E. Jacquelin, A. Bennani, and P. Hamelin, Force reconstruction: analysis and regularization of a deconvolution, J. Sound Vib, vol.265, p.81107, 2003.

Q. Leclere, C. Pezerat, B. Laulagnet, and L. Polac, Indirect measurement of main bearing loads in an operating diesel engine, J. Sound Vib, vol.286, issue.1-2, p.341361, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00414810

Y. Liu and W. S. Shepard, Reducing the impact of measurement errors when reconstructing dynamic forces, J. Vib. Acoust, vol.128, p.586593, 2006.

A. N. Thite and D. J. Thompson, The quantication of structure-borne transmission paths by inverse methods. Part 2 : Use of regularization techniques, J. Sound Vib, vol.264, issue.2, p.433451, 2003.

Y. Mao, X. Guo, and Y. Zhao, Experimental study of hammer impact identication on a steel cantilever beam, Exp. Tech, vol.34, issue.3, p.8285, 2010.

E. Turco, Tools for the numerical solution of inverse problems in structural mechanics: review and research perspectives, Eur. J. Environ. Civ. Eng, vol.21, issue.5, p.509554, 2017.

S. Boyd and L. Vandenberghe, Convex optimization, 2004.

C. Renzi, C. C. Pezerat, and J. Guyader, Vibration sources identication using vibratory measurements injected in a local nite element model, Proc. ISMA 2010, 2010.

D. Ginsberg and C. Fritzen, New approach for impact detection by nding sparse solution, Proc. ISMA 2014 -Int. Conf. Noise Vib. Eng. USD 2014 -Int. Conf. Uncertain. Struct. Dyn, p.20432056, 2014.

B. Qiao, X. Zhang, C. Wang, H. Zhang, and X. Chen, Sparse regularization for force identication using dictionaries, J. Sound Vib, vol.368, p.86, 2016.

B. Qiao, X. Zhang, J. Gao, and X. Chen, Impact-force sparse reconstruction from highly incomplete and inaccurate measurements, J. Sound Vib, vol.376, p.7294, 2016.

C. Pan, L. Yu, H. Liu, Z. , and W. Luo, Moving force identication based on redundant concatenated dictionary and weighted 1 -norm regularization, Mech. Syst. Signal Process, vol.98, p.3249, 2018.

M. Aucejo, Structural source identication using a generalized Tikhonov regularization, J. Sound Vib, vol.333, issue.22, p.56935707, 2014.

M. Aucejo and O. D. Smet, Bayesian source identication using local priors, Mech. Syst. Signal Process, p.120136, 2016.

M. Aucejo and O. D. Smet, A multiplicative regularization for force reconstruction, Mech. Syst. Signal Process, vol.85, p.730745, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02068499

P. M. Van-den, A. Berg, J. T. Abubakar, and . Fokkema, Multiplicative regularization for constrast prole inversion, Radio Sci, vol.38, p.80228031, 2003.

D. H. Brooks, G. F. Ahmad, R. S. Macleod, and G. M. Maratos, Inverse electrocardiography by simultaneous imposition of multiple constraints, IEEE Trans. Biomed. Eng, vol.46, issue.1, p.318, 1999.

M. Belge, L. Kilmer, and E. Miller, Wavelet domainimage restoration with adaptive edge-preserving regularization, IEEE Trans. Image Process, vol.9, issue.4, p.597608, 2000.

H. Zou and T. Hastie, Regularization and variable selection via the elastic net, J. R. Stat. Soc. B, vol.67, issue.2, p.301320, 2005.

Y. Lu, L. Shen, and Y. Xu, Multi-parameter regularization methods for highresolution image reconstruction with displacement errors, IEEE Trans. Circuits Syst. I Regul. Pap, vol.54, issue.8, p.17881799, 2007.

W. Wang, S. Lu, H. Mao, and J. Cheng, Multi-parameter Tikhonov regularization with the 0 sparsity constraint, Inverse Probl, vol.29, p.pp, 2013.

Q. Fan, D. Jiang, and Y. Jiao, A multi-parameter regularization model for image restoration, Signal Processing, vol.114, p.131142, 2015.

A. Deiveegan, Two-parameter regularization method for determining the heat source, Glob. J. Pure Appl. Math, vol.13, issue.8, p.39373950, 2017.

S. Li and Z. Peng, Seismic acoustic impedance inversion with multiparameter regularization, J. Geophys. Eng, vol.14, p.520532, 2017.

M. Belge, M. E. Kilmer, and E. Miller, Ecient determination of multiple regularization parameter in a generalized L-curve framework, Inverse Probl, vol.18, p.11611183, 2002.

