Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Recovering sparse vectors and low-rank matrices from noisy linear measurements has been the focus of much recent research. Various reconstruction algorithms have been studied, including l 1  and nuclear norm minimization as ll as l p  minimization with p &#60; 1. These algorithms are known to succeed if certain conditions on the measurement map are satisfied. Proofs for the recovery of matrices have so far been much more involved than in the vector case. ,  show how several classes of recovery conditions can be extended from vectors to matrices in a simple and transparent way, leading to the best known restricted isometry and nullspace conditions for matrix recovery. Our results rely on the ability to “vectorize” matrices through the use of a key singular value inequality.
['Samet Oymak', 'Karthik Mohan', 'Maryam Fazel', 'Babak Hassibi']
I am writing a research paper on a idea A simplified approach to recovery conditions for low rank matrices
[{"from": "human", "value": "I am writing a research paper on a idea A simplified approach to recovery conditions for low rank matrices"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Recovering sparse vectors and low-rank matrices from noisy linear measurements has been the focus of much recent research. Various reconstruction algorithms have been studied, including l 1  and nuclear norm minimization as ll as l p  minimization with p &#60; 1. These algorithms are known to succeed if certain conditions on the measurement map are satisfied. Proofs for the recovery of matrices have so far been much more involved than in the vector case. ,  show how several classes of recovery conditions can be extended from vectors to matrices in a simple and transparent way, leading to the best known restricted isometry and nullspace conditions for matrix recovery. Our results rely on the ability to \u201cvectorize\u201d matrices through the use of a key singular value inequality."}]