9 problems

Let $\Omega\subset\mathbb{R}^3$ be a compact domain, and let $\epsilon\in C^2(\mathcal{S}^2,\Omega)$ be an elastic strain field in an isotropic medium that satisfies equilibrium an…

Rubin's range characterization conjecture. A function $g\in C_c^\infty(\mathbb{S}^{n-1}\times(0,2))$ belongs to the range of the operator $f\mapsto\mathcal{M}f$ if and only if

The Shepp–Logan phantom is a standard test image for tomographic algorithms. A GQNN can represent it exactly with 10 coefficients, whereas an ALNN and a DNN are the neural-network…

Higher-order Compton scattering smoothing conjecture. For each scattering order $i$, $g_i$ is approximated by a Fourier integral operator $\mathcal{L}_i(\cdot,n_e)$ of order

Alaifari–Pierce–Steinerberger conjecture. In this lower bound, $\left\|f'\right\|_{L^2(I)}$ may be replaced by $\left\|f'\right\|_{L^1(I)}$.

The experiments compare TV-based and shearlet-plus-TV regularization for region-of-interest tomography, using a phantom whose features are piecewise constant. The observed superior…

Let $R$ be the model matrix, let $R^\dagger$ denote its minimum-norm pseudoinverse, let $\mathbf{g}$ be the measured data, and let $C_\beta$ be the smoothing operator associated wi…

Fix a domain, grid, obstacle, signal wave carrier, and function $f$ to be reconstructed. Let $L$ range over sets of broken and unbroken rays in the domain, where each ray is determ…

The broken-ray transform, also called the V-line transform, maps information about a medium to measurements along rays that may change direction at specified points. Its inversion…