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sfarrens / notebooks

A collection of tutorials presented via Jupyter Notebooks.
https://sfarrens.github.io/pages/tutorials.html
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Inverse problem notebook #1

Open JulienNGirard opened 7 years ago

JulienNGirard commented 7 years ago

Hey Sam, I have been through your Inverse problem notebook. It is very nice! I would have love to have this when I starting to learn about these things.

Here are my few 2-cent comments.

" Inverse Problem

For the inverse problem we will assume we already know Y and use this to work out X, so in other words we already have a set of data points and we want to work out the best fitting line."

It is a bit confusing as, in the backward problem, you said you are trying to estimate the model parameter (m and b) which is A. In your application, you have a set of points (x_i,y_i) and you want to estimate the coefficients of A. I think students may lose track here. Is there another way to put this in terms of "Having Y, and we are looking for X" in the case of a linear regression? X is supposed to be the matrix expression of your set of equations, so one has to "build" it to work out the parameters of A using the pseudo inverse.

However, it is correctly put in exercice 1.

Deconvolution section Forward Problem

Now we need to define our distortion matrix, which in this case will be the convolution of the PSF with the true image.

I would add "We will use the convolution theorem to perform this convolution using a simple Fourier transform". (with link to https://en.wikipedia.org/wiki/Convolution_theorem) OR put it as a comment of the fftconvolve function. As this theorem might not be know by everybody (especially undergrads and even some graduates students who are not specialist in Math/SP.......... 50% of my students where in that situation this year...)

Gradient descent section

For this approach we want to define a convex function that measures the accuracy of a given reconstruction

Likewise, I would give a 2 line definition of why you want to define a convex function. When I started to work on convex optimization, this was a mystery to me. Maybe you plan to do (or already did) a mathematical groundwork pynb with basic analysis and algebra? Or maybe just point to some link with definition. Same remarks about the definition of norms (l0, l1, l2, ln...) that come just after.

((((I would be particularly interested in a general nb which would address how you compute gradients in a matrix framework, from the definition of the norms. (this obviously will extend to computation of prox op...))))

Now, we can try this apporach to try to recover the original image.

==> approach.

The interactive thing is particularly neat.

Fortuneately

==> fortunately

Fortuneately this simply corresponds to rotating the PSF by 90.

==> why ?

Hint/solution section

Hints

==>tag

sfarrens commented 7 years ago

Hi Julien, thanks a lot for the feedback! I am planning update these notebooks for the next Astronomical Data Analysis (ADA9) summer school, so I will be sure to implement the changes you suggested.