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Dictionary learning for blind one bit compressed sensing

Zayyani, H ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1109/LSP.2015.2503804
  3. Publisher: Institute of Electrical and Electronics Engineers Inc
  4. Abstract:
  5. This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an unknown domain. In this context, the multiplication of measurement matrix A and sparse domain matrix φ, i.e., D = Aφ, should be learned. Hence, we use dictionary learning to train this matrix. Towards that end, an appropriate continuous convex cost function is suggested for one bit compressed sensing and a simple steepest-descent method is exploited to learn the rows of the matrix D. Experimental results show the effectiveness of the proposed algorithm against the case of no dictionary learning, specially with increasing the number of training signals and the number of sign measurements
  6. Keywords:
  7. One bit measurements ; Steepest-descent ; Compressed sensing ; Cost functions ; Matrix algebra ; Signal reconstruction ; Steepest descent method ; Convex cost function ; Dictionary learning ; Dictionary learning algorithms ; Measurement matrix ; One bit compressed sensing ; Original signal ; Random measurement ; Training signal ; Learning algorithms
  8. Source: IEEE Signal Processing Letters ; Volume 23, Issue 2 , 2016 , Pages 187-191 ; 10709908 (ISSN)
  9. URL: http://ieeexplore.ieee.org/document/7337377