9 problems

Sparse approximation conjecture. The sparse approximation result in Theorem $\mathrm{th:main}$ is also valid for the class of cartoon-like videos $\mathcal{G}^2(Z)$.

Extension conjecture. The algorithm can be readily extended to deal with significantly more general problems, either by appropriately extending its associated theory or by adjustin…

Condensed-subspace conjecture. A solution exists on a “condensed” subspace that can achieve similar approximation performance, and the optimization problem can therefore be reformu…

Let cylindrical cartoon-like images be the class of 4-dimensional images considered in the paper, and let $N$ denote the number of terms retained in an approximation. Optimality co…

Let $u_1,\ldots,u_n\in S^{d-1}$ be unit vectors for which there exist positive numbers $\alpha_1,\ldots,\alpha_n$ satisfying … where $I_d$ is the identity operator on…

Restricted-isometry conjecture. If $A$ has restricted 2-isometry property of order $tk$ with

The parametric partial differential equation and ordinary differential equation problems under consideration produce errors in numerical solver output, and the resulting error-vers…

Let $I_Z=\mathbb{R}^d$ have Gaussian weight … where $c$ is a normalizing constant. Sampling is prescribed according to the density … where $C$ is a normalization constant. Weighted…

Sparse-coding conjecture. Sensory systems may encode stimuli via sparse approximation. This conjecture connects probabilistic accounts of perception with the theoretical benefits o…