Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a novel algorithm — ProSparse Denoise — that can solve the sparsity recovery problem in the presence of noise when the dictionary is the union of Fourier and identity matrices. The algorithm is based on a proper use of Cadzow routine and Prony's method and exploits the duality of Fourier and identity matrices. The algorithm has low complexity compared to state of the art algorithms for sparse recovery since it relies on the Fast Fourier Transform (FFT) algorithm.  provide conditions on the noise that guarantees the correct recovery of the sparsity pattern. Our approach outperforms state of the art algorithms such as Basis Pursuit De-noise and Subspace Pursuit when the dictionary is the union of Fourier and identity matrices.
['Jon Onativia', 'Yue Lu', 'Pier Luigi Dragotti']
I am writing a research paper on a idea Prosparse denoise: Prony's based sparse pattern recovery in the presence of noise
[{"from": "human", "value": "I am writing a research paper on a idea Prosparse denoise: Prony's based sparse pattern recovery in the presence of noise"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a novel algorithm \u2014 ProSparse Denoise \u2014 that can solve the sparsity recovery problem in the presence of noise when the dictionary is the union of Fourier and identity matrices. The algorithm is based on a proper use of Cadzow routine and Prony's method and exploits the duality of Fourier and identity matrices. The algorithm has low complexity compared to state of the art algorithms for sparse recovery since it relies on the Fast Fourier Transform (FFT) algorithm.  provide conditions on the noise that guarantees the correct recovery of the sparsity pattern. Our approach outperforms state of the art algorithms such as Basis Pursuit De-noise and Subspace Pursuit when the dictionary is the union of Fourier and identity matrices."}]