Solving Ill Conditioned Problems By Minimizing Equation Error
Solving Ill Conditioned Problems By Minimizing Equation Error
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3. 4. Two dimensions The case n = 2, i. E. , the image domain P is a subset of R, can be handled by similar methods, but requires additional design choices. A fairly natural discrete finite difference approach proceeds with introduction of a grid of points iij, k), it>0, and variables w, j, t, cr\}lky o'm-*. And Vij^k, with the system of equations (1) _ "i, j, k ~ ^i-l, j, k ^i, J, k ~ 2 ' (2) ^ "'J, k ~ "i, j-l, k ^ij, k - UiJ, k = " and -'^Ui^k - -d, k 1 2 l' 2 4 2 . 1 2 1.
When these equatio...ns hold exactly, the data u is blurred from level k to level k + 1 by convolution against the kernel: J_ 16 More generally, the four equations above can be converted to a quadratic measure of equation error in the unknown variables. Gradient equations can be formed, and will once again be linear with local (three-by-three-by-three) dependence. The gra- dient equations can be used in either a steepest descent or in a conjugate gradient procedure to minimize equation error.
3. 5. Minimization Techniques The equation error E for the discretized deblurring problem can be minimized by any of a number of standard techniques.
What to read after Solving Ill Conditioned Problems By Minimizing Equation Error?
You can find similar books in the "Read Also" column, or choose other free books by Robert a Hummel to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
3. 4. Two dimensions The case n = 2, i. E. , the image domain P is a subset of R, can be handled by similar methods, but requires additional design choices. A fairly natural discrete finite difference approach proceeds with introduction of a grid of points iij, k), it>0, and variables w, j, t, cr\}lky o'm-*. And Vij^k, with the system of equations (1) _ "i, j, k ~ ^i-l, j, k ^i, J, k ~ 2 ' (2) ^ "'J, k ~ "i, j-l, k ^ij, k - UiJ, k = " and -'^Ui^k - -d, k 1 2 l' 2 4 2 . 1 2 1.
When these equatio...ns hold exactly, the data u is blurred from level k to level k + 1 by convolution against the kernel: J_ 16 More generally, the four equations above can be converted to a quadratic measure of equation error in the unknown variables. Gradient equations can be formed, and will once again be linear with local (three-by-three-by-three) dependence. The gra- dient equations can be used in either a steepest descent or in a conjugate gradient procedure to minimize equation error.
3. 5. Minimization Techniques The equation error E for the discretized deblurring problem can be minimized by any of a number of standard techniques.
What to read after Solving Ill Conditioned Problems By Minimizing Equation Error?
You can find similar books in the "Read Also" column, or choose other free books by Robert a Hummel to read onlineMoreLess
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