Geodesic
Restoring the signal by modules of measurement
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3-4 (2016), pp. 63-74 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Keywords: space, systems of vectorsв, injectivity of mappings, scalar products.
Mots-clés : signal 
@article{VSGU_2016_3-4_a5,
     author = {S. Ya. Novikov and M. E. Fedina},
     title = {Restoring the signal by modules of measurement},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {63--74},
     year = {2016},
     number = {3-4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2016_3-4_a5/}
}
TY  - JOUR
AU  - S. Ya. Novikov
AU  - M. E. Fedina
TI  - Restoring the signal by modules of measurement
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2016
SP  - 63
EP  - 74
IS  - 3-4
UR  - http://geodesic.mathdoc.fr/item/VSGU_2016_3-4_a5/
LA  - ru
ID  - VSGU_2016_3-4_a5
ER  - 
%0 Journal Article
%A S. Ya. Novikov
%A M. E. Fedina
%T Restoring the signal by modules of measurement
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2016
%P 63-74
%N 3-4
%U http://geodesic.mathdoc.fr/item/VSGU_2016_3-4_a5/
%G ru
%F VSGU_2016_3-4_a5
S. Ya. Novikov; M. E. Fedina. Restoring the signal by modules of measurement. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3-4 (2016), pp. 63-74. http://geodesic.mathdoc.fr/item/VSGU_2016_3-4_a5/

[1] Balan R., Casazza P., Edidin D., “On signal reconstruction without noizy phase”, Applied and Computational Harmonic Analysis, 20:3 (2006), 345–356 | DOI | MR | Zbl

[2] Bodmann B. G., Hammen N., Stable phase retrieval with low-redundancy frames, arXiv: 1302.5487 | MR

[3] Bandeira A., Cahill J., Mixon D., Nelson A., “Saving phase: Injectivity and stability for phase retrieval”, Applied and Computational Harmonic Analysis, 37:1 (2014), 106–125 | DOI | MR | Zbl

[4] Fickus M., Mixon D. G., Nelson A. A., Wang Ya., “Phase retrieval from very few measurements”, Linear Algebra and Its Applications, 449 (2014), 475–499 | DOI | MR | Zbl

[5] Novikov I. Ya., Protasov V. Yu., Skopina M. A., Wavelet theory, Physmatlit, M., 2005

[6] Novikov S. Ya., Likhobabenko M. A., Frames in finite-dimensional spaces, Samara University, Samara, 2013

[7] Alexeev B., Cahill J., Mixon D., “Full spark frames”, Journal of Fourier Analysis and Applications, 18:6 (2012), 1167–1194 | DOI | MR | Zbl

[8] Heinosaary T., Mazzarella I., Wolf M. M., Quantum tomography, arXiv: 1206.1405

[9] Horn R., Johnson Ch., Matrix Analysis, Mir, M., 1989

[10] Vogt A., “Position and momentum distributions do not determine the quantum mechanical state”, Mathematical Foundations of Quantum Theory, ed. Marlow A. R., Academic Press, New York, 1978, 365–372 | DOI | MR