Timeline for How to use DFT to solve this minimization problem?
Current License: CC BY-SA 3.0
6 events
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| Apr 24, 2020 at 15:50 | comment | added | schlodinger |
Hi @AlexanderChervov! I'm working on a problem similar to this, except that my h=v=0 but, the derivative of my matrix S is multiplied point-wise with a weight matrix W_x and W_y. I can follow the same procedure to solve the optimization problem, but when I apply FFT, I got F*(dx)F(W_x o dx(S)) where o is point wise multiplication. How can I isolate S to have a closed form formula for S? in other words, what is the DFT of point wise multiplication? thank you in advance!
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| Nov 9, 2011 at 14:42 | comment | added | Alexander Chervov | @Co why M=1+dx+dy? Good question I am also not very clear but I guess it is due to fact that dx and dy actss on different variables - I think I can clarify it, but may be tomorrow... | |
| Nov 9, 2011 at 14:40 | comment | added | Alexander Chervov | @Igor,Co Assume you need calculate Cv - just put F: F^{-1} * (F C F^{-1}) * F v . Why it speeds - calculation Cv takes n^2 operations. Assume FCF^{-1} is known to you - like in this example because C and it is diagonal like in this example since C= d/dx , under this assumption you need n-operations to calculate Diag * Cv . And nlogn to make FFT. So instead of original n^2 you get n log n. Is it clear ? Sorry need to run home. | |
| Nov 9, 2011 at 14:17 | comment | added | user19132 | why M=1+dx+dy? M-P inverse is only used in ||Mx-v|| (||x+dx x + dy x -v||) right? So how can M be 1+dx+dy in this example? And how to use FFT to speed up anything in M-P inverse? The paper says the trivial way to solve this equation is to use gradient decent, which is very very slow, so they come with a way to speed it up. | |
| Nov 9, 2011 at 13:11 | comment | added | Igor Rivin | I, for one, do not understand this answer. What do you mean "put F everywhere"? And why does that speed anything up? | |
| Nov 9, 2011 at 12:55 | history | answered | Alexander Chervov | CC BY-SA 3.0 |