RESTORING THE SIGNAL BY MODULES OF MEASUREMENT
- Authors: Novikov S.Y.1, Fedina M.E.2
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Affiliations:
- Department of Mathematical Statistics, Samara University, Samara, 443011, Russian Federation.
- Department of Security of Information Systems, Samara University, Samara, 443011, Russian Federation.
- Issue: Vol 22, No 3-4 (2016)
- Pages: 63-74
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/4258
- DOI: https://doi.org/10.18287/2541-7525-2016-22-3-4-63-74
- ID: 4258
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Abstract
The questions of the selection of vectors in finite-dimensional real and complex spaces so that the modules of scalar products of these vectors with the unknown vector were possible to restore it, are observed. Also, the injectivity of nonlinear mappings is studied.
About the authors
S. Y. Novikov
Department of Mathematical Statistics, Samara University, Samara, 443011, Russian Federation.
Author for correspondence.
Email: morenov.sv@ssau.ru
M. E. Fedina
Department of Security of Information Systems, Samara University, Samara, 443011, Russian Federation.
Email: morenov.sv@ssau.ru
References
- Balan R., Casazza P., Edidin D. On signal reconstruction without noizy phase. Applied and Computational Harmonic Analysis (ACHA). 2006. V. 20. I. 3. PP. 345–356.
- Bodmann B. G., Hammen N. Stable phase retrieval with low-redundancy frames.
- Bandeira A., Cahill J., Mixon D., Nelson A. Saving phase: Injectivity and stability for phase retrieval. Applied and Computational Harmonic Analysis (ACHA). 2014. V. 37. I. 1. PP. 106–125.
- Fickus M., Mixon D. G., Nelson A. A., Wang Ya. Phase retrieval from very few measurements. Linear Algebra and Its Applications. 2014. V. 449. PP. 475–499.
- Novikov I.Ya., Protasov V. Yu., Skopina M. A. Wavelet theory M.: Physmatlit, 2005.
- Novikov S. Ya., Likhobabenko M. A. Frames in finitedimensional spaces. Samara: Samara University, 2013.
- Alexeev B., Cahill J., Mixon D. Full spark frames. Journal of Fourier Analysis and Applications, 2012, V. 18, I. 6, pp. 1167–1194.
- Heinosaary T., Mazzarella I., Wolf M. M. Quantum tomography ...
- Horn R., Johnson Ch. Matrix Analysis. M.: Mir, 1989.
- Vogt A. Position and momentum distributions do not determine the quantum mechanical state. In: Mathematical Foundations of Quantum Theory (Marlow A. R.,ed.). Academic Press. New York, 1978, pp. 365–372.