S. Sarkar, S. R. Chowdhury, M. Venugopal, R. M. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).

[Crossref]

T. Raveendran, S. Sarkar, D. Roy, and R. M. Vasu, “A novel filtering framework through Girsanov correction for the identification of nonlinear dynamical systems,” Inverse Probl. 29, 065002 (2013).

[Crossref]

N. Pimprikar, J. Teresa, D. Roy, R. M. Vasu, and K. Rajan, “An approximately H1-optimal Petrov-Galerkin mesh-free method: application to computation of scattered light for optical tomography,” CMES—Computer Modeling in Engineering and Sciences 92, 33–61 (2013).

A. M. Stuart, “Inverse problems: a Bayesian perspective,” Acta Numerica 19, 451–559 (2010).

[Crossref]

B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements,” Phys. Med. Biol. 54, 285–305 (2009).

[Crossref]

D. M. Livings, S. L. Dance, and N. K. Nichols, “Unbiased ensemble square root filters,” Physica D 237, 1021–1028 (2008).

[Crossref]

K. Belkebir and A. G. Tijhuis, “Modified gradient method and modified Born method for solving a two-dimensional inverse scattering problem,” Inverse Probl. 17, 1671–1688 (2001).

[Crossref]

L. S. Ramachandra and D. Roy, “A new method for nonlinear two-point boundary value problems in solid mechanics,” J. Appl. Mech. 68, 776–786 (2001).

[Crossref]

D. Roy and L. S. Ramachandra, “A semi-analytical locally transversal linearization method for non-linear dynamical systems,” Int. J. Numer. Methods Eng. 51, 203–224 (2001).

[Crossref]

A. H. Hielscher, A. D. Klose, and K. M. Hansen, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imag. 18, 262–271 (1999).

[Crossref]

F. Natterer and F. Wübbeling, “A propagation-backpropagation method for ultrasound tomography,” Inverse Probl. 11, 1225–1232 (1995).

[Crossref]

W. C. Chew and Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imag. 9, 218–225 (1990).

[Crossref]

A. J. Devaney and G. Beylkin, “Diffraction tomography using arbitrary transmitter and receiver surfaces,” Ultrason. Imag. 6, 181–193 (1984).

M. Slaney, A. C. Kak, and L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microw. Theory Technol. 32, 860–874 (1984).

[Crossref]

B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements,” Phys. Med. Biol. 54, 285–305 (2009).

[Crossref]

K. Belkebir and A. G. Tijhuis, “Modified gradient method and modified Born method for solving a two-dimensional inverse scattering problem,” Inverse Probl. 17, 1671–1688 (2001).

[Crossref]

A. J. Devaney and G. Beylkin, “Diffraction tomography using arbitrary transmitter and receiver surfaces,” Ultrason. Imag. 6, 181–193 (1984).

W. C. Chew and Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imag. 9, 218–225 (1990).

[Crossref]

S. Sarkar, S. R. Chowdhury, M. Venugopal, R. M. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).

[Crossref]

D. M. Livings, S. L. Dance, and N. K. Nichols, “Unbiased ensemble square root filters,” Physica D 237, 1021–1028 (2008).

[Crossref]

P. Guo and A. J. Devaney, “Comparison of reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 22, 2338–2347 (2005).

[Crossref]

P. Guo and A. J. Devaney, “Digital microscopy using phase-shifting digital holography with two reference waves,” Opt. Lett. 29, 857–859 (2004).

[Crossref]

G. A. Tsihrintzis and A. J. Devaney, “Higher order (nonlinear) diffraction tomography: inversion of the Rytov series,” IEEE Trans. Inf. Theory 46, 1748–1761 (2000).

[Crossref]

M. H. Maleki and A. J. Devaney, “Phase retrieval and intensity-only reconstruction algorithm for optical diffraction tomography,” J. Opt. Soc. Am. A 10, 1086–1092 (1993).

[Crossref]

A. J. Devaney and G. Beylkin, “Diffraction tomography using arbitrary transmitter and receiver surfaces,” Ultrason. Imag. 6, 181–193 (1984).

A. H. Hielscher, A. D. Klose, and K. M. Hansen, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imag. 18, 262–271 (1999).

