TY - GEN
T1 - AN INTERPRETATION OF REGULARIZATION BY DENOISING AND ITS APPLICATION WITH THE BACK-PROJECTED FIDELITY TERM
AU - Yogev-Ofer, Einav
AU - Tirer, Tom
AU - Giryes, Raja
N1 - Publisher Copyright:
© 2021 IEEE
PY - 2021
Y1 - 2021
N2 - The vast majority of image recovery tasks are ill-posed problems. As such, methods that are based on optimization use cost functions that consist of both fidelity and prior (regularization) terms. A recent line of works imposes the prior by the Regularization by Denoising (RED) approach, which exploits the good performance of existing image denoising engines. Yet, the relation of RED to explicit prior terms is still not well understood, as previous work requires too strong assumptions on the denoisers. In this paper, we make two contributions. First, we show that the RED gradient can be seen as a (sub)gradient of a prior function—but taken at a denoised version of the point. As RED is typically applied with a relatively small noise level, this interpretation indicates a similarity between RED and traditional gradients. This leads to our second contribution: We propose to combine RED with the Back-Projection (BP) fidelity term rather than the common Least Squares (LS) term that is used in previous works. We show that the advantages of BP over LS for image deblurring and super-resolution, which have been demonstrated for traditional gradients, carry on to the RED approach.
AB - The vast majority of image recovery tasks are ill-posed problems. As such, methods that are based on optimization use cost functions that consist of both fidelity and prior (regularization) terms. A recent line of works imposes the prior by the Regularization by Denoising (RED) approach, which exploits the good performance of existing image denoising engines. Yet, the relation of RED to explicit prior terms is still not well understood, as previous work requires too strong assumptions on the denoisers. In this paper, we make two contributions. First, we show that the RED gradient can be seen as a (sub)gradient of a prior function—but taken at a denoised version of the point. As RED is typically applied with a relatively small noise level, this interpretation indicates a similarity between RED and traditional gradients. This leads to our second contribution: We propose to combine RED with the Back-Projection (BP) fidelity term rather than the common Least Squares (LS) term that is used in previous works. We show that the advantages of BP over LS for image deblurring and super-resolution, which have been demonstrated for traditional gradients, carry on to the RED approach.
KW - Back-Projection
KW - Image deblurring
KW - Inverse problems
KW - Regularization by Denoising
KW - Super-resolution
UR - http://www.scopus.com/inward/record.url?scp=85125578102&partnerID=8YFLogxK
U2 - 10.1109/ICIP42928.2021.9506499
DO - 10.1109/ICIP42928.2021.9506499
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AN - SCOPUS:85125578102
T3 - Proceedings - International Conference on Image Processing, ICIP
SP - 1649
EP - 1653
BT - 2021 IEEE International Conference on Image Processing, ICIP 2021 - Proceedings
PB - IEEE Computer Society
T2 - 2021 IEEE International Conference on Image Processing, ICIP 2021
Y2 - 19 September 2021 through 22 September 2021
ER -