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Removal of sparse noise from sparse signals

Zarmehi, N ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1016/j.sigpro.2019.01.002
  3. Publisher: Elsevier B.V , 2019
  4. Abstract:
  5. In this paper, we propose two methods for signal denoising where both signal and noise are sparse but in different domains. First, an optimization problem is proposed which is non-convex and NP-hard due to the existence of ℓ 0 norm in its cost function. Then, we propose two approaches to approximate and solve it. We also provide the proof of convergence for the proposed methods. The problem addressed in this paper arises in some applications for example in image denoising where the noise is sparse, signal reconstruction in the case of random sampling where the random mask is unknown, and error detection and error correction in the case of missing samples. The experimental results indicate that the proposed methods suitably achieve better performance than the state-of-the-art methods even with lower CPU-time. © 2019 Elsevier B.V
  6. Keywords:
  7. Alternating direction method of multipliers (ADMM) ; Image denoising ; Cost functions ; Error correction ; Alternating direction method of multiplier (ADMM) ; Different domains ; Optimization problems ; Random sampling ; Salt-and-pepper noise ; Sparse noise ; Sparse signals ; State-of-the-art methods ; Signal reconstruction
  8. Source: Signal Processing ; Volume 158 , 2019 , Pages 91-99 ; 01651684 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S016516841930009X