A fast and accurate algorithm for ℓ 1 minimization problems in compressive sampling

Feishe Chen, Lixin Shen, Bruce W. Suter, Yuesheng Xu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


An accurate and efficient algorithm for solving the constrained ℓ1-norm minimization problem is highly needed and is crucial for the success of sparse signal recovery in compressive sampling. We tackle the constrained ℓ1-norm minimization problem by reformulating it via an indicator function which describes the constraints. The resulting model is solved efficiently and accurately by using an elegant proximity operator-based algorithm. Numerical experiments show that the proposed algorithm performs well for sparse signals with magnitudes over a high dynamic range. Furthermore, it performs significantly better than the well-known algorithm NESTA (a shorthand for Nesterov’s algorithm) and DADM (dual alternating direction method) in terms of the quality of restored signals and the computational complexity measured in the CPU-time consumed.

Original languageEnglish (US)
Article number65
JournalEurasip Journal on Advances in Signal Processing
Issue number1
StatePublished - Dec 6 2015


  • Compressive sensing
  • Proximity operator
  • ℓ minimization

ASJC Scopus subject areas

  • Signal Processing
  • Hardware and Architecture
  • Electrical and Electronic Engineering


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