Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The problem has found applications in computer vision, computer graphics, and sensor network localization, among others. Its least squares solution can be approximated by either spectral relaxation or semidefinite programming follod by a rounding procedure, analogous to the approximation algorithms of MAX-CUT. The contribution of this paper is three-fold: First,  introduce a robust penalty function involving the sum of unsquared deviations and derive a relaxation that leads to a convex optimization problem; Second,  apply the alternating direction method to minimize the penalty function; Finally, under a specific model of the measurement noise and for both complete and random measurement graphs,  prove that the rotations are exactly and stably recovered, exhibiting a phase transition behavior in terms of the proportion of noisy measurements. Numerical simulations confirm the phase transition behavior for our method as ll as its improved accuracy compared to existing methods.
['Lanhui Wang', 'Amit Singer']
I am writing a research paper on a idea Exact and Stable Recovery of Rotations for Robust Synchronization
[{"from": "human", "value": "I am writing a research paper on a idea Exact and Stable Recovery of Rotations for Robust Synchronization"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The problem has found applications in computer vision, computer graphics, and sensor network localization, among others. Its least squares solution can be approximated by either spectral relaxation or semidefinite programming follod by a rounding procedure, analogous to the approximation algorithms of MAX-CUT. The contribution of this paper is three-fold: First,  introduce a robust penalty function involving the sum of unsquared deviations and derive a relaxation that leads to a convex optimization problem; Second,  apply the alternating direction method to minimize the penalty function; Finally, under a specific model of the measurement noise and for both complete and random measurement graphs,  prove that the rotations are exactly and stably recovered, exhibiting a phase transition behavior in terms of the proportion of noisy measurements. Numerical simulations confirm the phase transition behavior for our method as ll as its improved accuracy compared to existing methods."}]