Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work  characterize all ambiguities of the linear (aperiodic) one-dimensional convolution on two fixed finite-dimensional complex vector spaces. It will be shown that the convolution ambiguities can be mapped one-to-one to factorization ambiguities in the $z-$domain, which are generated by swapping the zeros of the input signals.  use this polynomial description to show a deterministic version of a recently introduced masked Fourier phase retrieval design. In the noise-free case a (convex) semi-definite program can be used to recover exactly the input signals if they share no common factors (zeros). Then,  reformulate the problem as deterministic blind deconvolution with prior knowledge of the autocorrelations. Numerically simulations show that our approach is also robust against additive noise.
['Philipp Walk', 'Peter Jung', 'Götz E. Pfander', 'Babak Hassibi']
I am writing a research paper on a idea Blind Deconvolution with Additional Autocorrelations via Convex Programs
[{"from": "human", "value": "I am writing a research paper on a idea Blind Deconvolution with Additional Autocorrelations via Convex Programs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work  characterize all ambiguities of the linear (aperiodic) one-dimensional convolution on two fixed finite-dimensional complex vector spaces. It will be shown that the convolution ambiguities can be mapped one-to-one to factorization ambiguities in the $z-$domain, which are generated by swapping the zeros of the input signals.  use this polynomial description to show a deterministic version of a recently introduced masked Fourier phase retrieval design. In the noise-free case a (convex) semi-definite program can be used to recover exactly the input signals if they share no common factors (zeros). Then,  reformulate the problem as deterministic blind deconvolution with prior knowledge of the autocorrelations. Numerically simulations show that our approach is also robust against additive noise."}]