# 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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### Can a bijection between function spaces be continuous if the space's domains are different?

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### A right-inverse property of a regression problem

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### Strategies to make the sum operation bijective in a contribution problem

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### Kernel of Radon transform in $\mathbb{R}^3$

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### Volterra equation of the first kind with an exponential kernel

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### An explicit reconstruction of a matrix from its minors

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### Which matrices can be realized as the Dirichlet-to-Neumann map for a given domain?

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### Reconstructing the Green's function of an initial-value problem of partial differential equation

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### How to numerically invert a bilateral (two-sided) Laplace transform?

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### Reference Request - Recovering a function from its definite integrals (inverse problem)

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### When does the gradient of a solution to elliptic equation vanish on the boundary?

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### inverse interpolation

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### Is there an English translation of Hadamard's classic French paper on well-posed problems?

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### Is $\delta(df \wedge df)=0$ an Euler-Lagrange equation?

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### Solution of Poisson equation vanishing at the boundary of any order

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### On the Integration and Manipulation of Expressions Involving Hypergeometric Functions

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### Is this result on an unconstrained inverse quadratic programming problem new or known already?

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### Approximating Uniform Distribution with Mixture of Gaussians

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### A question in inverse Galois Theory

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### How to find Suleimanova's work on the Nonnegative Inverse Eigenvalue Problem?

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### Are inverse eigenvalue problems (IEPs) hopeless and not a fruitful area of research?

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### Question related to Galois covering of Projective line over rational numbers

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### The jump set of $SBV$ function for different value of parameter in image denoising problem

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### Recent observation of gravitational waves

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### Spectra of certain totally positive matrices

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### Question on Inverse Galois Theory

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### Can one hear the shape of a drum for operators?

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### Under what hypothesis on the domain is the X-ray transform/John transform operator bounded?

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### Radon transform between affine grassmannians

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### Combining microlocal Helgason's support and Holmgren's theorem to prove injectivity of limited-angle Radon transform

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### Injectivity of the Funk transform for nonsmooth functions

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### What's that shape? Inferring a 3D shape from random shadows

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### Counting variables to look for invariances/range conditions

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### An unusual metric reconstruction problem

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### Certain inverse problem related to moments

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### Fredholm integral with functions constrained to [0;1]

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### Applications of Freiman's theorem?

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### How to check if a manifold can be foliated by strictly convex hypersurfaces?

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### Sample based inversion of the Radon transform

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### Uniquenss of domain with given interior newtonian potential

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### A integral equation with Discrete to result by inverse problem

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### Do position and momentum measurements determine a wave function?

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### General Radon-type inverse problem

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### Invertibility of an inverse problem

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### Geodesics in finite groups

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### Solving for a set of points from projections

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### Solving a functional equation

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### Inverse problem with a rank-1 update

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### Reconstructing set of points from one-dimensional images

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