[Crossref]

R. F. Harrington, Field Computation by Moment Method (Macmillan, 1968).

A. H. Hielscher, A. D. Klose, and K. M. Hansen, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imag. 18, 262–271 (1999).

[Crossref]

M. Slaney, A. C. Kak, and L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microw. Theory Technol. 32, 860–874 (1984).

[Crossref]

A. C. Kak, “Tomographic imaging with diffracting and non-diffracting sources,” in Array Signal Processing, S. Haykin, ed. (Prentice-Hall, 1985).

A. C. Kak and M. Slaney, “Tomographic imaging with diffracting sources,” in Principles of Computerized Tomographic Imaging (IEEE, 1988), pp. 203–273.

F. C. Klebaner, Introduction to Stochastic Calculus with Applications, 2nd ed. (Imperial College, 2005).

A. H. Hielscher, A. D. Klose, and K. M. Hansen, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imag. 18, 262–271 (1999).

[Crossref]

M. Slaney, A. C. Kak, and L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microw. Theory Technol. 32, 860–874 (1984).

[Crossref]

D. M. Livings, S. L. Dance, and N. K. Nichols, “Unbiased ensemble square root filters,” Physica D 237, 1021–1028 (2008).

[Crossref]

F. Natterer and F. Wübbeling, “A propagation-backpropagation method for ultrasound tomography,” Inverse Probl. 11, 1225–1232 (1995).

[Crossref]

D. M. Livings, S. L. Dance, and N. K. Nichols, “Unbiased ensemble square root filters,” Physica D 237, 1021–1028 (2008).

[Crossref]

N. Pimprikar, J. Teresa, D. Roy, R. M. Vasu, and K. Rajan, “An approximately H1-optimal Petrov-Galerkin mesh-free method: application to computation of scattered light for optical tomography,” CMES—Computer Modeling in Engineering and Sciences 92, 33–61 (2013).

N. Pimprikar, J. Teresa, D. Roy, R. M. Vasu, and K. Rajan, “An approximately H1-optimal Petrov-Galerkin mesh-free method: application to computation of scattered light for optical tomography,” CMES—Computer Modeling in Engineering and Sciences 92, 33–61 (2013).

L. S. Ramachandra and D. Roy, “A new method for nonlinear two-point boundary value problems in solid mechanics,” J. Appl. Mech. 68, 776–786 (2001).

[Crossref]

D. Roy and L. S. Ramachandra, “A semi-analytical locally transversal linearization method for non-linear dynamical systems,” Int. J. Numer. Methods Eng. 51, 203–224 (2001).

[Crossref]

T. Raveendran, S. Sarkar, D. Roy, and R. M. Vasu, “A novel filtering framework through Girsanov correction for the identification of nonlinear dynamical systems,” Inverse Probl. 29, 065002 (2013).

[Crossref]

S. Sarkar, S. R. Chowdhury, M. Venugopal, R. M. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).

[Crossref]

T. Raveendran, S. Sarkar, D. Roy, and R. M. Vasu, “A novel filtering framework through Girsanov correction for the identification of nonlinear dynamical systems,” Inverse Probl. 29, 065002 (2013).

[Crossref]

N. Pimprikar, J. Teresa, D. Roy, R. M. Vasu, and K. Rajan, “An approximately H1-optimal Petrov-Galerkin mesh-free method: application to computation of scattered light for optical tomography,” CMES—Computer Modeling in Engineering and Sciences 92, 33–61 (2013).

B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements,” Phys. Med. Biol. 54, 285–305 (2009).

[Crossref]

D. Roy, “A family of lower- and higher-order transversal linearization techniques in non-linear stochastic engineering dynamics,” Int. J. Numer. Methods Eng. 61, 764–790 (2004).

[Crossref]

L. S. Ramachandra and D. Roy, “A new method for nonlinear two-point boundary value problems in solid mechanics,” J. Appl. Mech. 68, 776–786 (2001).

[Crossref]

D. Roy and L. S. Ramachandra, “A semi-analytical locally transversal linearization method for non-linear dynamical systems,” Int. J. Numer. Methods Eng. 51, 203–224 (2001).

