IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
Some optimal design problems for nite frames
Autor/es:
PEDRO MASSEY; MARIANO RUIZ; DEMETRIO STOJANOFF
Lugar:
Nashville
Reunión:
Congreso; 5th International Conference on Computational Harmonic Analysis; 2014
Institución organizadora:
Vanderbilt University
Resumen:
In this talk we will consider the following two optimal design problems innite frame theory:- Given a redundant frame F={f_i}_{i=1}^n in C^d, we compute the spectral and geometrical structure of minimizers of the frame potential among the dual frames G={g_i}_{i=1}^n for F such that \sum_{i=1}^n || g_i||^2 \geq t and || T_{F#} - T_G||\leq \epsilon, where T_G denotes the synthesis operator of G and F# denotes the canonicaldual of F.- Given a frame F={f_i}_{i=1}^n in C^d, we compute the spectral and geometrical structure of the minimizers of the frame potential among all coherent perturbations VF={V f_i}_{i=1}^n where V is any invertible operator V such that ||V^*V - I||\leq \delta and det(V^*V)\geq s.The motivation of these problems is the search of numerical stable encoding-decoding schemes based on (perturbations) of F. Our approach relies in LidskiiĀ“s type inequalities (both additive and multiplicative) from matrix analysis theory.It turns out that the matrix models behind these two (seemingly unrelated) problems are intimately connected.