In this paper we address the question of the traps (local minima, quasi °at regions, and saddle points with null gradient) in phase recovery method based on the minimization of a quartic functional. In particular, we focus on the key role played by the ratio between the "essential dimension of data" Mind and the number of real unknowns Nr and we illustrate how it impacts on the presence of traps in the functional to be minimized. First, we show that such functional flattens when the essential dimension of data increases; and later, with reference to two different unknown sequences, we find the minimum value of the essential dimension of data Mind such that no traps exist in the functional. In this condition, the recovery of the solution is ensured independently of the initial guess that can be chosen completely at random.
The "traps" issue in a non-linear inverse problem: the phase retrieval in circular case
R. Moretta
;R. Pierri
2019
Abstract
In this paper we address the question of the traps (local minima, quasi °at regions, and saddle points with null gradient) in phase recovery method based on the minimization of a quartic functional. In particular, we focus on the key role played by the ratio between the "essential dimension of data" Mind and the number of real unknowns Nr and we illustrate how it impacts on the presence of traps in the functional to be minimized. First, we show that such functional flattens when the essential dimension of data increases; and later, with reference to two different unknown sequences, we find the minimum value of the essential dimension of data Mind such that no traps exist in the functional. In this condition, the recovery of the solution is ensured independently of the initial guess that can be chosen completely at random.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
