Image fusion via sparse regularization with non-convex penalties

Nantheera Anantrasirichai, Rencheng Zheng, Ivan Selesnick, Alin Achim

Research output: Contribution to journalArticlepeer-review


The L1 norm regularized least squares method is often used for finding sparse approximate solutions and is widely used in signal restoration. Basis pursuit denoising (BPD) performs noise reduction in this way. However, the shortcoming of using L1 norm regularization is the underestimation of the true solution. Recently, a class of non-convex penalties have been proposed to improve this situation. This kind of penalty function is non-convex itself, but preserves the convexity property of the whole cost function. This approach has been confirmed to offer good performance in 1-D signal denoising. This paper demonstrates the aforementioned method to 2-D signals (images) and applies it to multisensor image fusion. The problem is posed as an inverse one and a corresponding cost function is judiciously designed to include two data attachment terms. The whole cost function is proved to be convex upon suitably choosing the non-convex penalty, so that the cost function minimization can be tackled by convex optimization approaches, which comprise simple computations. The performance of the proposed method is benchmarked against a number of state-of-the-art image fusion techniques and superior performance is demonstrated both visually and in terms of various assessment measures.

Original languageEnglish (US)
Pages (from-to)355-360
Number of pages6
JournalPattern Recognition Letters
StatePublished - Mar 2020


  • Convex optimization
  • Cost function
  • Image fusion
  • Multifocus image
  • Multispectral image
  • Noisy image
  • Non-convex penalties
  • Sparse approximate solutions

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


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