[Crossref]

M. Venugopal, D. Roy, and R. M. Vasu, “A new evolutionary Bayesian approach incorporating additive path correction for nonlinear inverse problems,” arxiv.org/pdf/1305.2702.

S. Sarkar, S. R. Chowdhury, M. Venugopal, R. M. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).

[Crossref]

T. Raveendran, S. Sarkar, D. Roy, and R. M. Vasu, “A novel filtering framework through Girsanov correction for the identification of nonlinear dynamical systems,” Inverse Probl. 29, 065002 (2013).

[Crossref]

M. Slaney, A. C. Kak, and L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microw. Theory Technol. 32, 860–874 (1984).

[Crossref]

A. C. Kak and M. Slaney, “Tomographic imaging with diffracting sources,” in Principles of Computerized Tomographic Imaging (IEEE, 1988), pp. 203–273.

A. M. Stuart, “Inverse problems: a Bayesian perspective,” Acta Numerica 19, 451–559 (2010).

[Crossref]

N. Pimprikar, J. Teresa, D. Roy, R. M. Vasu, and K. Rajan, “An approximately H1-optimal Petrov-Galerkin mesh-free method: application to computation of scattered light for optical tomography,” CMES—Computer Modeling in Engineering and Sciences 92, 33–61 (2013).

K. Belkebir and A. G. Tijhuis, “Modified gradient method and modified Born method for solving a two-dimensional inverse scattering problem,” Inverse Probl. 17, 1671–1688 (2001).

[Crossref]

G. A. Tsihrintzis and A. J. Devaney, “Higher order (nonlinear) diffraction tomography: inversion of the Rytov series,” IEEE Trans. Inf. Theory 46, 1748–1761 (2000).

[Crossref]

S. Sarkar, S. R. Chowdhury, M. Venugopal, R. M. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).

[Crossref]

T. Raveendran, S. Sarkar, D. Roy, and R. M. Vasu, “A novel filtering framework through Girsanov correction for the identification of nonlinear dynamical systems,” Inverse Probl. 29, 065002 (2013).

[Crossref]

N. Pimprikar, J. Teresa, D. Roy, R. M. Vasu, and K. Rajan, “An approximately H1-optimal Petrov-Galerkin mesh-free method: application to computation of scattered light for optical tomography,” CMES—Computer Modeling in Engineering and Sciences 92, 33–61 (2013).

B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements,” Phys. Med. Biol. 54, 285–305 (2009).

[Crossref]

H. M. Varma, R. M. Vasu, and A. K. Nandakumaran, “Direct reconstruction of complex refractive index distribution from boundary measurement of intensity and normal derivative of intensity,” J. Opt. Soc. Am. A 24, 3089–3099 (2007).

[Crossref]

N. Jayashree, G. K. Datta, and R. M. Vasu, “Optical tomographic microscope for quantitative imaging of phase objects,” Appl. Opt. 39, 277–283 (2000).

[Crossref]

M. Venugopal, D. Roy, and R. M. Vasu, “A new evolutionary Bayesian approach incorporating additive path correction for nonlinear inverse problems,” arxiv.org/pdf/1305.2702.

S. Sarkar, S. R. Chowdhury, M. Venugopal, R. M. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).

[Crossref]

M. Venugopal, D. Roy, and R. M. Vasu, “A new evolutionary Bayesian approach incorporating additive path correction for nonlinear inverse problems,” arxiv.org/pdf/1305.2702.

W. C. Chew and Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imag. 9, 218–225 (1990).

[Crossref]

F. Natterer and F. Wübbeling, “A propagation-backpropagation method for ultrasound tomography,” Inverse Probl. 11, 1225–1232 (1995).

[Crossref]

A. M. Stuart, “Inverse problems: a Bayesian perspective,” Acta Numerica 19, 451–559 (2010).

[Crossref]

N. Pimprikar, J. Teresa, D. Roy, R. M. Vasu, and K. Rajan, “An approximately H1-optimal Petrov-Galerkin mesh-free method: application to computation of scattered light for optical tomography,” CMES—Computer Modeling in Engineering and Sciences 92, 33–61 (2013).