C. Brezinski, M. Redivo-zaglia, G. Rodriguez, and S. Seatzu, Multiparameter regularization techniques for ill-conditioned linear systems, Numer. Math, vol.94, p.203228, 2003.

K. Ito, B. Jin, and T. Takeuchi, Multi-parameter Tikhonov regularization, Methods Appl. Anal, vol.18, issue.1, p.3146, 2011.

Z. Wang, Multi-parameter Tikhonov regularization and model function approach to the damped Morozov principle for choosing regularization, J. Comput. Appl. Math, vol.236, p.18151832, 2012.

F. S. Bazan, S. Borges, and J. B. Francisco, On a generalization of Reginska's parameter choice rule and its numerical realization in large-scale multiple-parameter Tikhonov regularization, Appl. Math. Comput, vol.219, p.21002113, 2012.

M. Green, Statistics of Images, the TV Algorithm of Rudin-Osher-Fatemi for Image Denoising and an Improved Denoising Algorithm, 2002.

M. Nikolova, A variational approach to remove outliers and impulse noise, J. Math. Imaging Vis, vol.20, issue.1-2, p.99120, 2004.

T. Le, R. Chartrand, and T. J. Asaki, A variational approach to reconstructing images corrupted by Poisson noise, J. Math. Imaging Vis, vol.27, p.257263, 2007.

A. Chambolle, Total Variation Minimization and a Class of Binary MRF Models, Lect. Notes Comput. Sci, vol.3757, p.136152, 2005.

R. Tibshirani, Regression shrinkage and selection via the Lasso, J. R. Stat. Soc. Ser. B, vol.58, issue.1, p.267288, 1996.

M. Hintermuller and T. Wu, Nonconvex T V q -models in image restoration: Analysis and a trust-region regularization based superlineraly convergennt solver, 2011.

J. Antoni, A Bayesian approach to sound source reconstruction: Optimal basis, regularization, and focusing, J. Acoust. Soc. Am, vol.131, issue.4, p.28732890, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00776324

C. Faure, F. Ablitzer, J. Antoni, and C. Pezerat, Empirical and fully Bayesian approaches for the identication of vibration sources from transverse displacement measurements, Mech. Syst. Signal Process, vol.94, p.180201, 2017.

M. Aucejo and O. D. Smet, On a full Bayesian inference for force reconstruction problems, Mech. Syst. Signal Process, vol.104, p.3659, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02068508

M. Aucejo, O. D. Smet, and J. F. Deü, On a space-time regularization for force reconstruction problems, Mech. Syst. Signal Process, vol.118, p.549567, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02068528

M. Aucejo and O. D. Smet, On a general Iteratively Reweighted algorithm for solving force reconstruction problems, J. Sound Vib, vol.458, p.388, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02179323

P. C. Hansen, Regularization tools: A matlab package for analysis and solution of discrete ill-posed problems, Numer. algorithms, vol.6, p.135, 1994.

G. H. Golub, M. Heath, and G. Wahba, Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics, vol.21, issue.2, p.215223, 1979.

O. Scherzer, The use of Morozov's discrepancy principle for Tikhonov regularization for solving nonlinear ill-posed problems, Computing, vol.51, p.4560, 1993.

P. C. Hansen, Rank-Decient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion, 1998.

A. Pereira, J. Antoni, and Q. Leclere, Empirical Bayesian regularization of the inverse acoustic problem, Appl. Acoust, vol.97, p.1129, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01176879

P. Rodriguez and B. Wohlberg, Ecient Minimization Method for a Generalized Total Variation Functional, IEEE Trans. Image Process, vol.18, issue.2, p.322332, 2009.

R. Chartrand and V. Stavena, Nonconvex regularization for image segmentation, Proc. Int. Conf. Image Process. Comput. Vis. Pattern Recognit, 2007.

M. Nikolova, M. K. Ng, S. Zhang, and W. Ching, Ecient reconstruction of piecewise constant images using nonsmooth nonconvex minimization, SIAM J. Imaging Sci, vol.1, issue.1, p.225, 2008.

P. J. Green, Iteratively Reweighted Least Squares for Maximum Likelihood Estimation, and some Robust and Resistant Alternatives, J. R. Stat. Soc. Ser. B, vol.46, issue.2, p.149192, 1984.

P. Rodriguez and B. Wohlberg, An Iteratively Weighted Norm Algorithm for Total Variation Regularization, Proc. 2006 Asilomar Conf. Signals, Syst. Comput, 2006.