Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the problem of estimating a low-rank positive semidefinite (PSD) matrix from a set of rank-one measurements using sensing vectors composed of i.i.d. standard Gaussian entries, which are possibly corrupted by arbitrary outliers. This problem arises from applications, such as phase retrieval, covariance sketching, quantum space tomography, and por spectrum estimation.  first propose a convex optimization algorithm that seeks the PSD matrix with the minimum   $\ell _1$  -norm of the observation residual. The advantage of our algorithm is that it is free of parameters, therefore, eliminating the need for tuning parameters and allowing easy implementations.  establish that with high probability, a low-rank PSD matrix can be exactly recovered as soon as the number of measurements is large enough, even when a fraction of the measurements are corrupted by outliers with arbitrary magnitudes. Moreover, the recovery is also stable against bounded noise. With the additional information of an upper bound of the rank of the PSD matrix,  propose another nonconvex algorithm based on subgradient descent that demonstrates excellent empirical performance in terms of computational efficiency and accuracy.
['Yuanxin Li', 'Yue Sun', 'Yuejie Chi']
I am writing a research paper on a idea Low-Rank Positive Semidefinite Matrix Recovery From Corrupted Rank-One Measurements
[{"from": "human", "value": "I am writing a research paper on a idea Low-Rank Positive Semidefinite Matrix Recovery From Corrupted Rank-One Measurements"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the problem of estimating a low-rank positive semidefinite (PSD) matrix from a set of rank-one measurements using sensing vectors composed of i.i.d. standard Gaussian entries, which are possibly corrupted by arbitrary outliers. This problem arises from applications, such as phase retrieval, covariance sketching, quantum space tomography, and por spectrum estimation.  first propose a convex optimization algorithm that seeks the PSD matrix with the minimum   $\\ell _1$  -norm of the observation residual. The advantage of our algorithm is that it is free of parameters, therefore, eliminating the need for tuning parameters and allowing easy implementations.  establish that with high probability, a low-rank PSD matrix can be exactly recovered as soon as the number of measurements is large enough, even when a fraction of the measurements are corrupted by outliers with arbitrary magnitudes. Moreover, the recovery is also stable against bounded noise. With the additional information of an upper bound of the rank of the PSD matrix,  propose another nonconvex algorithm based on subgradient descent that demonstrates excellent empirical performance in terms of computational efficiency and accuracy."}]