Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  focus on the robust principal component analysis (RPCA) problem, and review a range of old and new convex formulations for the problem and its variants.  then review dual smoothing and level set techniques in convex optimization, present several novel theoretical results, and apply the techniques on the RPCA problem. In the final sections,  show a range of numerical experiments for simulated and real-world problems.
['Aleksandr Y. Aravkin', 'Stephen Becker']
I am writing a research paper on a idea Dual Smoothing and Level Set Techniques for Variational Matrix Decomposition
[{"from": "human", "value": "I am writing a research paper on a idea Dual Smoothing and Level Set Techniques for Variational Matrix Decomposition"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  focus on the robust principal component analysis (RPCA) problem, and review a range of old and new convex formulations for the problem and its variants.  then review dual smoothing and level set techniques in convex optimization, present several novel theoretical results, and apply the techniques on the RPCA problem. In the final sections,  show a range of numerical experiments for simulated and real-world problems."}]