# Tagged Questions

Inverse problems involve for example reconstruction of an object based on physical measurements and finding a best model/parameters out of a family given observed data. Typically the corresponding "forward" problems are well-posed and can be solved straightforwardly, while the inverse problems are ...

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### How to solve an inverse problem $d=Ax_1 + Ax_2$

In the optimization problems, there is an operator, $A$, which transforms the model, $x$, to the data domain, $d$. Generally, we don't know the model and we are trying to find it according to the ...
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### What is the difference between FISTA and Nesterov's second method?

I am going to solve an inverse problem. This problem has a $L_2-L_1$ norm cost function. The $L_2$ norm is for residual and the $L_1$ norm is for model coefficients. The cost function can be ...
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### Using the Affine cipher, do we need $a^{-1}$ if we know gcd(a,26)=1?

I have just attempted the affine cipher with the word "code" $CODE = 02140304$ Lets choose our key as $(5,3)$, so our encryption is $y=5x+3$ $13211823=NVSX$ Now, to undo the code, I would have to ...
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### Inverse problems with Graphical Approximation and Graphs

Suppose an inverse problem with graphical approximation for the system where only a small subset of system features are known hence undetermined scenario. The system can be represented by a graph. ...
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### References on Inverse Problems, Approximation theory and Algebraic geometry

For example, you approximate structure functions of finite simple graphs in cases where only cut sets of the systems are known. The inverse problem means to build possible scenarios in underdetermined ...
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### Direct numerical solutions for first kind Volterra integral equations

For clearly deliver my purpose, I rewrite this question. Consider first kind Volterra integral equations $$\int_0^t k(t,s)f(s)ds=g(t) \quad 0\leq t\leq T$$ where $k(t,s)$ is continuous but not ...
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### Cartesian to Spherical coordinate conversion specific case when Φ is zero and θ is indeterminant

Following is the conversion for spherical to cartesian coordinate \begin{align} x &= r \cos\theta \sin\varphi \\ y &= r \sin\theta \sin\varphi \\ z &= r \cos\varphi \end{align} and we are ...
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### Can one hear the *material* of a drumhead?

"Can one hear the shape of a drum?" is a well known problem, originating from Kac, 1966, that questions whether an (idealized) drum head is completely specified by its spectrum. That is: is the ...
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### how can we solve this equation without mellin transform?

given the equation (functional equation) $$f(x)+f(2x)+f(3x)+.... =g(x)$$ we can use the Mobius tranform to obtain $$f(x)=\sum_{n=1}^{\infty}g(nx)\mu(n)$$ however, what can we do with the ...
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### Reference request: Inverse problem with stochastic error term

In many inverse problems there is an an error term resp. disturbance like $\|{y_\delta} - y \| \le \delta$ with noise level $\delta$, because only noisy data $y_\delta$ are known. Now I'm interested ...