Sparse adaptive iteratively-weighted thresholding algorithm (SAITA) for Lp-regularization using the multiple sub-dictionary representation

Yunyi Li, Jie Zhang, Shangang Fan, Jie Yang, Jian Xiong, Xiefeng Cheng, Hikmet Sari, Fumiyuki Adachi, Guan Gui

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


Both L1/2 and L2/3 are two typical non-convex regularizations of Lp (0<p <1), which can be employed to obtain a sparser solution than the L1 regularization. Recently, the multiple-state sparse transformation strategy has been developed to exploit the sparsity in L1 regularization for sparse signal recovery, which combines the iterative reweighted algorithms. To further exploit the sparse structure of signal and image, this paper adopts multiple dictionary sparse transform strategies for the two typical cases p∈{1/2,2/3} based on an iterative Lp thresholding algorithm and then proposes a sparse adaptive iterative-weighted Lp thresholding algorithm (SAITA). Moreover, a simple yet effective regularization parameter is proposed to weight each sub-dictionary-based Lp regularizer. Simulation results have shown that the proposed SAITA not only performs better than the corresponding L1 algorithms but can also obtain a better recovery performance and achieve faster convergence than the conventional single-dictionary sparse transform-based Lp case. Moreover, we conduct some applications about sparse image recovery and obtain good results by comparison with relative work.

Original languageEnglish
Article number2920
JournalSensors (Switzerland)
Issue number12
Publication statusPublished - 2017 Dec 15


  • Adaptive weighted
  • Image restoration
  • Iterative thresholding
  • L-norm regularization
  • Multiple dictionaries
  • Single–dictionary

ASJC Scopus subject areas

  • Analytical Chemistry
  • Biochemistry
  • Atomic and Molecular Physics, and Optics
  • Instrumentation
  • Electrical and Electronic Engineering

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