Poisson Tensor Completion via Nonconvex Regularization and Nonlocal Self-Similarity for Multi-dimensional Image Recovery

The problem of Poisson tensor completion aims to recover a tensor from partial observations in the presence of Poisson noise. Existing approaches utilized the transformed tensor nuclear norm to explore the low-rankness of a tensor, which is the ℓ 1 norm of singular values vectors of all frontal slic...

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Vydané v:	Journal of scientific computing Ročník 102; číslo 3; s. 76
Hlavní autori:	Qiu, Duo, Xia, Sijia, Yang, Bei, Li, Bo, Zhang, Xiongjun
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.03.2025 Springer Nature B.V
Predmet:	Algorithms Computational Mathematics and Numerical Analysis Decomposition Fourier transforms Hyperspectral imaging Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Methods Multidimensional methods Regularization Self-similarity Tensors Theoretical 90C30 Multi-dimensional image recovery Proximal alternating minimization 15A69 Nonconvex regularization Poisson tensor completion Nonlocal self-similarity
ISSN:	0885-7474, 1573-7691
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Popis
Shrnutí:	The problem of Poisson tensor completion aims to recover a tensor from partial observations in the presence of Poisson noise. Existing approaches utilized the transformed tensor nuclear norm to explore the low-rankness of a tensor, which is the ℓ 1 norm of singular values vectors of all frontal slices of a tensor in the transformed domain. Nevertheless, the ℓ 1 norm is suboptimal due to its biased estimate. In this paper, we propose a nonconvex model based on transformed tensor nuclear norm for Poisson tensor completion. In order to explore the global low-rankness of the underlying tensor, a family of nonconvex functions are employed onto the singular values of all frontal slices of a tensor in the transformed domain. Furthermore, the nonlocal self-similarity is incorporated into the nonconvex model to describe the similar structures and characterize the intrinsic details of multi-dimensional images. A proximal alternating minimization algorithm is developed to solve the resulting models, whose convergence is established under very mild conditions. Extensive numerical examples on hyperspectral images, video images, and fluorescence microscope images demonstrate that the proposed approach outperforms several state-of-the-art methods.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0885-7474 1573-7691
DOI:	10.1007/s10915-025-02801-8