Timeline for How to use DFT to solve this minimization problem?
Current License: CC BY-SA 3.0
9 events
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| Apr 22, 2020 at 12:29 | comment | added | schlodinger | You can get using the "Gateau" definition of derivative. Namely, if you have a function J, you can get it's Gateau derivative in point S, using the formula: lim (epsilon ->0) 1/epsilon * [J(S + epsilon * M) - J(S)] | |
| Nov 20, 2011 at 5:54 | comment | added | user19132 | How to get the differential of the objective function? Why it's Df(S)(M)=2⟨S−I,M⟩+β(2⟨∂xS−h,∂xM⟩+2⟨∂yS−v,∂yM⟩)? | |
| Nov 10, 2011 at 8:45 | comment | added | user19132 | @Alex I learned DFT from <Digital Image Processing> by Gonzalez, seems it omits some important theories. I will refer to some other book. Anyway, thank you:-) | |
| Nov 10, 2011 at 8:13 | comment | added | Alexander Chervov | @Co Yes. F - stands for DFT matrix. The fact that x F f(t) = F d/t f(t) which is the same as x =F^{-1} d/dt F is simple basic fact which is described in any textbook on Fourier analysis. In discrete version it is related to the fact that F^{-1} DiagMatr F = Circulant. I am sorry I have not any text book at hand to point out the pages. But I think looking on Wikipedia you can find it relevant textbooks. | |
| Nov 10, 2011 at 7:54 | vote | accept | user19132 | ||
| Nov 10, 2011 at 7:54 | comment | added | user19132 | @Alex Thank you! F is the DFT Matrix right? Can you give me some books or something I can find some proof of it? | |
| Nov 10, 2011 at 6:10 | comment | added | Alexander Chervov | @Co "DFT diagonalizes the gradient" - means Fourier transform of d/dx is diagonal operator - this means that if you consider F * d/dx * F^{-1} - this will be diagonal matrix. Formula F * d/dx * F^{-1} is usually abbreviated as F(d/dx). (For mathematician such an abbreviation is natural - induced action of operators on matrices). | |
| Nov 10, 2011 at 4:29 | comment | added | user19132 | Thanks! I think that's what I'm looking for! But what does "the fact that the DFT diagonalizes the gradient" mean? I've read it somewhere but don't get it. Anywhere I can find some detail? | |
| Nov 9, 2011 at 20:08 | history | answered | hoecker | CC BY-SA 3.0 |