K. A. Thomson, Ö. L. Gülder, E. J. Weckman, R. A. Fraser, G. J. Smallwood, and D. R. Snelling, "Soot concentration and temperature measurements in coannular, nonpremixed CH4/air laminar flames at pressures up to 4 MPa," Combust. Flame 140, 222-232 (2005).

[CrossRef]

A. Schwarz, "Multitomographic flame analysis with a Schlieren apparatus," Meas. Sci. Technol. 7, 406-413 (1996).

[CrossRef]

M. Deutsch and I. Beniaminy, "Derivative-free inversion of Abel's integral equation," J. Appl. Phys. 54, 137-143 (1983).

[CrossRef]

M. Deutsch and I. Beniaminy, "Derivative-free inversion of Abel's integral equation," Appl. Phys. Lett. 41, 27-28 (1983).

[CrossRef]

C. K. Chan and P. Lu, "On the stability of the solution of Abel's integral equation," J. Phys. A 14, 575-578 (1981).

[CrossRef]

R. S. Anderssen, "Stable procedures for the inversion of Abel's equation," J. Inst. Math. Appl. 17, 329-342 (1976).

[CrossRef]

A. N. Tikhonov, "Inverse problems in heat conduction," J. Eng. Phys. 29, 816-820 (1975).

[CrossRef]

G. N. Ramachandran and A. V. Lakshminarayanan, "Three-dimensional reconstruction from radiographs and electron micrographs: applications of convolutions instead of Fourier transforms," Proc. Natl. Acad. Sci. U.S.A. 69, 2236-2240 (1971).

[CrossRef]

L. A. Shepp and B. F. Logan, "Reconstructing interior head tissue from x-ray transmissions," IEEE Trans. Nucl. Sci. NS-21, 228-236 (1971).

R. S. Anderssen, "Stable procedures for the inversion of Abel's equation," J. Inst. Math. Appl. 17, 329-342 (1976).

[CrossRef]

M. Deutsch and I. Beniaminy, "Derivative-free inversion of Abel's integral equation," J. Appl. Phys. 54, 137-143 (1983).

[CrossRef]

M. Deutsch and I. Beniaminy, "Derivative-free inversion of Abel's integral equation," Appl. Phys. Lett. 41, 27-28 (1983).

[CrossRef]

C. K. Chan and P. Lu, "On the stability of the solution of Abel's integral equation," J. Phys. A 14, 575-578 (1981).

[CrossRef]

M. Deutsch and I. Beniaminy, "Derivative-free inversion of Abel's integral equation," J. Appl. Phys. 54, 137-143 (1983).

[CrossRef]

M. Deutsch and I. Beniaminy, "Derivative-free inversion of Abel's integral equation," Appl. Phys. Lett. 41, 27-28 (1983).

[CrossRef]

K. A. Thomson, Ö. L. Gülder, E. J. Weckman, R. A. Fraser, G. J. Smallwood, and D. R. Snelling, "Soot concentration and temperature measurements in coannular, nonpremixed CH4/air laminar flames at pressures up to 4 MPa," Combust. Flame 140, 222-232 (2005).

[CrossRef]

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981), pp. 28-30.

R. Gorenflo and S. Vessella, Abel Integral Equations: Analysis and Applications, Lecture Notes in Mathematics (Springer, 1991).

K. A. Thomson, Ö. L. Gülder, E. J. Weckman, R. A. Fraser, G. J. Smallwood, and D. R. Snelling, "Soot concentration and temperature measurements in coannular, nonpremixed CH4/air laminar flames at pressures up to 4 MPa," Combust. Flame 140, 222-232 (2005).

[CrossRef]

J. Hadamard, Lectures on Cauchy's Problem in Linear Differential Equations (Yale U. Press, 1923).

P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (SIAM, 1998).

[CrossRef]

G. N. Ramachandran and A. V. Lakshminarayanan, "Three-dimensional reconstruction from radiographs and electron micrographs: applications of convolutions instead of Fourier transforms," Proc. Natl. Acad. Sci. U.S.A. 69, 2236-2240 (1971).

[CrossRef]

L. A. Shepp and B. F. Logan, "Reconstructing interior head tissue from x-ray transmissions," IEEE Trans. Nucl. Sci. NS-21, 228-236 (1971).

C. K. Chan and P. Lu, "On the stability of the solution of Abel's integral equation," J. Phys. A 14, 575-578 (1981).

[CrossRef]

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981), pp. 28-30.

G. N. Ramachandran and A. V. Lakshminarayanan, "Three-dimensional reconstruction from radiographs and electron micrographs: applications of convolutions instead of Fourier transforms," Proc. Natl. Acad. Sci. U.S.A. 69, 2236-2240 (1971).

