Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Though the method of least squares has been used for a long time in solving signal processing problems, in the recent field of sparse recovery from compressed measurements, this method has not been given much attention.   show that a method in the least squares family, known in the literature as Orthogonal Least Squares (OLS), adapted for compressed recovery problems, has competitive recovery performance and computation complexity, that makes it a suitable alternative to popular greedy methods like Orthogonal Matching Pursuit (OMP).  show that with a slight modification, OLS can exactly recover a $K$-sparse signal, embedded in an $N$ dimensional space ($K<<N$) in $M=\mathcal{O}(K\log (N/K))$ no of measurements with Gaussian dictionaries.  also show that OLS can be easily implemented in such a way that it requires $\mathcal{O}(KMN)$ no of floating point operations similar to that of OMP.  performance of OLS is also studied with sensing matrices with correlated dictionary, in which algorithms like OMP does not exhibit good recovery performance.  study the recovery performance of OLS in a specific dictionary called \emph{generalized hybrid dictionary}, which is shown to be a correlated dictionary, and show numerically that OLS has is far superior to OMP in these kind of dictionaries in terms of recovery performance. Finally  provide analytical justifications that corroborate the findings in the numerical illustrations.
['Samrat Mukhopadhyay', 'Prateek Vashishtha and', 'Mrityunjoy Chakraborty']
I am writing a research paper on a idea Signal Recovery in Uncorrelated and Correlated Dictionaries Using Orthogonal Least Squares
[{"from": "human", "value": "I am writing a research paper on a idea Signal Recovery in Uncorrelated and Correlated Dictionaries Using Orthogonal Least Squares"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Though the method of least squares has been used for a long time in solving signal processing problems, in the recent field of sparse recovery from compressed measurements, this method has not been given much attention.   show that a method in the least squares family, known in the literature as Orthogonal Least Squares (OLS), adapted for compressed recovery problems, has competitive recovery performance and computation complexity, that makes it a suitable alternative to popular greedy methods like Orthogonal Matching Pursuit (OMP).  show that with a slight modification, OLS can exactly recover a $K$-sparse signal, embedded in an $N$ dimensional space ($K<<N$) in $M=\\mathcal{O}(K\\log (N/K))$ no of measurements with Gaussian dictionaries.  also show that OLS can be easily implemented in such a way that it requires $\\mathcal{O}(KMN)$ no of floating point operations similar to that of OMP.  performance of OLS is also studied with sensing matrices with correlated dictionary, in which algorithms like OMP does not exhibit good recovery performance.  study the recovery performance of OLS in a specific dictionary called \\emph{generalized hybrid dictionary}, which is shown to be a correlated dictionary, and show numerically that OLS has is far superior to OMP in these kind of dictionaries in terms of recovery performance. Finally  provide analytical justifications that corroborate the findings in the numerical illustrations."}]