G. A. Tsihrintzis and A. J. Devaney, “Higher order (nonlinear) diffraction tomography: inversion of the Rytov series,” IEEE Trans. Inf. Theory 46, 1748–1761 (2000).

[Crossref]

W. C. Chew and Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imag. 9, 218–225 (1990).

[Crossref]

A. H. Hielscher, A. D. Klose, and K. M. Hansen, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imag. 18, 262–271 (1999).

[Crossref]

M. Slaney, A. C. Kak, and L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microw. Theory Technol. 32, 860–874 (1984).

[Crossref]

D. Roy, “A family of lower- and higher-order transversal linearization techniques in non-linear stochastic engineering dynamics,” Int. J. Numer. Methods Eng. 61, 764–790 (2004).

[Crossref]

D. Roy and L. S. Ramachandra, “A semi-analytical locally transversal linearization method for non-linear dynamical systems,” Int. J. Numer. Methods Eng. 51, 203–224 (2001).

[Crossref]

T. Raveendran, S. Sarkar, D. Roy, and R. M. Vasu, “A novel filtering framework through Girsanov correction for the identification of nonlinear dynamical systems,” Inverse Probl. 29, 065002 (2013).

[Crossref]

F. Natterer and F. Wübbeling, “A propagation-backpropagation method for ultrasound tomography,” Inverse Probl. 11, 1225–1232 (1995).

[Crossref]

K. Belkebir and A. G. Tijhuis, “Modified gradient method and modified Born method for solving a two-dimensional inverse scattering problem,” Inverse Probl. 17, 1671–1688 (2001).

[Crossref]

L. S. Ramachandra and D. Roy, “A new method for nonlinear two-point boundary value problems in solid mechanics,” J. Appl. Mech. 68, 776–786 (2001).

[Crossref]

A. H. Andersen, “Tomography transform and inverse in geometrical optics,” J. Opt. Soc. Am. A 4, 1385–1395 (1987).

[Crossref]

P. Guo and A. J. Devaney, “Comparison of reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 22, 2338–2347 (2005).

[Crossref]

M. H. Maleki and A. J. Devaney, “Phase retrieval and intensity-only reconstruction algorithm for optical diffraction tomography,” J. Opt. Soc. Am. A 10, 1086–1092 (1993).

[Crossref]

G. Gbur and E. Wolf, “Hybrid diffraction tomography without phase information,” J. Opt. Soc. Am. A 19, 2194–2202 (2002).

[Crossref]

M. A. Anastasio, D. Shi, Y. Huang, and G. Gbur, “Image reconstruction in spherical-wave intensity diffraction tomography,” J. Opt. Soc. Am. A 22, 2651–2661 (2005).

[Crossref]

H. M. Varma, R. M. Vasu, and A. K. Nandakumaran, “Direct reconstruction of complex refractive index distribution from boundary measurement of intensity and normal derivative of intensity,” J. Opt. Soc. Am. A 24, 3089–3099 (2007).

[Crossref]

B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements,” Phys. Med. Biol. 54, 285–305 (2009).

[Crossref]

S. Sarkar, S. R. Chowdhury, M. Venugopal, R. M. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).

[Crossref]

D. M. Livings, S. L. Dance, and N. K. Nichols, “Unbiased ensemble square root filters,” Physica D 237, 1021–1028 (2008).

[Crossref]

A. J. Devaney and G. Beylkin, “Diffraction tomography using arbitrary transmitter and receiver surfaces,” Ultrason. Imag. 6, 181–193 (1984).

A. C. Kak and M. Slaney, “Tomographic imaging with diffracting sources,” in Principles of Computerized Tomographic Imaging (IEEE, 1988), pp. 203–273.

A. C. Kak, “Tomographic imaging with diffracting and non-diffracting sources,” in Array Signal Processing, S. Haykin, ed. (Prentice-Hall, 1985).

R. F. Harrington, Field Computation by Moment Method (Macmillan, 1968).

F. C. Klebaner, Introduction to Stochastic Calculus with Applications, 2nd ed. (Imperial College, 2005).

M. Venugopal, D. Roy, and R. M. Vasu, “A new evolutionary Bayesian approach incorporating additive path correction for nonlinear inverse problems,” arxiv.org/pdf/1305.2702.