6 problems

Let $f$ have $d$ continuous derivatives on each interval between its jump discontinuities, and suppose its Fourier data are used in Eckhoff's algebraic reconstruction method. Let…

Algebraic reconstruction conjecture. There is a nonlinear algebraic procedure reconstructing any such signal from its first $N$ Fourier coefficients with overall accuracy of order

Reconstruction conjecture. For each $n>2N+1$, the points $x_i$ and the values of $f$ between the points $x_i$ can be reconstructed from the first $n$ Fourier coefficients of $f$ wi…

Let $A_1,\dots,A_G\in\mathbb{R}^{m\times n}$ be measurement operators whose entries are independently and identically distributed according to a standard Gaussian distribution. Let…

The signals take values in a finite alphabet such as $\mathcal{X}_2=\{0,1\}$, $\mathcal{X}_3=\{-1,0,1\}$, or $\mathcal{X}_5=\{-2,-1,0,1,2\}$, and the proposed reconstruction method…

In an $N$-dimensional complex vector space, intensity measurements are measurements of the squared magnitudes of inner products with chosen measurement vectors, and signal recovery…