Enhanced electrical impedance tomography via the Mumford–Shah functional
ESAIM: Control, Optimisation and Calculus of Variations (2001)
- Volume: 6, page 517-538
- ISSN: 1292-8119
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top- [A1] L. Ambrosio, A compactness theorem for a new class of functions of bounded variation. Boll. Un. Mat. Ital. B 3 (1989) 857-881. Zbl0767.49001MR1032614
- [A2] L. Ambrosio, Existence theory for a new class of variational problems. Arch. Rational Mech. Anal. 111 (1990) 291-322. Zbl0711.49064MR1068374
- [A-F-P] L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. Clarendon Press, Oxford (2000). Zbl0957.49001MR1857292
- [A-T1] L. Ambrosio and V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via -convergence. Comm. Pure Appl. Math. 43 (1990) 999-1036. Zbl0722.49020MR1075076
- [A-T2] L. Ambrosio and V.M. Tortorelli, On the approximation of free discontinuity problem. Boll. Un. Mat. Ital. B 6 (1992) 105-123. Zbl0776.49029MR1164940
- [B-Z] A. Blake and A. Zisserman, Visual Reconstruction. The MIT Press, Cambridge Mass, London (1987). MR919733
- [Bo-V] E. Bonnetier and M. Vogelius, An elliptic regularity result for a composite medium with “touching” fibers of circular cross-section. SIAM J. Math. Anal. 31 (2000) 651-677. Zbl0947.35044
- [Br] A. Braides, Approximation of Free-Discontinuity Problems. Springer-Verlag, Berlin Heidelberg New York (1998). Zbl0909.49001MR1651773
- [C] A.P. Calderón, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics. Sociedade Brasileira de Matemática, Rio de Janeiro (1980) 65-73. MR590275
- [Co-Ta] G. Congedo and I. Tamanini, On the existence of solutions to a problem in multidimensional segmentation. Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991) 175-195. Zbl0729.49003MR1096603
- [DM] G. Dal Maso, An Introduction to -convergence. Birkhäuser, Boston Basel Berlin (1993). Zbl0816.49001MR1201152
- [DG-Ca-L] E. De Giorgi, M. Carriero and A. Leaci, Existence theorem for a minimum problem with free discontinuity set. Arch. Rational Mech. Anal. 108 (1989) 195-218. Zbl0682.49002MR1012174
- [D] D.C. Dobson, Stability and Regularity of an Inverse Elliptic Boundary Value Problem, Ph.D. Thesis. Rice University, Houston (1990).
- [D-S] D.C. Dobson and F. Santosa, An image-enhancement technique for electrical impedance tomography. Inverse Problems 10 (1994) 317-334. Zbl0805.35149MR1269010
- [E-G] L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton Ann Arbor London (1992). Zbl0804.28001MR1158660
- [I] V. Isakov, Inverse Problems for Partial Differential Equations. Springer-Verlag, New York Berlin Heidelberg (1998). Zbl0908.35134MR1482521
- [Gi] E. Giusti, Minimal Surfaces and Functions of Bounded Variation. Birkhäuser, Boston Basel Stuttgart (1984). Zbl0545.49018MR775682
- [K-St] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications. Academic Press, New York London Toronto (1980). Zbl0457.35001MR567696
- [Ko-V] R.V. Kohn and M. Vogelius, Determining conductivity by boundary measurements. Comm. Pure Appl. Math. 37 (1984) 289-298. Zbl0586.35089MR739921
- [Li-V] Y.Y. Li and M. Vogelius, Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients. Arch. Rational Mech. Anal. 153 (2000) 91-151. Zbl0958.35060MR1770682
- [M] N.G. Meyers, An -estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 17 (1963) 189-205. Zbl0127.31904MR159110
- [Mu-Sh1] D. Mumford and J. Shah, Boundary detection by minimizing functionals, I, in Proc. IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE Computer Society Press/North-Holland, Silver Spring Md./Amsterdam (1985) 22-26.
- [Mu-Sh2] D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42 (1989) 577-685. Zbl0691.49036MR997568
- [Sy-U] J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem. Ann. Math. 125 (1987) 153-169. Zbl0625.35078MR873380
- [Tr] G.M. Troianiello, Elliptic Differential Equations and Obstacle Problems. Plenum Press, New York London (1987). Zbl0655.35002MR1094820