[CrossRef]

A. Schwarz, "Multitomographic flame analysis with a Schlieren apparatus," Meas. Sci. Technol. 7, 406-413 (1996).

[CrossRef]

L. A. Shepp and B. F. Logan, "Reconstructing interior head tissue from x-ray transmissions," IEEE Trans. Nucl. Sci. NS-21, 228-236 (1971).

K. A. Thomson, Ö. L. Gülder, E. J. Weckman, R. A. Fraser, G. J. Smallwood, and D. R. Snelling, "Soot concentration and temperature measurements in coannular, nonpremixed CH4/air laminar flames at pressures up to 4 MPa," Combust. Flame 140, 222-232 (2005).

[CrossRef]

K. A. Thomson, Ö. L. Gülder, E. J. Weckman, R. A. Fraser, G. J. Smallwood, and D. R. Snelling, "Soot concentration and temperature measurements in coannular, nonpremixed CH4/air laminar flames at pressures up to 4 MPa," Combust. Flame 140, 222-232 (2005).

[CrossRef]

K. A. Thomson, Ö. L. Gülder, E. J. Weckman, R. A. Fraser, G. J. Smallwood, and D. R. Snelling, "Soot concentration and temperature measurements in coannular, nonpremixed CH4/air laminar flames at pressures up to 4 MPa," Combust. Flame 140, 222-232 (2005).

[CrossRef]

A. N. Tikhonov, "Inverse problems in heat conduction," J. Eng. Phys. 29, 816-820 (1975).

[CrossRef]

R. Gorenflo and S. Vessella, Abel Integral Equations: Analysis and Applications, Lecture Notes in Mathematics (Springer, 1991).

K. A. Thomson, Ö. L. Gülder, E. J. Weckman, R. A. Fraser, G. J. Smallwood, and D. R. Snelling, "Soot concentration and temperature measurements in coannular, nonpremixed CH4/air laminar flames at pressures up to 4 MPa," Combust. Flame 140, 222-232 (2005).

[CrossRef]

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981), pp. 28-30.

C. J. Cremers and R. C. Birkebak, "Application of the Abel integral equation to spectrographic data," Appl. Opt. 5, 1057-1063 (1966).

[CrossRef]
[PubMed]

R. J. Hall and P. A. Bonczyk, "Sooting flame thermometry using emission/absorption tomography," Appl. Opt. 29, 4590-4598 (1990).

[CrossRef]
[PubMed]

C. J. Dasch, "One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered backprojection methods," Appl. Opt. 31, 1146-1152 (1992).

[CrossRef]
[PubMed]

M. Deutsch and I. Beniaminy, "Derivative-free inversion of Abel's integral equation," Appl. Phys. Lett. 41, 27-28 (1983).

[CrossRef]

K. A. Thomson, Ö. L. Gülder, E. J. Weckman, R. A. Fraser, G. J. Smallwood, and D. R. Snelling, "Soot concentration and temperature measurements in coannular, nonpremixed CH4/air laminar flames at pressures up to 4 MPa," Combust. Flame 140, 222-232 (2005).

[CrossRef]

L. A. Shepp and B. F. Logan, "Reconstructing interior head tissue from x-ray transmissions," IEEE Trans. Nucl. Sci. NS-21, 228-236 (1971).

M. Deutsch and I. Beniaminy, "Derivative-free inversion of Abel's integral equation," J. Appl. Phys. 54, 137-143 (1983).

[CrossRef]

A. N. Tikhonov, "Inverse problems in heat conduction," J. Eng. Phys. 29, 816-820 (1975).

[CrossRef]

R. S. Anderssen, "Stable procedures for the inversion of Abel's equation," J. Inst. Math. Appl. 17, 329-342 (1976).

[CrossRef]

C. K. Chan and P. Lu, "On the stability of the solution of Abel's integral equation," J. Phys. A 14, 575-578 (1981).

[CrossRef]

A. Schwarz, "Multitomographic flame analysis with a Schlieren apparatus," Meas. Sci. Technol. 7, 406-413 (1996).

[CrossRef]

G. N. Ramachandran and A. V. Lakshminarayanan, "Three-dimensional reconstruction from radiographs and electron micrographs: applications of convolutions instead of Fourier transforms," Proc. Natl. Acad. Sci. U.S.A. 69, 2236-2240 (1971).

[CrossRef]

R. Gorenflo and S. Vessella, Abel Integral Equations: Analysis and Applications, Lecture Notes in Mathematics (Springer, 1991).

J. Hadamard, Lectures on Cauchy's Problem in Linear Differential Equations (Yale U. Press, 1923).

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981), pp. 28-30.

P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (SIAM, 1998).

[CrossRef]