# Questions tagged [inverse-problems]

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 often ill-posed. Not to be confused with the (inverse) tag.

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### Approach to finding a function for a binary pattern

Below is a binary matrix of shape [64,63]. I want to find an equation to compute the values of this matrix as a function of rows and column indices. Are there any common strategies to attack such ...
38 views

### $L^2$ norm of inverse differential operator

This has come up in Lemma 1 of Mandache's 2001 paper on exponential instability for the inverse problem of the Schrodinger operator. Let $\Omega = B(0,1)$ in $\mathbb{R}^d$. Suppose $r_0\in (0,1)$ and ...
107 views

### Determine the structure of all finite sets $A$ of integers such that $|A| = k$ and $|2A| = 2k + 1$.

An exercise in Nathanson's text: Additive Number Theory, Inverse problems and the geometry of sumsets is the following (Excercise 16, P.No.37): Determine the structure of all finite sets $A$ of ...
8 views

### Condition inequality in perturbed LS

I have two matrices $A \in \mathcal{M}_{n,d}(\mathbb{R})$ and $B \in \mathcal{M}_{d,d}(\mathbb{R})$ with $B$ being symmetric definite-positive. I am trying to find a condition on $A$ for which I have ...
24 views

### Computing $L^2$ norm on a curved domain

I am currently working in a field related to elastography which tries to solve an inverse problem (of elasticity) similar to the one described below. Given a measured displacement field $u_{measured}$...
29 views

### References on parameter identification for ODE models from time-series data

Say I've got a system of ODEs, e.g. a generalized Lotka-Volterra system of the form: $$\dot x_i = x_i \left( r_i + \sum_{j=1}^n b_{ij} x_j \right),$$ where I've got $n$ ODEs and a total of $n^2 + n$ ...
34 views

### Given the distance between more than 3 points and no prerequisite for coordinate values, can the distance formula be reversed?

Very similar to this, but the accepted solution given only works for 3 points, not n. I have a filled-out logic grid of distances between 16 points and I would like to plot a plausible configuration ...
22 views

### Equivalence of two Riemannian metrics

So I have this problem on a course on geometric inverse problems. I am working in $\mathbb{R}^n$. I have the metrics $$g_1=c(r)^{-2} dr^2+(r/c(r))^2 d\theta^2$$ and $$g_2=a(r)^2dr^2+b(r)^2d\theta^2.$$ ...