On the existence of the solution for one-dimensional discrete phase retrieval problem
Research output: Contribution to journal › Article › Scientific › peer-review
|Number of pages||8|
|Journal||Signal, Image and Video Processing|
|Publication status||Published - 2017|
|Publication type||A1 Journal article-refereed|
We consider the discrete form of the one-dimensional phase retrieval (1-D DPhR) problem from the point of view of input magnitude data. The direct method can provide a solution to the 1-D DPhR problem if certain conditions are satisfied by the input magnitude data, namely the corresponding trigonometric polynomial must be nonnegative. To test positivity of a trigonometric polynomial a novel DFT-based criterion is proposed. We use this DFT criterion for different sets of input magnitude data to evaluate whether the direct method applied to the 1-D DPhR problem leads to a solution in all explored cases.
- Discrete Fourier transform, Phase retrieval, Positive trigonometric polynomials, Signal reconstruction