Year: 2016
Type: article
Abstract: Whenever we use devices to take measurements, calibration is indispensable. While\n the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be\n quite difficult, expensive and sometimes even impossible to implement. We study a\n challenging problem called self-calibration, i.e., the task of designing an algorithm for\n devices so that the algorithm is able to perform calibration automatically. More precisely,\n we consider the setup $\\boldsymbol{y} = \\mathcal{A}(\\boldsymbol{d}) \\boldsymbol{x} +\n \\boldsymbol{\\epsilon}$ where only partial information about the sensing matrix\n $\\mathcal{A}(\\boldsymbol{d})$ is known and where $\\mathcal{A}(\\boldsymbol{d})$ linearly\n depends on $\\boldsymbol{d}$. The goal is to estimate the calibration parameter\n $\\boldsymbol{d}$ (resolve the uncertainty in the sensing process) and the signal/object of\n interests $\\boldsymbol{x}$ simultaneously. For three different models of practical\n relevance we show how such a bilinear inverse problem, including blind deconvolution as an\n important example, can be solved via a simple linear least squares approach. As a\n consequence, the proposed algorithms are numerically extremely efficient, thus allowing for\n real-time deployment. Explicit theoretical guarantees and stability theory are derived and\n the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications\n in imaging sciences and signal processing are discussed and numerical simulations are\n presented to demonstrate the effectiveness and efficiency of our approach.
Authors: Shuyang Ling, Thomas Strohmer
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2575581645