Convex recovery from interferometric measurements

Abstract

This note formulates a deterministic recovery result for vectors $x$ from quadratic measurements of the form $(Ax{)}_i\overline{(Ax{)}_j}$ for some left-invertible $A$. Recovery is exact, or stable in the noisy case, when the couples $(i,j)$ are chosen as edges of a well-connected graph. One possible way of obtaining the solution is as a feasible point of a simple semidefinite program. Furthermore, we show how the proportionality constant in the error estimate depends on the spectral gap of a data-weighted graph Laplacian. Such quadratic measurements have found applications in phase retrieval, angular synchronization, and more recently interferometric waveform inversion.

References in corpus (2)

• Matrix estimation by Universal Singular Value Thresholding
• Measurements and Kernels for Source-Structure Inversions in Noise Tomography

Cited by in corpus (13)

• Compressive Phase Retrieval via Generalized Approximate Message Passing
• Tightness of the maximum likelihood semidefinite relaxation for angular synchronization
• A Riemannian low-rank method for optimization over semidefinite matrices with block-diagonal constraints
• Undersampled Phase Retrieval with Outliers
• Exact Imaging of Extended Targets Using Multistatic Interferometric Measurements
• A Generalization of Wirtinger Flow for Exact Interferometric Inversion
• Focused blind deconvolution
• Approximating the Little Grothendieck Problem over the Orthogonal and Unitary Groups
• Exact and Stable Recovery of Rotations for Robust Synchronization
• Reconstructing Video from Interferometric Measurements of Time-Varying Sources
• Stable rank one matrix completion is solved by two rounds of semidefinite programming relaxation
• Performance Analysis of Convex LRMR based Passive SAR Imaging
• Dictionary Learning Phase Retrieval from Noisy Diffraction Patterns