Adjoint Bilateral Filter and Its Application to Optimization-based Image Processing

Keiichiro Shirai, Kenjiro Sugimoto, Sei Ichiro Kamata

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This study primarily presents efficient tools for optimization-based image processing using a bilateral filter (BF). Generally, for image restoration, e.g., deblurring, a forward operation and its adjoint operation pair are required to solve inverse problems via iterative approaches such as the gradient method. Image data comprise millions of variables; thus, the operations should be performed as image filters rather than matrix products because of the considerable matrix size. This approach is known as a matrix-free approach, i.e., filter form, because it is executed without explicitly generating an enormous matrix. When BF is incorporated into optimization, its matrix-free adjoint BF is required to solve the optimization problem. This study discusses the matrix-free adjoint BF and its constant-time algorithm to solve optimization problems in a practical time frame. The experimental results demonstrate that the proposed method yields sufficient filtering accuracy for solving inverse problems. Furthermore, BF-based optimization improves accuracy by adjusting the image quality of resultant images.

Original languageEnglish
Article numbere10
JournalAPSIPA Transactions on Signal and Information Processing
Issue number1
Publication statusPublished - 2022 Apr 26

ASJC Scopus subject areas

  • Signal Processing
  • Information Systems


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