Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The theory of compressed sensing shows that samples in the form of random projections are optimal for recovering sparse signals in high-dimensional spaces (i.e., finding needles in haystacks), provided the measurements are noiseless. Hover, noise is almost always present in applications, and compressed sensing suffers from it. The signal to noise ratio per dimension using random projections is very poor, since sensing energy is equally distributed over all dimensions. Consequently, the ability of compressed sensing to locate sparse components degrades significantly as noise increases. It is possible, in principle, to improve performance by "shaping" the projections to focus sensing energy in proper dimensions. The main question addressed here is, can projections be adaptively shaped to achieve this focusing effect? The ansr is yes, and  demonstrate a simple, computationally efficient procedure that does so.
['Rui M. Castro', 'J. Haupt', 'Robert D. Nowak', 'Gil Raz']
I am writing a research paper on a idea Finding needles in noisy haystacks
[{"from": "human", "value": "I am writing a research paper on a idea Finding needles in noisy haystacks"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The theory of compressed sensing shows that samples in the form of random projections are optimal for recovering sparse signals in high-dimensional spaces (i.e., finding needles in haystacks), provided the measurements are noiseless. Hover, noise is almost always present in applications, and compressed sensing suffers from it. The signal to noise ratio per dimension using random projections is very poor, since sensing energy is equally distributed over all dimensions. Consequently, the ability of compressed sensing to locate sparse components degrades significantly as noise increases. It is possible, in principle, to improve performance by \"shaping\" the projections to focus sensing energy in proper dimensions. The main question addressed here is, can projections be adaptively shaped to achieve this focusing effect? The ansr is yes, and  demonstrate a simple, computationally efficient procedure that does so."}]