13 problems

Let $f_i$ be more general discontinuous measurement functions, and consider uniform and nonuniform recovery error rates for structured signal recovery from nonlinear observations.…

Let $\mathcal{Q} \subseteq \mathbb{R}^n$ be a class of signals of interest, let $g_{\theta}:\mathbb{R}^p\to\mathbb{R}^n$ be a neural network parameterized by…

Let $S$ be a general variance matrix, and consider signal matrices whose singular vectors may be localized or delocalized. Delocalization necessity conjecture. Some amount of deloc…

Multi-reference alignment moment recovery conjecture. Suppose that the $q$-th moment of $y$ determines $x$ uniquely, possibly up to some intrinsic symmetries. Then $x$ is determine…

Random sampling conjecture. The orbit of a generic signal $x\in\mathbb{C}^N$ can be recovered from $O(N)$ random samples of its high-order spectra with high probability.

Let $K$ signals be represented through their averaged mean, power spectrum, and bispectrum, and let $G_{\Pi,L}x$ denote the orbit of the underlying signal under the parameterized s…

Let $F$ be a frame and $F_s$ a submatrix formed by selecting columns according to the sampling pattern in the analog coding problem. The objective is the expected trace of the inve…

Let $F$ be a frame, let $F_s$ denote the submatrix obtained by retaining a sampling pattern of its columns, and let the reconstruction error be measured in the analog coding setup…

Consider the perturbed Fourier compressed-sensing recovery problem studied in the source, whose signal and perturbation structure is exploited by the proposed algorithm. Measuremen…

Let Algorithm A1 be the proposed recovery algorithm for the perturbed Fourier compressed-sensing problem, and compare it with the standard compressed sensing, MMV, and GMMV approac…

Let Algorithm A1 estimate a signal $\boldsymbol{x}$ and parameters $\boldsymbol{\beta}$ from measurements in the structured perturbed Fourier compressed-sensing problem, where the…

Let $N$, $r$, and $n$ be positive integers. Let $\Omega_1,\Omega_2,\cdots,\Omega_n$ be $n$ subsets of $r$ elements chosen uniformly at random from $\{1,\cdots,N\}$. Define … for…

Proportional recoverable sparsity conjecture. For multidimensional signals, when the number of measurements is proportional to $N^d$, the recoverable sparsity of the gradient suppo…