相关论文: The Condition Number in Phase Retrieval from Inten…
In this paper, we primarily focus on analyzing the stability property of phase retrieval by examining the bi-Lipschitz property of the map $\Phi_{\boldsymbol{A}}(\boldsymbol{x})=|\boldsymbol{A}\boldsymbol{x}|\in \mathbb{R}_+^m$, where…
The problem of phase retrieval is to determine a signal $f\in \mathcal{H}$, with $\mathcal{H}$ a Hilbert space, from intensity measurements $|F(\omega)|$, where $F(\omega):=\langle f , \varphi_\omega\rangle$ are measurements of $f$ with…
The aim of this paper is to study the stability of the $\ell_1$ minimization for the compressive phase retrieval and to extend the instance-optimality in compressed sensing to the real phase retrieval setting. We first show that the…
The classical phase retrieval problem arises in contexts ranging from speech recognition to x-ray crystallography and quantum state tomography. The generalization to matrix frames is natural in the sense that it corresponds to quantum…
In this paper we prove two results regarding reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem"). First we show that phase retrievability as an algebraic property implies that nonlinear maps are…
A frame $(x_j)_{j\in J}$ for a Hilbert space $H$ is said to do phase retrieval if for all distinct vectors $x,y\in H$ the magnitude of the frame coefficients $(|\langle x, x_j\rangle|)_{j\in J}$ and $(|\langle y, x_j\rangle|)_{j\in J}$…
Phase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in the deterministic setting phase retrieval from frame…
Let $(\Omega,\Sigma,\mu)$ be a measure space, and $1\leq p\leq \infty$. A subspace $E\subseteq L_p(\mu)$ is said to do stable phase retrieval (SPR) if there exists a constant $C\geq 1$ such that for any $f,g\in E$ we have $$…
Recent advances in convex optimization have led to new strides in the phase retrieval problem over finite-dimensional vector spaces. However, certain fundamental questions remain: What sorts of measurement vectors uniquely determine every…
Phase retrieval is concerned with recovering a function $f$ from the absolute value of its Fourier transform $|\widehat{f}|$. We study the stability properties of this problem in Lebesgue spaces. Our main results shows that $$ \|…
A frame $(x_j)_{j\in J}$ for a Hilbert space $H$ is said to do phase retrieval if for all distinct vectors $x,y\in H$ the magnitude of the frame coefficients $(|\langle x, x_j\rangle|)_{j\in J}$ and $(|\langle y, x_j\rangle|)_{j\in J}$…
In this paper, we focus on low-rank phase retrieval, which aims to reconstruct a matrix $\mathbf{X}_0\in \mathbb{R}^{n\times m}$ with ${\mathrm{ rank}}(\mathbf{X}_0)\le r$ from noise-corrupted amplitude measurements…
We consider the one-dimensional Schroedinger equation on a ring, with the cubic term, of either self-attractive or repulsive sign, confined to a narrow segment. This setting can be realized in optics and Bose-Einstein condensates. For the…
In this paper, we consider the phase retrieval problem in which one aims to recover a signal from the magnitudes of affine measurements. Let $\{{\mathbf a}_j\}_{j=1}^m \subset {\mathbb H}^d$ and ${\mathbf b}=(b_1, \ldots,…
The stability of an approximating sequence $(A_n)$ for an operator $A$ usually requires, besides invertibility of $A$, the invertibility of further operators, say $B, C, \dots$, that are well-associated to the sequence $(A_n)$. We study…
In this short note, we consider the worst case noise robustness of any phase retrieval algorithm which aims to reconstruct all nonvanishing vectors $\mathbf{x} \in \mathbb{C}^d$ (up to a single global phase multiple) from the magnitudes of…
Recent results in the literature provide computational evidence that stabilized semi-implicit time-stepping method can efficiently simulate phase field problems involving fourth-order nonlinear dif- fusion, with typical examples like the…
The aim of noisy phase retrieval is to estimate a signal $\mathbf{x}_0\in \mathbb{C}^d$ from $m$ noisy intensity measurements $b_j=\left\lvert \langle \mathbf{a}_j,\mathbf{x}_0 \rangle \right\rvert^2+\eta_j, \; j=1,\ldots,m$, where…
We derive bounds for the minimum and maximum eigenvalues and the spectral condition number of matrices for isogeometric discretizations of elliptic partial differential equations in an open, bounded, simply connected Lipschitz domain…
We study information theoretic limits of recovering an unknown $n$ dimensional, complex signal vector $\mathbf{x}_\star$ with unit norm from $m$ magnitude-only measurements of the form $y_i = |(\mathbf{A} \mathbf{x}_\star)_i|^2, \; i = 1,2…