Reconstruction of signals from magnitudes of redundant representations: The complex case
R Balan - Foundations of Computational Mathematics, 2016 - Springer
Foundations of Computational Mathematics, 2016•Springer
This paper is concerned with the question of reconstructing a vector in a finite-dimensional
complex Hilbert space when only the magnitudes of the coefficients of the vector under a
redundant linear map are known. We present new invertibility results as well as an iterative
algorithm that finds the least-square solution, which is robust in the presence of noise. We
analyze its numerical performance by comparing it to the Cramer–Rao lower bound.
complex Hilbert space when only the magnitudes of the coefficients of the vector under a
redundant linear map are known. We present new invertibility results as well as an iterative
algorithm that finds the least-square solution, which is robust in the presence of noise. We
analyze its numerical performance by comparing it to the Cramer–Rao lower bound.
Abstract
This paper is concerned with the question of reconstructing a vector in a finite-dimensional complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new invertibility results as well as an iterative algorithm that finds the least-square solution, which is robust in the presence of noise. We analyze its numerical performance by comparing it to the Cramer–Rao lower bound.
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