Information and resolution

• Published in: Conference record - Asilomar Conference on Signals, Systems, & Computers pp. 313 - 317
• Main Author: Fannjiang, Albert
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.10.2017
• Subjects: Filtering theory; Image reconstruction; Image resolution; Integrated circuits; Measurement uncertainty; Multiple signal classification; null vector; one-bit intensity measurement; optimal weighting; Resolution length; Signal resolution; spectral vector
• ISSN: 2576-2303
• DOI: 10.1109/ACSSC.2017.8335191

The issue of resolution with complex-field measurement is first reviewed with emphasis on superresolution, discrete versus continuous measurement, and full versus compressive measurement. The main focus of the paper is on the other extreme: one-bit intensity measurement which collects the least amount of information from each sensor by proper thresholding. Reconstruction from one-bit intensity measurement is related to reconstruction from zero-crossings and is much harder than reconstruction from complex-field measurement. The proposed method, dubbed the null vector, is a linearization of phase retrieval and takes the form of a quadratic optimization with a row submatrix subject to an ellipsoidal constraint. The null vector differs from the spectral vector in two ways: (i) the former uses an ellipsoidal constraint while the latter uses the spheroidal constraint; (ii) the former uses binary, threshold-crossing information while the latter uses the intensity information to weight the quadratic optimization (i.e. row submatrix versus weighted matrix). Both contribute to the superior performance of the null vector. Further, the question of optimal weighting is explored to improve the performance of the null vector.