APSIPA Transactions on Signal and Information Processing > Vol 11 > Issue 1

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

Keiichiro Shirai, Shinshu University, Japan, keiichi@shinshu-u.ac.jp , Kenjiro Sugimoto, Japan R&D Center, Xiaomi, Japan, Sei-ichiro Kamata, Waseda University, Japan
Suggested Citation
Keiichiro Shirai, Kenjiro Sugimoto and Sei-ichiro Kamata (2022), "Adjoint Bilateral Filter and Its Application to Optimization-based Image Processing", APSIPA Transactions on Signal and Information Processing: Vol. 11: No. 1, e10. http://dx.doi.org/10.1561/116.00000046

Publication Date: 26 Apr 2022
© 2022 K. Shirai, K. Sugimoto and S. Kamata


Open Access

This is published under the terms of CC BY-NC.

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In this article:
1. Introduction 
2. Preliminaries 
3. Proposed Methods 
4. Results and Discussion 
5. Applications to Optimization-based Image Processing 
6. Conclusion 


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, that is, 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.