A. Tikhonov. Ill-Posed Problems in Natural Sciences. Coronet, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that can account for global illumination changes. The estimation of a dense correspondence registration field is an ill posed problem. The number of unknown variables is usually higher than the number of constraints. Additional smoothness constraints are considered to cope with this limitation [16]. Such techniques have good performance when dealing with images with low SNR but are not efficient with shapes since they cannot guarantee an oneto one correspondence between the source and the target shape image. Global alignment methods are an alternative to the complete recovery of the ....

....well as estimating the optical flow between two images are topics of increasing interest. Dense motion registration estimation is an ill posed problem since the number of variables to be recovered is larger than the number of available constraints. Smoothness as well as other form of constraints [16] were employed to cope with this limitation. Such components are efficient when used within an image registration problem that refers to structures with limited discontinuities. On the other hand, in the case of shapes such constraints cannot be used in a straightforward manner. The lack of ....

A. Tikhonov. Ill-Posed Problems in Natural Sciences. Coronet, 1992.

....ST lines. It is also possible to improve the solution by imposing conditions based on optimality criteria or a priori information. In addition, the inverse problem is technically ill posed, thus leading to solutions that may be unstable with respect to small perturbations of the projections (e.g. Tikhonov and Goncharsky (1987)) The ill posedness may be particularly relevant in the calculation of ST of spatial random fields. The stability of the ST solutions for random fields can be improved by using frequency filters that smooth out the fluctuations of the field (Jain (1989) Several schemes have been investigated ....

A. N. Tikhonov and A. V. Goncharsky (1987), Ill-Posed Problems in the Natural Sciences,Mir Publishers, Moscow.

....discussion of the problem) can be found in [77] where a joint optimization of derivative and blurring filters in the frequency domain is described. The smoothness term in (17) regularizes the ill posed problem of motion estimation (aperture effect) thus turning it into a well posed problem 5 [87]. Then, the scalar balancing the constant intensity assumption against motion smoothness is termed a regularization constant. For practical reasons, the equation (17) is often expressed in discrete form where the first term is replaced by J 1 (d) 13) and the second term becomes a discrete ....

A. Tikhonov and A. Goncharsky, eds., Ill-posed problems in the natural sciences. Moscow: MIR Publishers, 1987.

....crossvalidation, and the L curve criterion. Numerical experiments are used to determine the efficiency and robustness of the various methods. 1 Introduction The solution of ill posed linear systems and linear least squares problems is a frequent task in numerical analysis. We refer the reader to [5,17,30] for an overview of applications. In this paper we consider the (overdetermined) linear system b = Ax e; where A is an m by n matrix with m n, b and e are vectors of size m, and x is an n vector. The matrix A and the vector b are given, and e is assumed to be a random noise vector. The ....

Andrei N. Tikhonov, Ill-Posed Problems in Natural Sciences, Proceedings of the International Conference, TVP Science Publishers, Moscow, 1992.

.... Besides Tikhonov regularization, discrete regularization techniques include truncated singular value decomposition (TSVD) generalized singular value decomposition (GSVD) maximum entropy, and a number of generalized least squares schemes, including Twomey and variants of Tikhonov methods [39] [40], 41] 42] 35] All of the previously mentioned methods share a common thread, in that these methods try to reduce the effects of solving an ill conditioned system by restoring continuity of the solution onto the data. Most of these methods employ operations that try to balance the amount of ....

.... the regularization parameter [35] Recent work in inverse electrocardiography by Brooks et al. has focused on methods to improve the a priori estimation of the regularization parameter [43] 44] 45] For a more in depth treatment of ill posed inverse problems, the reader is referred to [39] [40], 42] 35] For specific information on electrocardiographic inverse problems, see the review articles [46] 47] A particularly useful reference for discrete ill posed problems June 29, 1997 DRAFT 9 is the Matlab [48] package developed by Per Christian Hansen, which is freely available via ....

Tikhonov, A.N. and Goncharsky, A.V., Ill-Posed Problems in the Natural Sciences, MIR Publishers, Moscow, 1987.

....large perturbation of the solution. Hadamard believed that ill posed problems were artificial in that they would not describe physical systems. He was wrong, though, and today there is a vast amount of literature on ill posed problems arising in many areas of science and engineering, cf. e.g. [14, 15, 16, 32, 57, 61, 63, 69, 79]. The classical example of an ill posed problem is a Fredholm integral equation of the first kind with a square integrable kernel [31] Z b a K(s; t) f(t) dt = g(s) c s d ; 2.1) where the right hand side g and the kernel K are given, and where f is the unknown solution. If the solution f is ....

A. N. Tikhonov & A. V. Goncharsky, Ill-Posed Problems in the Natural Sciences, MIR Publishers, Moscow, 1987.

....discussion of the problem) can be found in [76] where a joint optimization of derivative and blurring filters in the frequency domain is described. The smoothness term in (17) regularizes the ill posed problem of motion estimation (aperture effect) thus turning it into a well posed problem 4 [86]. Then, the scalar balancing the constant intensity assumption against motion smoothness is termed a regularization constant. For practical reasons, the equation (17) is often expressed in discrete form where the first term is replaced by J 1 (d) 13) and the second term becomes a discrete ....

A. Tikhonov and A. Goncharsky, eds., Ill-posed problems in the natural sciences. Moscow: MIR Publishers, 1987. 40 On models, criteria and search strategies for motion estimation

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A. Tikhonov. Ill-Posed Problems in Natural Sciences. Coronet, 1992.

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Tikhonov, A.: Ill-Posed Problems in Natural Sciences. Coronet (1992)

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A. N. Tikhonov and A. V. Goncharskyy, Ill-Posed Problems in the Natural Sciences. Moscow, Russia: Mir Publishers, 1987.

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Tikhonov, A.N. and Goncharsky, A.V (Eds.) (1987). Ill-Posed Problems in the Natural Sciences. MIR Publishers, Moscow.

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Tikhonov, A. N. & Goncharsky A. V., Ill-posed Problems in the Natural Sciences, Moscow, MIR publishers, (1987).

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Tikhonov, A. N. & Goncharsky A. V., Ill-posed Problems in the Natural Sciences, Moscow, MIR publishers, (1987).

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A. N. Tikhonov and A. V. Goncharsky, eds., Ill-posed Problems in the Natural Sciences, MIR Publishers, Moscow, 1987.

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