Norm minimized Scattering Data from Intensity Spectra
A. Seel, A. Davtyan, U. Pietsch, O. Loffeld
TL;DR
This paper introduces a method using $l_1$ minimization in compressive sensing to reconstruct scattering data from intensity spectra, specifically applying a Kalman filter approach to coherent X-ray scattering.
Contribution
It develops a novel quadratic compressive sensing framework with a Kalman filter for reconstructing scattering data from intensity measurements.
Findings
Successful reconstruction of scattering data from intensity spectra
Extension of $l_1$ minimization to non-linear quadratic observations
Application to coherent X-ray scattering data
Abstract
We apply the minimizing technique of compressive sensing (CS) to non-linear quadratic observations. For the example of coherent X-ray scattering we provide the formulae for a Kalman filter approach to quadratic CS and show how to reconstruct the scattering data from their spatial intensity distribution.
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Taxonomy
TopicsMedical Imaging Techniques and Applications · Numerical methods in inverse problems · Microwave Imaging and Scattering Analysis