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L0soft: ℓ0 minimization via soft thresholding

Sadeghi, M ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.23919/EUSIPCO.2019.8903024
  3. Publisher: European Signal Processing Conference, EUSIPCO , 2019
  4. Abstract:
  5. We propose a new algorithm for finding sparse solution of a linear system of equations using `0 minimization. The proposed algorithm relies on approximating the non-smooth `0 (pseudo) norm with a differentiable function. Unlike other approaches, we utilize a particular definition of `0 norm which states that the `0 norm of a vector can be computed as the `1 norm of its sign vector. Then, using a smooth approximation of the sign function, the problem is converted to `1 minimization. This problem is solved via iterative proximal algorithms. Our simulations on both synthetic and real data demonstrate the promising performance of the proposed scheme. © 2019 IEEE
  6. Keywords:
  7. Compressed sensing ; Iterative hard thresholding ; Iterative soft thresholding ; Proximal algorithms ; Iterative methods ; Linear systems ; Differentiable functions ; Linear system of equations ; Proximal algorithm ; Smooth approximation ; Soft thresholding ; Sparse representation ; Synthetic and real data ; Signal processing
  8. Source: 27th European Signal Processing Conference, EUSIPCO 2019, 2 September 2019 through 6 September 2019 ; Volume 2019-September , 2019 ; 22195491 (ISSN); 9789082797039 (ISBN)
  9. URL: https://ieeexplore.ieee.org/document/8903024