Selection of regularization parameter for optical topography.

The choice of the regularization parameter has a profound effect on the solution of ill-posed inverse problems such as optical topography. We review 11 different methods for selecting the Tikhonov regularization parameter that have been described previously in the literature. We test them on two trial problems, deblurring and optical topography, and conclude that the L-curve method is the method of choice, though in particularly ill-posed problems, generalized cross-validation may provide an alternative.

[1]  A Adler,et al.  Objective selection of hyperparameter for EIT , 2006, Physiological measurement.

[2]  Andy Adler,et al.  Accounting for erroneous electrode data in electrical impedance tomography. , 2004, Physiological measurement.

[3]  P. Hansen.  The discrete picard condition for discrete ill-posed problems , 1990 .

[4]  Y. Hosoda,et al.  Regularization Using QR Factorization and the Estimation of the Optimal Parameter , 2001 .

[5]  D. Boas,et al.  Improving the diffuse optical imaging spatial resolution of the cerebral hemodynamic response to brain activation in humans. , 2004, Optics letters.

[6]  G. Wahba.  Spline models for observational data , 1990 .

[7]  Richard A. Davis,et al.  Time Series: Theory and Methods (2nd ed.). , 1992 .

[8]  Adam P. Gibson,et al.  A frequency multiplexed near infrared topography system for imaging functional activity in the brain , 2005 .

[9]  ProblemsPer Christian HansenDepartment.  The L-curve and its use in the numerical treatment of inverse problems , 2000 .

[10]  Gene H. Golub,et al.  Matrix computations , 1983 .

[11]  Mark H. Johnson,et al.  Investigation of depth dependent changes in cerebral haemodynamics during face perception in infants , 2007, Physics in medicine and biology.

[12]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[13]  Teresa Reginska,et al.  A Regularization Parameter in Discrete Ill-Posed Problems , 1996, SIAM J. Sci. Comput..

[14]  Simon R Arridge,et al.  Comparison of methods for optimal choice of the regularization parameter for linear electrical impedance tomography of brain function , 2008, Physiological measurement.

[15]  Per Christian Hansen,et al.  REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems , 1994, Numerical Algorithms.

[16]  D. M. Titterington,et al.  A Study of Methods of Choosing the Smoothing Parameter in Image Restoration by Regularization , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Martin Wolf,et al.  Progress of near-infrared spectroscopy and topography for brain and muscle clinical applications. , 2007, Journal of biomedical optics.

[18]  P. Hansen.  Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion , 1987 .

[19]  J. Hebden.  Advances in optical imaging of the newborn infant brain. , 2003, Psychophysiology.

[20]  Eric L. Miller,et al.  Comparison of linear reconstruction techniques for 3D DPDW imaging of absorption coefficient , 1999, Photonics West - Biomedical Optics.

[21]  C. Vogel.  Non-convergence of the L-curve regularization parameter selection method , 1996 .

[22]  Andy Adler,et al.  Electrical impedance tomography: regularized imaging and contrast detection , 1996, IEEE Trans. Medical Imaging.

[23]  Dianne P. O'Leary,et al.  The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems , 1993, SIAM J. Sci. Comput..

[24]  D. Delpy,et al.  A frequency multiplexed near infra-red topography system for imaging functional activation in the brain , 2004 .

[25]  M. Hanke.  Limitations of the L-curve method in ill-posed problems , 1996 .

[26]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[27]  A. Yodh,et al.  Diffuse optical correlation tomography of cerebral blood flow during cortical spreading depression in rat brain. , 2006, Optics express.

[28]  Gene H. Golub,et al.  Tikhonov Regularization and Total Least Squares , 1999, SIAM J. Matrix Anal. Appl..

[29]  Grace Wahba,et al.  Spline Models for Observational Data , 1990 .

[30]  C. Vogel.  Computational Methods for Inverse Problems , 1987 .

[31]  Limin Wu.  A PARAMETER CHOICE METHOD FOR TIKHONOV REGULARIZATION , 2003 .

[32]  Per Christian Hansen,et al.  Deconvolution and Regularization with Toeplitz Matrices , 2002, Numerical Algorithms.

[33]  D. Titterington,et al.  A cautionary note about crossvalidatory choice , 1989 .

[34]  Simon R. Arridge,et al.  Three-dimensional whole-head optical tomography of passive motor evoked responses in the neonate , 2006, NeuroImage.

[35]  Gene H. Golub,et al.  Generalized cross-validation as a method for choosing a good ridge parameter , 1979, Milestones in Matrix Computation.

[36]  Tianzi Jiang,et al.  Improving performance of reflectance diffuse optical imaging using a multicentered mode. , 2006, Journal of biomedical optics.

[37]  P. Hansen,et al.  Exploiting Residual Information in the Parameter Choice for Discrete Ill-Posed Problems , 2006 .

[38]  V. Ntziachristos,et al.  Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging. , 2003, Medical physics.

[39]  J. Mandeville,et al.  The Accuracy of Near Infrared Spectroscopy and Imaging during Focal Changes in Cerebral Hemodynamics , 2001, NeuroImage.

[40]  Atsushi Maki,et al.  Measurement system for noninvasive dynamic optical topography , 1999, Photonics West - Biomedical Optics.