A variational approach for restoring images corrupted by noisy blur kernels and additive noise

Kwok Po NG, Wei Wang*, Xile Zhao

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

4 Citations (Scopus)


In this paper, we study a deblurring algorithm for distorted images by random impulse response. We propose and develop a convex optimization model to recover the underlying image and the blurring function simultaneously. The objective function is composed of 3 terms: the data-fitting term between the observed image and the product of the estimated blurring function and the estimated image, the squared difference between the estimated blurring function and its mean, and the total variation regularization term for the estimated image. We theoretically show that under some mild conditions, the resulting objective function can be convex in which the global minimum value is unique. The numerical results confirm that the peak-to-signal-noise-ratio and structural similarity of the restored images by the proposed algorithm are the best when the proposed objective function is convex. We also present a proximal alternating minimization scheme to solve the resulting minimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed model and the efficiency of the numerical scheme.

Original languageEnglish
Article numbere2100
JournalNumerical Linear Algebra with Applications
Issue number6
Publication statusPublished - Dec 2017

Scopus Subject Areas

  • Algebra and Number Theory
  • Applied Mathematics

User-Defined Keywords

  • convex optimization
  • image restoration
  • proximal alternating minimization
  • random blurring function
  • total variation


Dive into the research topics of 'A variational approach for restoring images corrupted by noisy blur kernels and additive noise'. Together they form a unique fingerprint.

Cite this