solution by means of a suitable scaling matrix. © Published under licence by IOP Publishing Ltd.
2013
3rd International Workshop on New Computational Methods for Inverse Problems, NCMIP 2013
Cachan, fra
22 maggio 2013
464
012006
Porta, F.; Cornelio, A.; Zanni, L.; Prato, M.
Filter factor analysis of scaled gradient methods for linear least squares / Porta, F.; Cornelio, A.; Zanni, L.; Prato, M.. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6588. - STAMPA. - 464:1(2013), p. 012006. (Intervento presentato al convegno 3rd International Workshop on New Computational Methods for Inverse Problems, NCMIP 2013 tenutosi a Cachan, fra nel 22 maggio 2013) [10.1088/1742-6596/464/1/012006].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1328631
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