1D Fermat Number Transform deconvolution #14
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Build fails cause this PR is not merged yet JuliaRegistries/General#7482 |
| h = [3, 2, 0, 0] | ||
| y = [3, 5, 3, 0] | ||
| x = fermat(y, h, 4, 17) | ||
| @test Circulant(h) * x == y |
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Circular convolution again, it uses the same fft approach as above
https://github.com/JuliaMatrices/SpecialMatrices.jl/blob/master/src/toeplitz.jl#L54
I have feeling that we need some package with better api to perform convolution. I don't like the fact that floating point arithmetic is used here.
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It looks like you have a plan 🙂
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The biggest limitation of this method is that each element of H matrix needs to have inverse, what is hard to achieve for real data, so I'm not sure if Deconvolution.jl is good place for algorithms like this.
While currently implemented methods are probably easier to use in practice, I don't see why this would be a problem for including this method here 😉
| h = [3, 2, 0, 0] | ||
| y = [3, 5, 3, 0] | ||
| x = fermat(y, h, 4, 17) | ||
| @test Circulant(h) * x == y |
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It looks like you have a plan 🙂
| xm = ifnt(H_inv .* fnt(convolved, g, q), g, q) | ||
| x0 = mod.(Dm * xm, q) | ||
| x0[x0 .>= bias] .-= q | ||
| x = x0 |
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x will be exactly the same thing as x0, this means that chaning x0 will have the same effect on x and vice versa. Is this what you want?
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Yes, this assignment is just to follow variable naming form the paper, x0 is not modified later, and new variable xj is introduced later int the loop.
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@giordano build is green, but please do not merge yet, I need to add docs and replace fft with precise integer convolution. To do that I think I will start a new project for integer DSP algorithms. |
I implemented 1D case of FNT deconvolution what partially solves #2 I'll update docs if it makes sense.
The biggest limitation of this method is that each element of H matrix needs to have inverse, what is hard to achieve for real data, so I'm not sure if Deconvolution.jl is good place for algorithms like this.