{
  "id": "1904.01821",
  "version": "v1",
  "published": "2019-04-03T07:55:22.000Z",
  "updated": "2019-04-03T07:55:22.000Z",
  "title": "Fourier Phase Retrieval with Extended Support Estimation via Deep Neural Network",
  "authors": [
    "Kyung-Su Kim",
    "Sae-Young Chung"
  ],
  "categories": [
    "stat.ML",
    "cs.LG"
  ],
  "abstract": "We consider the problem of sparse phase retrieval from Fourier transform magnitudes to recover $k$-sparse signal vector $x^{\\circ}$ and its support $\\mathcal{T}$. To improve the reconstruction performance of $x^{\\circ}$, we exploit extended support estimate $\\mathcal{E}$ of size larger than $k$ satisfying $\\mathcal{E} \\supseteq \\mathcal{T}$. We propose a learning method for the deep neural network to provide $\\mathcal{E}$ as an union of equivalent solutions of $\\mathcal{T}$ by utilizing modulo Fourier invariances and suggest a searching technique for $\\mathcal{T}$ by iteratively sampling $\\mathcal{E}$ from the trained network output and applying the hard thresholding to $\\mathcal{E}$. Numerical results show that our proposed scheme has a superior performance with a lower complexity compared to the local search-based greedy sparse phase retrieval method and a state-of-the-art variant of the Fienup method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-03T07:55:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deep neural network",
      "fourier phase retrieval",
      "extended support estimation",
      "search-based greedy sparse phase",
      "greedy sparse phase retrieval method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}